Class 12 Math Ch-6 समाकलन MCQs

नीचे दिए गए सभी Questions Bihar Board परीक्षा 2026 के लिए “Very Important Questions” (अत्यंत महत्वपूर्ण प्रश्न) हैं। इन सभी Class 12th के (Mathematics/गणित) = गणित भाग-1 (Hindi Medium) Book Chapter-6 समाकलन का Questions का Solve का  वीडियो Youtube और Website पर Upload किया गया है।

1. $\int \frac{dx}{x^2 + 16} =$ [BSEB, 2023 A]
(A) $\frac{1}{4} \tan^{-1} \frac{x}{4} + k$
(B) $\tan^{-1} \frac{x}{4} + k$
(C) $\frac{1}{4} \sin^{-1} \frac{x}{4} + k$
(D) $\frac{1}{4} \cos^{-1} \frac{x}{4} + k$

2. $\int \sin x dx =$ [BSEB, 2017 C]
(A) $-\cos x + K$
(B) $\sin x + K$
(C) $-\sin x + K$
(D) $\tan x + K$

3. $\int e^x (\tan x + \log \sec x) dx =$ [BSEB, 2024 A]
(A) $e^x \tan x + k$
(B) $e^x \log \sec x + k$
(C) $e^x \sec x + k$
(D) $e^x \log \tan x + k$

4. $\int_0^{\pi/2} \log \cot \theta \, d\theta =$ [BSEB, 2021 A]
(A) $\frac{\pi}{2} \log 2$
(B) $\frac{\pi}{4} \log 2$
(C) $2\pi \log 2$
(D) 0

5. $\int \frac{dx}{e^{-x}} =$ [BSEB, 2025 A]
(A) $\frac{-1}{e^{-x}} + k$
(B) $e^x + k$
(C) $\frac{1}{e^{-x}} \cdot \frac{1}{x^2} + k$
(D) $-e^{-x} + k$

6. $\int e^x (x^3 + 3x^2) dx =$ [BSEB, 2023 A]
(A) $3x^2 e^x + k$
(B) $x^2 e^x + k$
(C) $x^3 e^x + k$
(D) $3x^3 \cdot x^2 + k$

7. $\int \frac{dx}{x(x+2)} =$ [BSEB, 2024 A]
(A) $\log |\frac{x}{x+2}| + c$
(B) $\frac{1}{2} \log |\frac{x}{x+2}| + c$
(C) $\log |x| + c$
(D) $\log |x+2| + c$

8. $\int_{-1}^1 |x| \, dx =$ [BSEB, 2021 A]
(A) 0
(B) 1
(C) 2
(D) $1/2$

9. $\int \tan(\tan^{-1} x) dx =$ [BSEB, 2025 A]
(A) $\frac{x^2}{2} + k$
(B) $\frac{x}{2} + k$
(C) $x + k$
(D) $\log \sec(\tan^{-1} x) + k$

10. $\int \frac{dx}{\sin^2 x \cos^2 x} =$ [BSEB, 2023 A]
(A) $\tan x + \cot x + k$
(B) $\tan x – \cot x + k$
(C) $\tan x \cot x + k$
(D) $\sin x + \cos x + k$

11. $\int_0^{\pi/4} \tan^2 \theta d\theta =$ [BSEB, 2017 C, 2020 A]
(A) $1 – \frac{\pi}{4}$
(B) $1 + \frac{\pi}{4}$
(C) $-1 – \frac{\pi}{4}$
(D) $\frac{\pi}{4} – 1$

12. $\int \frac{\log x}{x} dx =$ [BSEB, 2024 A]
(A) $\frac{1}{2}(\log x)^2 + c$
(B) $-\frac{1}{2}(\log x)^2 + c$
(C) $\frac{2}{x^2} + c$
(D) $-\frac{2}{x^2} + c$

13. $\int_2^4 \frac{dx}{x} =$ [BSEB, 2017 C]
(A) $\log 2$
(B) $\log 4$
(C) $-\log 2$
(D) $-\log 4$

14. $\int e^x (\cot x + \log \sin x) \, dx =$ [BSEB, 2022 A]
(A) $e^x \cot x + k$
(B) $e^x \log \sin x + k$
(C) $e^x \sin x + k$
(D) $e^x \cos x + k$

15. $\int \frac{dx}{1 + 36x^2} =$ [BSEB, 2023 A]
(A) $6 \tan^{-1} 6x + k$
(B) $3 \tan^{-1} 5x + k$
(C) $\frac{1}{6} \tan^{-1} 6x + k$
(D) $\tan^{-1} 6x + k$

16. $\int \sqrt{\cos x} \cdot \sin x \, dx =$ [BSEB, 2024 A]
(A) $\frac{2}{3}(\cos x)^{3/2} + c$
(B) $-\frac{2}{3}(\cos x)^{3/2} + c$
(C) $(\cos x)^{3/2} + c$
(D) $-(\cos x)^{3/2} + c$

17. $\int \sec^4 x \tan x \, dx =$ [BSEB, 2024 A]
(A) $5 \tan^5 x + c$
(B) $\frac{1}{5} \sec^5 x + c$
(C) $5 \log |\cos x| + c$
(D) $\tan^5 x + c$

18. $\int_1^9 \frac{1}{\sqrt{x}} dx =$ [BSEB, 2024 A]
(A) 2
(B) $\pi/6$
(C) $\pi/4$
(D) $\pi/2$

19. $\int \frac{x^2 – 1}{x^2 + 1} dx =$ [BSEB, 2025 A]
(A) $x – 2 \tan^{-1} x + k$
(B) $x + 2 \tan^{-1} x + k$
(C) $x – \tan^{-1} x + k$
(D) $\tan^{-1} x + k$

20. $\int \frac{\sin^{-1} x}{\sqrt{1-x^2}} \, dx =$ [BSEB, 2021 A]
(A) $\frac{(\sin^{-1} x)^2}{2} + k$
(B) $\sin^{-1} x + k$
(C) $(\sin^{-1} x)^2 + k$
(D) $2 \sin^{-1} x + k$

21. $\int \frac{dx}{2 – 3x} =$ [BSEB, 2024 A]
(A) $-3 \log |2 – 3x| + c$
(B) $-\frac{1}{3} \log |2 – 3x| + c$
(C) $-\log |2 – 3x| + c$
(D) $2 \tan^{-1} x + c$

22. $\int \log 2 \, dx =$ [BSEB, 2021 A]
(A) $x + k$
(B) $\log 2 + k$
(C) $x \log 2 + k$
(D) $x^2 \log 2 + k$

23. $\int \frac{dx}{a^2 + x^2} =$ [BSEB, 2018 A]
(A) $\frac{1}{a} \tan^{-1} \frac{a}{x} + C$
(B) $\tan^{-1} \frac{x}{a} + C$
(C) $\frac{1}{a} \tan^{-1} \frac{x}{a} + C$
(D) $\frac{1}{a} \tan^{-1} x + C$

24. $\int_1^2 x^3 \, dx =$ [BSEB, 2015 A]
(A) $15/4$
(B) $14/4$
(C) $16/4$
(D) 4

25. $\int \frac{x^3 dx}{1 + x^8} =$ [BSEB, 2024 A]
(A) $\tan^{-1} x^4 + c$
(B) $4 \tan^{-1} x^4 + c$
(C) $\frac{1}{4} \tan^{-1} x^4 + c$
(D) $2 \tan^{-1} x^4 + c$

26. $\int_0^{\pi/2} \sin x \cos x dx =$ [BSEB, 2025 A]
(A) 1
(B) $1/2$
(C) $-1$
(D) $1/4$

27. $\int \frac{1}{\sqrt{1-x^2}} dx =$ [BSEB, 2021 A]
(A) $\sin^{-1} x + k$
(B) $\cos^{-1} x + k$
(C) $\tan^{-1} x + k$
(D) $\sec^{-1} x + k$

28. $\int x e^{2x} dx =$ [BSEB, 2022 A]
(A) $(2x – 1) \frac{e^{2x}}{4} + k$
(B) $(x – 1) \frac{e^{2x}}{4} + k$
(C) $\frac{x e^{2x}}{4} + k$
(D) $\frac{(x – 2) e^{2x}}{4} + k$

29. $\int_0^1 (x + 2x + 3x^2 + 4x^3) dx =$ [BSEB, 2025 A]
(A) 10
(B) $5/2$
(C) $7/2$
(D) $1/2$

30. $\int \sin \frac{3x}{4} dx =$ [BSEB, 2023 A]
(A) $k – \cos \frac{3x}{4}$
(B) $k + \frac{3}{4} \cos \frac{3x}{4}$
(C) $k – \frac{4}{3} \cos \frac{3x}{4}$
(D) $k + \frac{4}{3} \cos \frac{3x}{4}$

31. $\int x e^x dx =$ [BSEB, 2024 A]
(A) $e^x + c$
(B) $x – 1 + c$
(C) $e^x(x – 1) + c$
(D) $e^x(x + 1) + c$

32. $\int x^{3/2} dx =$ [BSEB, 2022 A]
(A) $\frac{2}{3}x^{3/2} + k$
(B) $\frac{2}{5}x^{5/2} + k$
(C) $\frac{2}{5}x^{2/5} + k$
(D) $\frac{5}{2}x^{5/2} + k$

33. $\int_\alpha^\beta \phi(x) dx + \int_\beta^\alpha \phi(x) dx =$ [BSEB, 2018 A, 2021 A, 2025 A]
(A) 1
(B) $2\int_\alpha^\beta \phi(x) dx$
(C) $-2\int_\beta^\alpha \phi(x) dx$
(D) 0

34. $\int e^x (\cos x – \sin x) dx =$ [BSEB, 2023 A]
(A) $e^x \sin x + k$
(B) $e^x \cos x + k$
(C) $-e^x \sin x + k$
(D) $k – e^x \cos x$

35. $\int \frac{dx}{x} =$ [BSEB, 2020 A, 2023 A]
(A) $x + k$
(B) $\frac{1}{x^2} + k$
(C) $\log |x| + k$
(D) $-\frac{1}{x^2} + k$

36. $\int_0^{\pi/2} \sin^2 x dx =$ [BSEB, 2017 C]
(A) $\frac{\pi}{4}$
(B) $-\frac{\pi}{4}$
(C) $\frac{\pi}{2}$
(D) $-\frac{\pi}{2}$

37. $\int \cosec^2 x \, dx =$ [BSEB, 2016 A]
(A) $\tan x + k$
(B) $-\cot x + k$
(C) $\cot x + k$
(D) $-\tan x + k$

38. $\int \sqrt{1 + \cos 2x} dx =$ [BSEB, 2018 A, 2024 A]
(A) $\sqrt{2} \cos x + C$
(B) $\sqrt{2} \sin x + C$
(C) $-\cos x – \sin x + C$
(D) $\sqrt{2} \sin \frac{x}{2} + C$

39. $\int_{-\pi/2}^{\pi/2} \sin^9 x dx =$ [BSEB, 2022 A]
(A) 0
(B) 1
(C) 5
(D) 11

40. $\int \sec^2 (3x + 5) \, dx =$ [BSEB, 2019 A]
(A) $\frac{1}{3} \tan(3x+5) + k$
(B) $3 \tan(3x+5) + k$
(C) $\tan(3x+5) + k$
(D) $\frac{1}{5} \tan(3x+5) + k$

41. $\int \frac{x e^x}{(x+1)^2} dx =$ [BSEB, 2018 A]
(A) $\frac{e^x}{(x+1)^2} + C$
(B) $\frac{e^x}{x+1} + C$
(C) $\frac{e^x}{x+1} + C$
(D) $\frac{-e^x}{(x+1)^2} + C$

42. $\int x^2 e^{x^3} dx =$ [BSEB, 2018 A, 2020 A]
(A) $e^{x^3} + C$
(B) $\frac{1}{3}e^{x^3} + C$
(C) $e^{x^2} + C$
(D) $\frac{1}{3}e^{x^2} + C$

43. $\int_a^b dx =$ [BSEB, 2022 A]
(A) $b – a$
(B) $b + a$
(C) $b/a$
(D) $ab$

44. $\int e^x [\sin^{-1} x + \frac{1}{\sqrt{1-x^2}}] dx =$ [BSEB, 2024 A]
(A) $e^x \cdot \frac{1}{\sqrt{1-x^2}} + c$
(B) $e^x \sin^{-1} x + c$
(C) $\frac{e^2}{2} + c$
(D) $e^x \cos^{-1} x + c$

45. $\int_0^{\pi/2} \frac{\cos \theta}{\cos \theta + \sin \theta} d\theta =$ [BSEB, 2021 A]
(A) $\pi$
(B) $\pi/2$
(C) $\pi/3$
(D) $\pi/4$

46. $\int \frac{\cos \sqrt{x}}{\sqrt{x}} dx =$ [BSEB, 2024 A]
(A) $2 \sin \sqrt{x} + c$
(B) $\sin \sqrt{x} + c$
(C) $\cos \sqrt{x} + c$
(D) $2 \cos \sqrt{x} + c$

47. $\int_{-\pi/2}^{\pi/2} \sin^7 x dx =$ [BSEB, 2023 A]
(A) $-1$
(B) 0
(C) 1
(D) 2

48. $\int_0^1 x^2 dx =$ [BSEB, 2022 A]
(A) $1/3$
(B) 0
(C) 1
(D) $-1/3$

49. $\int \cos \frac{7x}{9} dx =$ [BSEB, 2023 A]
(A) $k + \sin \frac{7x}{9}$
(B) $\frac{7}{9} \sin \frac{7x}{9} + k$
(C) $\frac{9}{7} \sin \frac{7x}{9} + k$
(D) $x + \cos \frac{7x}{9}$

50. $\int \sec^2 \frac{17x}{23} dx =$ [BSEB, 2023 A]
(A) $x + \frac{17}{23} \tan \frac{17x}{23}$
(B) $k – \frac{17}{23} \tan \frac{17x}{23}$
(C) $k + \frac{23}{17} \tan \frac{17x}{23}$
(D) $k – \frac{23}{17} \tan \frac{17x}{23}$

51. $\int \sqrt{a^2 – x^2} dx =$ [BSEB, 2024 A]
(A) $\frac{x}{2} \sqrt{a^2 – x^2} + \frac{a^2}{2} \sin^{-1} \frac{x}{a} + c$
(B) $\frac{a^2}{2} \sin^{-1} \frac{x}{a} + c$
(C) $\frac{x}{2} \sqrt{a^2 – x^2} – \frac{a^2}{2} \sin^{-1} \frac{x}{a} + c$
(D) $\frac{x}{2} \sqrt{x^2 – a^2} – \frac{a^2}{2} \sin^{-1} \frac{x}{a} + c$

52. $\int 4^x dx =$ [BSEB, 2023 A]
(A) $4^x + k$
(B) $\frac{4^{x+1}}{x+1} + k$
(C) $\frac{4^x}{\log 4} + k$
(D) $\frac{4x}{\log 4} – k$

53. $\int_0^{\pi/2} \cos x \, dx =$ [BSEB, 2017 A, 2021 A]
(A) 0
(B) 1
(C) $-1$
(D) $\pi/2$

54. $\int_0^{\pi/2} \frac{\sqrt{\sin x}}{\sqrt{\sin x} + \sqrt{\cos x}} dx =$ [BSEB, 2020 A, 2025 A]
(A) $\pi/2$
(B) $\pi/4$
(C) 0
(D) 1

55. $\int \frac{dx}{x^2 – a^2} =$ [BSEB, 2019 A]
(A) $\frac{1}{2a} \log |\frac{x-a}{x+a}| + k$
(B) $\frac{1}{2a} \log |\frac{x+a}{x-a}| + k$
(C) $\frac{1}{a} \tan^{-1} \frac{x}{a} + k$
(D) $\log |x + \sqrt{x^2-a^2}| + k$

56. $\int_0^{\pi/2} \sin x dx =$ [BSEB, 2022 A]
(A) 0
(B) 1
(C) $-1$
(D) 2

57. $\int \tan^2 x dx =$ [BSEB, 2024 A]
(A) $\tan x + x + c$
(B) $\tan x – x + c$
(C) $\cot x + x + c$
(D) $\cot x – x + c$

58. $\int (4x^3 – 6) dx =$ [BSEB, 2023 A]
(A) $4x^3 – 6x + k$
(B) $x^4 – 6x^2 + k$
(C) $x^4 – 3x^2 + k$
(D) $\frac{4x^3}{3} – 3x^2 + k$

59. $\int \frac{dx}{1 + \cos x} =$ [BSEB, 2023 A]
(A) $\tan \frac{x}{2} + k$
(B) $\cot \frac{x}{2} + k$
(C) $\frac{1}{2} \tan \frac{x}{2} + k$
(D) $2 \tan \frac{x}{2} + k$

60. $\int \sqrt{x} \, dx =$ [BSEB, 2021 A]
(A) $\frac{2}{3} x^{3/2} + k$
(B) $\frac{3}{2} x^{3/2} + k$
(C) $\frac{2}{3} x^{1/2} + k$
(D) $\frac{1}{2\sqrt{x}} + k$

61. $\int e^{3x} dx =$ [BSEB, 2020 A]
(A) $e^{3x} + k$
(B) $\frac{e^{3x}}{3} + k$
(C) $3e^{3x} + k$
(D) $e^x + k$

62. $\int_0^a \frac{f(x)}{f(x) + f(a-x)} dx =$ [BSEB, 2021 A]
(A) $a$
(B) $a/2$
(C) 0
(D) $2a$

63. $\int_0^1 x(1 – x)^{10} dx =$ [BSEB, 2022 A]
(A) $\frac{1}{132}$
(B) $\frac{5}{132}$
(C) $\frac{7}{132}$
(D) $\frac{45}{244}$

64. $\int_0^1 e^x dx =$ [BSEB, 2021 A, 2025 A]
(A) $e – 1$
(B) $\frac{e – 1}{e}$
(C) $\frac{e^2 – 1}{e}$
(D) $\frac{3^2 – 1}{2}$

65. $\int \cos 3x \, dx =$ [BSEB, 2020 A]
(A) $\frac{\sin 3x}{3} + k$
(B) $-\frac{\sin 3x}{3} + k$
(C) $3 \sin 3x + k$
(D) $-3 \sin 3x + k$

66. $\int_1^4 \sqrt{x} \, dx =$ [BSEB, 2022 A]
(A) $14/3$
(B) $11/3$
(C) $19/3$
(D) $22/3$

67. $\int \frac{dx}{x^2 + a^2} =$ [BSEB, 2019 A, 2024 A]
(A) $\tan^{-1} \frac{x}{a} + k$
(B) $\frac{1}{a} \tan^{-1} \frac{x}{a} + k$
(C) $\frac{1}{a} \sin^{-1} \frac{x}{a} + k$
(D) $\frac{1}{2a} \log \frac{x-a}{x+a} + k$

68. $\int \sin x \cdot \cos x \, dx =$ [BSEB, 2021 A]
(A) $\frac{1}{2} \sin 2x + k$
(B) $\frac{\sin x}{2} + k$
(C) $\frac{\sin^2 x}{2} + k$
(D) $\frac{\cos^2 x}{2} + k$

69. $\int \frac{dx}{\sqrt{x^2 + a^2}} =$ [BSEB, 2020 A]
(A) $\log |x + \sqrt{x^2 + a^2}| + k$
(B) $\log |x – \sqrt{x^2 + a^2}| + k$
(C) $\frac{1}{a} \tan^{-1} \frac{x}{a} + k$
(D) $\sin^{-1} \frac{x}{a} + k$

70. $\int_{-\pi/2}^{\pi/2} \cos x dx =$ [BSEB, 2021 A]
(A) 2
(B) 1
(C) 0
(D) 4

71. $\int_0^{\pi/2} \cos 2x dx =$ [BSEB, 2024 A]
(A) 0
(B) 1
(C) $-1$
(D) 2

72. $\int (x + 2)^2 dx =$ [BSEB, 2021 A]
(A) $(x + 2)^3 + k$
(B) $\frac{x^2}{2} + k$
(C) $\frac{x^2}{2} + 2x + k$
(D) $\log(x + 2) + k$

73. $\int_0^{\pi/6} \cos x \cos 2x dx =$ [BSEB, 2024 A]
(A) $5/6$
(B) $1/6$
(C) $5/12$
(D) $-5/12$

74. $\int_0^1 f(x) dx =$ [BSEB, 2018 A, 2022 A]
(A) 0
(B) 1
(C) 2
(D) $1/2$

75. $\int \sqrt{a^2 – x^2} dx =$ [BSEB, 2018 A]
(A) $\frac{x}{2} \sqrt{a^2 – x^2} + \frac{a^2}{2} \sin^{-1} \frac{x}{a} + c$
(B) $\frac{x}{2} \sqrt{a^2 – x^2} – \frac{a^2}{2} \sin^{-1} \frac{x}{a} + c$
(C) $\frac{a^2}{2} \sin^{-1} \frac{x}{a} + c$
(D) $\log |x + \sqrt{x^2-a^2}| + c$

76. $\int (x + \cos 2x) dx =$ [BSEB, 2024 A]
(A) $\frac{1}{2} x \sin 2x + \frac{1}{4} \cos 2x + c$
(B) $\frac{1}{4} x \sin 2x – \frac{1}{4} \cos 2x + c$
(C) $2x \sin 2x + 4 \cos 2x + c$
(D) $\frac{x^2}{2} + \frac{\sin 2x}{2} + c$

77. $\int_1^3 dx =$ [BSEB, 2021 A]
(A) 4
(B) 2
(C) 3
(D) $1/2$

78. $\int e^x dx =$ [BSEB, 2020 A]
(A) $e^x + c$
(B) $e^{2x} + c$
(C) $x e^x + c$
(D) $\frac{e^x}{2} + c$

79. $\int \frac{1}{x^2+1} dx =$ [BSEB, 2017 A]
(A) $\tan^{-1} x + k$
(B) $\sin^{-1} x + k$
(C) $\log(x^2+1) + k$
(D) $\cot^{-1} x + k$

80. $\int x^5 dx =$ [BSEB, 2022 A]
(A) $x^6/6 + k$
(B) $5x^4 + k$
(C) $x^4/4 + k$
(D) $x^6 + k$

81. $\int \sec x dx =$ [BSEB, 2024 A]
(A) $\log |\sec x + \tan x| + k$
(B) $\log |\sec x – \tan x| + k$
(C) $\tan x + k$
(D) $\sec x \tan x + k$

82. $\int \cos x dx =$ [BSEB, 2025 A]
(A) $\sin x + k$
(B) $-\sin x + k$
(C) $\cos x + k$
(D) $-\cos x + k$

83. $\int_0^1 x^n dx =$ [BSEB, 2021 A]
(A) $1/(n+1)$
(B) $1/n$
(C) $n+1$
(D) 0

84. $\int 2^x dx =$ [BSEB, 2022 A]
(A) $2^x \log 2 + k$
(B) $2^x/\log 2 + k$
(C) $2^{x+1} + k$
(D) $x 2^{x-1} + k$

85. $\int_0^{\pi/2} \sin^3 x dx =$ [BSEB, 2023 A]
(A) $2/3$
(B) $1/3$
(C) $4/3$
(D) 0

86. $\int e^{2x} dx =$ [BSEB, 2025 A]
(A) $e^{2x} + k$
(B) $2e^{2x} + k$
(C) $\frac{1}{2} e^{2x} + k$
(D) $e^x + k$

87. $\int \frac{1}{1+x^2} dx =$ [BSEB, 2023 A]
(A) $\tan^{-1} x + k$
(B) $\cot^{-1} x + k$
(C) $\sin^{-1} x + k$
(D) $\cos^{-1} x + k$

88. $\int \cot x dx =$ [BSEB, 2024 A]
(A) $\log |\sin x| + k$
(B) $\log |\cos x| + k$
(C) $-\cosec^2 x + k$
(D) $\tan x + k$

89. $\int \frac{dx}{x^2-1} =$ [BSEB, 2020 A]
(A) $\frac{1}{2} \log |\frac{x-1}{x+1}| + k$
(B) $\frac{1}{2} \log |\frac{x+1}{x-1}| + k$
(C) $\tan^{-1} x + k$
(D) $\sin^{-1} x + k$

90. $\int \frac{dx}{x^2+4} =$ [BSEB, 2021 A]
(A) $\frac{1}{2} \tan^{-1} \frac{x}{2} + k$
(B) $\tan^{-1} \frac{x}{2} + k$
(C) $\frac{1}{4} \tan^{-1} \frac{x}{4} + k$
(D) $\sin^{-1} \frac{x}{2} + k$

91. $\int \sec^2 x dx =$ [BSEB, 2025 A]
(A) $\tan x + k$
(B) $-\tan x + k$
(C) $\cot x + k$
(D) $-\cot x + k$

92. $\int_0^1 \frac{dx}{1+x^2} =$ [BSEB, 2022 A]
(A) $\pi/4$
(B) $\pi/2$
(C) 1
(D) 0

93. $\int \sin 2x dx =$ [BSEB, 2023 A]
(A) $-\frac{1}{2} \cos 2x + k$
(B) $\frac{1}{2} \cos 2x + k$
(C) $2 \cos 2x + k$
(D) $-2 \cos 2x + k$

94. $\int e^x (f(x) + f'(x)) dx =$ [BSEB, 2024 A]
(A) $e^x f(x) + k$
(B) $e^x f'(x) + k$
(C) $e^x + k$
(D) $f(x) + k$

95. $\int x^n dx =$ [BSEB, 2025 A]
(A) $\frac{x^{n+1}}{n+1} + k$
(B) $n x^{n-1} + k$
(C) $\frac{x^n}{n} + k$
(D) $x^{n+1} + k$

96. $\int_0^\pi \sin x dx =$ [BSEB, 2021 A]
(A) 2
(B) 0
(C) 1
(D) $-2$

97. $\int \frac{dx}{\sqrt{x}} =$ [BSEB, 2020 A]
(A) $2\sqrt{x} + k$
(B) $\sqrt{x} + k$
(C) $\frac{1}{2\sqrt{x}} + k$
(D) $x + k$

98. $\int_1^e \frac{1}{x} dx =$ [BSEB, 2024 A]
(A) 1
(B) 0
(C) $e$
(D) $\log e$

99. $\int \tan x dx =$ [BSEB, 2023 A]
(A) $\log |\sec x| + k$
(B) $\log |\cos x| + k$
(C) $\sec^2 x + k$
(D) $-\log |\sec x| + k$

100. $\int 0 dx =$ [BSEB, 2025 A]
(A) $k$
(B) 0
(C) 1
(D) $x$

Bihar Board Class 12th के (Mathematics/गणित) = गणित भाग-1 (Hindi Medium) Book Chapter-6 समाकलन के Exam 2026 MCQs Questions Answer Key

101. \( \int \frac{dx}{x^2 + 16} = ? \) [BSEB, 2019 A]
(A) \( \frac{1}{16} \tan^{-1} \frac{x}{16} + k \)
(B) \( \frac{1}{4} \tan^{-1} \frac{x}{4} + k \)
(C) \( \frac{1}{4} \tan^{-1} \frac{4}{x} + k \)
(D) \( \frac{1}{4} \tan^{-1} \frac{16}{x^2} + k \)

102. \( \int \frac{dx}{\sqrt{x}} = \) [BSEB, 2015, 2019 C]
(A) \( \sqrt{x} + k \)
(B) \( 2\sqrt{x} + k \)
(C) \( x + k \)
(D) \( \frac{2}{3} x^{3/2} + k \)

103. \( \int_{-1}^{1} \log \left( \frac{3+x}{3-x} \right) dx = \) [BSEB, 2023 A]
(A) \( 0 \)
(B) \( 1 \)
(C) \( 2 \log 3 \)
(D) \( 3 \log 2 \)

104. \( \int e^x (\tan x + \log \sec x) dx = \) [BSEB, 2021 A]
(A) \( e^x \tan x + k \)
(B) \( e^x \log \sec x + k \)
(C) \( e^x \log \cos x + k \)
(D) \( e^x \sec x + k \)

105. \( \int \sin \theta \cdot \text{cosec } \theta \, d\theta = \) [BSEB, 2019 C]
(A) \( \sin \theta + k \)
(B) \( \text{cosec } \theta + k \)
(C) \( \frac{\sin^2 \theta}{2} + k \)
(D) \( \theta + k \)

106. \( \int e^{3x} dx = \) [BSEB, 2023 A]
(A) \( e^{3x} + k \)
(B) \( \frac{e^{3x}}{3} + k \)
(C) \( 3e^{3x} + k \)
(D) \( e^x + k \)

107. \( \int \frac{3x^2 + 2}{x^3 + 2x} dx = \) [BSEB, 2023 A]
(A) \( \sin^{-1}(x^3 + 2x) + k \)
(B) \( \tan^{-1}(3x^2 + 2) + k \)
(C) \( \log |x^3 + 2x + 1| + k \)
(D) \( \log |x^3 + 2x| + k \)

108. \( \int \sec x \, dx = \) [BSEB, 2016 C, 2019 A, 2024 A]
(A) \( \log \sec x \)
(B) \( \log |\sec x + \tan x| + k \)
(C) \( \log (\sec x – \tan x) \)
(D) \( \sec x \cdot \tan x \)

109. \( \int_{0}^{1} \frac{\tan^{-1} x}{1 + x^2} dx = \) [BSEB, 2022 A]
(A) \( \frac{\pi^2}{8} \)
(B) \( \frac{\pi^2}{12} \)
(C) \( \frac{\pi^2}{16} \)
(D) \( \frac{\pi^2}{32} \)

110. \( \int (\sin^{-1} x + \cos^{-1} x) dx = \) [BSEB, 2016 C]
(A) \( \frac{\pi}{2} + C \)
(B) \( \frac{\pi}{2} x + C \)
(C) \( \frac{2}{\sqrt{1-x^2}} + C \)
(D) \( x + C \)

111. \( \int \frac{dx}{x^2 – 1} = \) [BSEB, 2022 A]
(A) \( \sin^{-1} x + k \)
(B) \( \frac{1}{2} \log \left| \frac{x-1}{x+1} \right| + k \)
(C) \( \frac{1}{2} \log \left| \frac{x+1}{x-1} \right| + k \)
(D) \( \sqrt{1 – x^2} + k \)

112. \( \int_{-a}^{a} \tan x \, dx = \) [BSEB, 2022 A, 2024 A]
(A) \( 0 \)
(B) \( 1 \)
(C) \( 2 \)
(D) \( -1 \)

113. \( \int \left( \frac{\cos^2 x + \sin^2 x}{\text{cosec } x} \right) dx = \) [BSEB, 2022 A, 2025 A]
(A) \( k + \text{cosec } x \)
(B) \( k – \sin x \)
(C) \( k + \sin x \)
(D) \( k – \cos x \)

114. \( \int \frac{dx}{1 + \cos x} = \) [BSEB, 2015]
(A) \( \tan \frac{x}{2} + k \)
(B) \( \frac{1}{2} \tan \frac{x}{2} + k \)
(C) \( 2 \tan \frac{x}{2} \)
(D) \( \tan^2 \frac{x}{2} \)

115. \( \int \frac{\cos \sqrt{x}}{\sqrt{x}} dx = \) [BSEB, 2021 A, 2024 A]
(A) \( 2 \sin \sqrt{x} + k \)
(B) \( \sqrt{x} \sin \sqrt{x} + k \)
(C) \( \frac{1}{2} \sin \sqrt{x} + k \)
(D) \( \sin \sqrt{x} + k \)

116. \( \int_{0}^{a} \frac{f(x)}{f(x) + f(a-x)} dx = \) [BSEB, 2021 A, 2023 A]
(A) \( a \)
(B) \( 2a \)
(C) \( a/2 \)
(D) \( 0 \)

117. \( \int \text{cosec}^2 x \, dx = ? \) [BSEB, 2019 A]
(A) \( \tan x + c \)
(B) \( -\cot x + c \)
(C) \( 2 \text{cosec } x + c \)
(D) \( -2 \text{cosec } x + c \)

118. 0 का x के सापेक्ष समाकलन होता है : [BSEB, 2016 A]
(A) \( 0 \)
(B) \( k \)
(C) \( x + k \)
(D) \( x^2 + k \)

119. \( \int \sec^2 4x \, dx = \) [BSEB, 2023 A]
(A) \( \tan 4x + k \)
(B) \( \frac{1}{4} \tan 4x + k \)
(C) \( 4 \tan 4x + k \)
(D) \( 8 \tan 4x + k \)

120. \( \int \frac{dx}{\sqrt{1 – x^2}} = \) [BSEB, 2022 A]
(A) \( \tan^{-1} x + k \)
(B) \( \sin^{-1} x + k \)
(C) \( \cos^{-1} x + k \)
(D) \( \sec^{-1} x + k \)

121. \( \int \frac{3 dx}{\sqrt{1 – 9x^2}} = \) [BSEB, 2023 A]
(A) \( \tan^{-1} 3x + k \)
(B) \( \sec^{-1} 3x + k \)
(C) \( \sin^{-1} 3x + k \)
(D) \( \cos^{-1} 3x + k \)

122. \( \int_{4}^{9} \sqrt{x} \, dx = ? \) [BSEB, 2020 A]
(A) \( \frac{38}{3} \)
(B) \( \frac{35}{3} \)
(C) \( \frac{36}{7} \)
(D) \( \frac{45}{3} \)

123. \( \int e^x (\sin x + \cos x) dx = \) [BSEB, 2020 A, 2024 A]
(A) \( e^x \sin x + k \)
(B) \( e^x \cos x + k \)
(C) \( -e^x \sin x + k \)
(D) \( -e^x \cos x + k \)

124. \( \int \text{cosec } x \, dx = ? \) [BSEB, 2020 A]
(A) \( \log |\tan \frac{x}{2}| + k \)
(B) \( \log |\cot \frac{x}{2}| + k \)
(C) \( \log |\sin \frac{x}{2}| + k \)
(D) \( \log |\cos \frac{x}{2}| + k \)

125. \( \int \frac{dx}{x^2 + 4} = \) [BSEB, 2022 A, 2025 A]
(A) \( \frac{1}{2} \sin^{-1} \frac{x}{2} + k \)
(B) \( \frac{1}{2} \cos^{-1} \frac{x}{2} + k \)
(C) \( \frac{1}{2} \tan^{-1} \frac{x}{2} + k \)
(D) \( \tan^{-1} x + k \)

126. \( \int_{-1}^{1} x^{17} \cos^4 x \, dx = \) [BSEB, 2023 A]
(A) \( 0 \)
(B) \( 1 \)
(C) \( \frac{3}{17} \)
(D) \( \frac{14}{3} \)

127. \( \int \frac{dx}{x^2 + a^2} = \) [BSEB, 2016 A, 2016 C, 2024 A]
(A) \( \frac{1}{a} \tan^{-1} \frac{x}{a} + k \)
(B) \( \frac{1}{a} \tan^{-1} (x+a) + k \)
(C) \( \sin^{-1} \frac{x}{a} + k \)
(D) \( \cos^{-1} \frac{x}{a} + k \)

128. \( \int_{-1}^{1} |x| dx = \) [BSEB, 2021 A, 2024 A]
(A) \( 1 \)
(B) \( 0 \)
(C) \( 2 \)
(D) \( 1/2 \)

129. \( \int \frac{3 \cos x – 2 \sin x}{2 \cos x + 3 \sin x} dx = \) [BSEB, 2023 A]
(A) \( 2 \cos x + 3 \sin x + k \)
(B) \( \log |2 \cos x + 3 \sin x| + k \)
(C) \( \tan^{-1} (3 \sin \frac{x}{2}) + k \)
(D) \( 2 \tan \frac{x}{2} + k \)

130. \( \int x^5 dx = \) [BSEB, 2017 A]
(A) \( \frac{x^6}{6} + k \)
(B) \( \frac{x^5}{5} + k \)
(C) \( \frac{x^7}{7} + k \)
(D) \( \frac{x^8}{8} + k \)

131. \( \int \frac{dx}{\sin^2 x} = \) [BSEB, 2021 A]
(A) \( \tan x + k \)
(B) \( -\cot x + k \)
(C) \( \sec x + k \)
(D) \( -\text{cosec } x + k \)

132. \( \int e^x \sec x (1 + \tan x) dx = \) [BSEB, 2019 A]
(A) \( e^x \cos x + c \)
(B) \( e^x \sec x + c \)
(C) \( e^x \sin x + c \)
(D) \( e^x \tan x + c \)

133. \( \int (4e^{3x} + 1) dx = \) [BSEB, 2022 A]
(A) \( 4e^{3x} + k \)
(B) \( \frac{4}{3} e^{3x} + x + k \)
(C) \( 12e^{3x} + x + k \)
(D) \( 12e^{3x} + k \)

134. \( \int \tan x \, dx = ? \) [BSEB, 2020 A]
(A) \( \log |\sec x| + k \)
(B) \( \log |\sin x| + k \)
(C) \( \log |\cos x| + k \)
(D) \( \log |\text{cosec } x| + k \)

135. \( \int \sec^2(3x + 5) dx = ? \) [BSEB, 2020 A]
(A) \( \frac{1}{3} \tan(3x + 5) + k \)
(B) \( -\frac{1}{3} \tan(3x + 5) + k \)
(C) \( \frac{1}{5} \tan(3x + 5) + k \)
(D) \( -\frac{1}{5} \tan(3x + 5) + k \)

136. \( \int_{0}^{\pi/2} \sin^2 x \cos x \, dx = ? \) [BSEB, 2019 A]
(A) \( \frac{1}{3} \)
(B) \( \frac{1}{4} \)
(C) \( \frac{1}{2} \)
(D) \( \frac{\pi}{2} \)

137. \( \int \frac{e^x}{x} (1 + x \log x) dx = \) [BSEB, 2022 A]
(A) \( e^x \log x + k \)
(B) \( \frac{e^x}{x} + k \)
(C) \( e^x + \log x + k \)
(D) \( e^x x + k \)

138. \( \int_{2}^{3} \frac{1}{x} dx = ? \) [BSEB, 2019 A]
(A) \( \log \frac{2}{3} \)
(B) \( \log \frac{3}{2} \)
(C) \( \log \frac{1}{2} \)
(D) \( \log \frac{x}{2} \)

139. \( \int \frac{dx}{x^2 + 5} = \) [BSEB, 2023 A]
(A) \( \tan^{-1} \frac{x}{5} + k \)
(B) \( \tan^{-1} \frac{x}{\sqrt{5}} + k \)
(C) \( \frac{1}{\sqrt{5}} \tan^{-1} \frac{x}{\sqrt{5}} + k \)
(D) \( \sqrt{5} \tan^{-1} \frac{x}{\sqrt{5}} + k \)

140. \( \int_{0}^{2} e^{x/2} dx = ? \) [BSEB, 2020 A]
(A) \( 2(e – 1) \)
(B) \( 2(e + 1) \)
(C) \( 2(1 – e) \)
(D) \( 2(e^2 – 1) \)

141. \( \int \frac{dx}{1 – \sin x} = \) [BSEB, 2016 A]
(A) \( \tan x – \sec x + k \)
(B) \( \tan x + \sec x + k \)
(C) \( \tan^2 x + \sec^2 x + k \)
(D) \( 2(\tan x – \sec x) + k \)

142. \( \int x^2 \sin x^3 dx = \dots \) [BSEB, 2020 A]
(A) \( \frac{1}{3} \cos x^3 + c \)
(B) \( -\frac{1}{3} \cos x^3 + c \)
(C) \( -\frac{1}{3} \cos x^3 + c \)
(D) \( \frac{1}{2} \sin^2 x^3 + c \)

143. \( \int \frac{\sec^2 x}{\text{cosec}^2 x} dx = \dots \) [BSEB, 2020 A]
(A) \( \cot x + x + c \)
(B) \( \cot x – x + c \)
(C) \( \tan x – x + c \)
(D) \( \tan x + x + c \)

144. \( \int_{1}^{\sqrt{3}} \frac{dx}{1 + x^2} = ? \) [BSEB, 2020 A]
(A) \( \frac{\pi}{12} \)
(B) \( \frac{\pi}{6} \)
(C) \( \frac{\pi}{3} \)
(D) \( \frac{2\pi}{3} \)

145. \( \int \frac{dx}{x} = \) [BSEB, 2017 A, 2022 A]
(A) \( x + k \)
(B) \( \frac{1}{x^2} + k \)
(C) \( -\frac{1}{x^2} + k \)
(D) \( \log x + k \)

146. \( \int_{0}^{\pi} 2 \cos x \, dx = ? \) [BSEB, 2019 A, 2021 A]
(A) \( -1 \)
(B) \( 1 \)
(C) \( \frac{\pi}{2} \)
(D) \( 0 \)

147. \( \int_{a}^{b} x^3 dx = \) [BSEB, 2017 A]
(A) \( \frac{b^3 – a^3}{3} \)
(B) \( \frac{b^4 – a^4}{4} \)
(C) \( \frac{b^2 – a^2}{2} \)
(D) \( 0 \)

148. \( \int e^x \left( \frac{1}{x} – \frac{1}{x^2} \right) dx = \) [BSEB, 2023 A]
(A) \( \frac{1}{x} e^x + k \)
(B) \( -xe^x + k \)
(C) \( k – \frac{1}{x} e^x \)
(D) \( k – \frac{1}{x^2} e^x \)

149. \( \int \frac{dx}{x^2 + a^2} = \) [BSEB, 2021 A, 2024 A]
(A) \( \tan^{-1} \frac{x}{a} + k \)
(B) \( \frac{1}{a} \tan^{-1} \frac{x}{a} + k \)
(C) \( \frac{1}{a} \sin^{-1} \frac{x}{a} + k \)
(D) \( \frac{1}{a} \cos^{-1} \frac{x}{a} + k \)

150. \( \int \frac{dx}{\sqrt{2x – x^2}} \) का मान है : [BSEB, 2020 A]
(A) \( \sin^{-1}(x-1) + c \)
(B) \( \sin^{-1}(1+x) + c \)
(C) \( \sin^{-1}(1+x^2) + c \)
(D) \( -\sqrt{2x – x^2} + c \)

151. \( \int \frac{dx}{\sin^2 x \cos^2 x} = ? \) [BSEB, 2020 A]
(A) \( \tan x – \cot x + k \)
(B) \( \tan x + \cot x + k \)
(C) \( -\tan x + \cot x + k \)
(D) \( -\tan x – \cot x + k \)

152. \( \int_{-1}^{1} \sin^{17} x \cos^3 x \, dx = \) [BSEB, 2023 A]
(A) \( \frac{12}{5} \)
(B) \( 0 \)
(C) \( 1 \)
(D) \( \frac{3}{5} \)

153. \( 3 \int dx = \) [BSEB, 2022 A]
(A) \( 3x + k \)
(B) \( 3 + k \)
(C) \( \frac{1}{3} + k \)
(D) \( 1 + k \)

154. \( \int_{0}^{1} \frac{dx}{1 + x^2} = ? \) [BSEB, 2019 A]
(A) \( -\frac{\pi}{4} \)
(B) \( \frac{\pi}{4} \)
(C) \( \frac{\pi}{2} \)
(D) \( \frac{\pi}{2} – \frac{\pi}{4} \)

155. \( \int \sin^3 \theta \text{cosec}^2 \theta \, d\theta = \) [BSEB, 2023 A]
(A) \( c + \theta \)
(B) \( c + \cos \theta \)
(C) \( c – \cos \theta \)
(D) \( c + \sin \theta \)

156. \( \int (4 \cos x – 5 \sin x) dx = \) [BSEB, 2023 A]
(A) \( k + 4 \sin x + 5 \cos x \)
(B) \( k – 4 \sin x – 5 \cos x \)
(C) \( k + 4 \sin x – 5 \cos x \)
(D) \( k – 4 \sin x + 5 \cos x \)

157. \( \int \frac{x+2}{x^2 – 4} dx = \) [BSEB, 2023 A]
(A) \( \log |x + 2| + k \)
(B) \( \log |x^2 – 4| + k \)
(C) \( \log |x – 2| + k \)
(D) \( \log |\frac{x+2}{x-2}| + k \)

158. \( 25 \int \sec 5x \tan 5x \, dx = \) [BSEB, 2023 A]
(A) \( 25 \sec 5x + k \)
(B) \( 5 \sec 5x + k \)
(C) \( 25 \tan 5x + k \)
(D) \( \sec 5x + k \)

159. \( 3 \int_{0}^{3} x^2 dx = \) [BSEB, 2023 A]
(A) \( \frac{81}{4} \)
(B) \( \frac{243}{4} \)
(C) \( 0 \)
(D) \( \frac{9}{4} \)

160. \( \int_{-\pi/6}^{\pi/6} \tan \theta \, d\theta = \) [BSEB, 2023 A]
(A) \( 0 \)
(B) \( 1 \)
(C) \( 2 \)
(D) \( 3 \)

161. \( \int 0 dx = \) [BSEB, 2017 A]
(A) \( k \)
(B) \( 0 \)
(C) \( 1 \)
(D) \( -1 \)

162. \( \int x^n dx, n \neq 0 = \) [BSEB, 2016 C, 2019 A]
(A) \( \frac{x^{n-1}}{n-1} + C \)
(B) \( \frac{x^{n+1}}{n+1} + C \)
(C) \( x^{n-1} + C \)
(D) \( x^{n+1} + C \)

163. \( \int \frac{dx}{1+x^2} = \) [BSEB, 2016 C, 2019 A]
(A) \( \cot^{-1} x + C \)
(B) \( \tan^{-1} x + C \)
(C) \( \sec^{-1} x + C \)
(D) \( \text{cosec}^{-1} x + C \)

164. \( \int_{a}^{b} e^x dx = \) [BSEB, 2016 C, 2022 A]
(A) \( (e^b – e^a) \)
(B) \( e^{a-b} \)
(C) \( e^a – e^b \)
(D) \( e^{a+b} \)

165. \( \int_{-\pi/4}^{\pi/4} \sin^3 x \, dx = \) [BSEB, 2022 A]
(A) \( 0 \)
(B) \( 1 \)
(C) \( 2 \)
(D) \( \frac{3}{\sqrt{2}} \)

166. \( \int \frac{dx}{e^x + e^{-x}} = \) [BSEB, 2022 A]
(A) \( \tan^{-1}(e^x) + k \)
(B) \( \tan^{-1}(e^{-x}) + k \)
(C) \( \log |e^x + e^{-x}| + k \)
(D) \( x + k \)

167. \( \int_{-\pi/2}^{\pi/2} \sin^9 x \, dx = \) [BSEB, 2009, 2019 A]
(A) \( -1 \)
(B) \( 1 \)
(C) \( 0 \)
(D) इनमें से कोई नहीं

168. \( 3 \int \sqrt{x} \, dx = \) [BSEB, 2022 A, 2023 A]
(A) \( 2x^{3/2} + k \)
(B) \( 4x^3 + k \)
(C) \( 3x^{3/2} + k \)
(D) \( 6x^{3/2} + k \)

169. \( \int 1 \cdot dx = \) [BSEB, 2015, 2019 C, 2020 A]
(A) \( x + k \)
(B) \( 1 + k \)
(C) \( \frac{x^2}{2} + k \)
(D) \( \log x + k \)

170. \( \int_{a}^{b} x^5 dx = \) [BSEB, 2015]
(A) \( b^3 – a^3 \)
(B) \( \frac{b^6 – a^6}{6} \)
(C) \( \frac{a^6 – b^6}{6} \)
(D) \( a^5 – b^5 \)

171. \( \int \frac{\cos 2x \, dx}{(\sin x + \cos x)^2} = \) [BSEB, 2011, 2015, 2021 A]
(A) \( -\frac{1}{\sin x + \cos x} + C \)
(B) \( \log |\sin x + \cos x| + C \)
(C) \( \log |\sin x – \cos x| + C \)
(D) \( \frac{1}{(\sin x + \cos x)^2} \)

172. \( 2 \int \frac{1}{1 + 4x^2} dx = \) [BSEB, 2022 A]
(A) \( \tan^{-1} x + k \)
(B) \( \log |1 + 4x^2| + k \)
(C) \( \tan^{-1} 2x + k \)
(D) \( \sin^{-1} 2x + k \)

173. \( \int \frac{\sec^2(\log x)}{x} dx = ? \) [BSEB, 2020 A]
(A) \( \tan(\log x) + k \)
(B) \( -\tan(\log x) + k \)
(C) \( \cot(\log x) + k \)
(D) \( -\cot(\log x) + k \)

174. \( \int_{0}^{\pi/2} \frac{\sin x – \cos x}{1 + \sin x \cos x} dx \) का मान क्या है? [2016 C]
(A) \( 1 \)
(B) \( \frac{\pi}{2} \)
(C) \( 0 \)
(D) \( \pi – \frac{\pi}{2} \)

175. \( \int \cos x \, dx = \) [BSEB, 2019 C]
(A) \( -\sin x + k \)
(B) \( \cos x + k \)
(C) \( \sin x + k \)
(D) \( -\cos x + k \)

176. \( \int_{0}^{\pi/2} \frac{dx}{1 + \tan^2 x} = \) [BSEB, 2019 A]
(A) \( 0 \)
(B) \( 1 \)
(C) \( \frac{\pi}{2} \)
(D) \( \frac{\pi}{4} \)

177. \( \int_{1}^{\sqrt{3}} \frac{dx}{1 + x^2} = ? \) [BSEB, 2020 A]
(A) \( \frac{\pi}{12} \)
(B) \( \frac{\pi}{6} \)
(C) \( \frac{\pi}{3} \)
(D) \( \frac{2\pi}{3} \)

178. \( \int \left( \frac{\cos 2\theta – 1}{\cos 2\theta + 1} \right) d\theta = \) [BSEB, 2019 A]
(A) \( \tan \theta – \theta + c \)
(B) \( \theta + \tan \theta + c \)
(C) \( \theta – \tan \theta + c \)
(D) \( -\theta – \cot \theta + c \)

179. \( \int e^x (\cot x + \log \sin x) dx = ? \) [BSEB, 2020 A]
(A) \( e^x \log \sin x + k \)
(B) \( e^x \cot x + k \)
(C) \( e^x \sin x + k \)
(D) \( e^x \cos x + k \)

180. \( \int \frac{\sin \sqrt{x}}{\sqrt{x}} dx = \) [BSEB, 2021 A]
(A) \( 2 \cos \sqrt{x} + k \)
(B) \( -2 \cos \sqrt{x} + k \)
(C) \( \frac{\cos \sqrt{x}}{2} + k \)
(D) \( -\frac{\cos \sqrt{x}}{2} + k \)

181. \( \int \frac{\cos 2x}{\cos^2 x \sin^2 x} dx = \) [BSEB, 2021 A]
(A) \( -\cot x – \tan x + k \)
(B) \( \cot x + \tan x + k \)
(C) \( \cot x – \tan x + k \)
(D) \( \tan x – \cot x + k \)

182. \( \int \frac{dx}{x \log x} = \) [BSEB, 2021 A]
(A) \( \log x + k \)
(B) \( \log (\log x) + k \)
(C) \( (\log x)^2 + k \)
(D) \( \frac{1}{\log x} + k \)

183. \( \int_{0}^{1} x(1-x)^{10} dx = \) [BSEB, 2023 A]
(A) \( \frac{1}{110} \)
(B) \( \frac{1}{121} \)
(C) \( \frac{1}{132} \)
(D) \( \frac{1}{144} \)

184. \( \int \sqrt{1 + \cos 2x} \, dx = \) [BSEB, 2024 A]
(A) \( \sqrt{2} \sin x + k \)
(B) \( -\sqrt{2} \cos x + k \)
(C) \( \sqrt{2} \cos x + k \)
(D) \( 2 \sin x + k \)

185. \( \int_{0}^{\pi/2} \log (\tan x) dx = \) [BSEB, 2022 A, 2024 A]
(A) \( \pi/2 \)
(B) \( \pi/4 \)
(C) \( 0 \)
(D) \( 1 \)

186. \( \int \frac{dx}{\sqrt{x^2 – a^2}} = \) [BSEB, 2021 A]
(A) \( \log |x + \sqrt{x^2 – a^2}| + k \)
(B) \( \log |x – \sqrt{x^2 – a^2}| + k \)
(C) \( \sin^{-1} \frac{x}{a} + k \)
(D) \( \frac{1}{a} \sec^{-1} \frac{x}{a} + k \)

187. \( \int_{0}^{\pi/4} \tan^2 x \, dx = \) [BSEB, 2021 A]
(A) \( 1 – \frac{\pi}{4} \)
(B) \( \frac{\pi}{4} – 1 \)
(C) \( 1 + \frac{\pi}{4} \)
(D) \( \frac{\pi}{4} \)

188. \( \int \frac{1}{x^2 + 2x + 2} dx = \) [BSEB, 2021 A]
(A) \( \tan^{-1}(x+1) + k \)
(B) \( \sin^{-1}(x+1) + k \)
(C) \( \log |x^2 + 2x + 2| + k \)
(D) \( \tan^{-1} x + k \)

189. \( \int_{0}^{\pi/2} \frac{\sqrt{\sin x}}{\sqrt{\sin x} + \sqrt{\cos x}} dx = \) [BSEB, 2018 A, 2023 A]
(A) \( \pi/2 \)
(B) \( \pi/4 \)
(C) \( 0 \)
(D) \( \pi \)

190. \( \int \frac{x^4 – 1}{x^2 + 1} dx = \) [BSEB, 2022 A]
(A) \( \frac{x^3}{3} + x + k \)
(B) \( \frac{x^3}{3} – x + k \)
(C) \( \frac{x^3}{3} + k \)
(D) \( x^3 – x + k \)

191. \( \int_{0}^{a} x \, dx = \) [BSEB, 2024 A]
(A) \( a \)
(B) \( a^2 \)
(C) \( a^2/2 \)
(D) \( 0 \)

192. \( \int_{a}^{b} x^2 dx = ? \) [BSEB, 2019 A]
(A) \( \frac{b^3 – a^3}{3} \)
(B) \( \frac{a^3 – b^3}{3} \)
(C) \( \frac{a^2 – b^2}{2} \)
(D) \( \frac{b^2 – a^2}{2} \)

Bihar Board Class 12th के (Mathematics/गणित) = गणित भाग-1 (Hindi Medium) Book Chapter-6 समाकलन के Exam 2026 MCQs Questions Answer Key