INTEGRATION Grand Master Bikram Sutradhar GRAND MASTER BIKRAM SUTRADHAR

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📘 INTEGRATION – 200 QUESTIONS (Easy to Pro)

Class 11 • Class 12 • JEE Main • JEE Advanced

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Exercise: Integration

1. $$ \int x^2 \, dx $$

2. $$ \int (3x^2-5x+7)\,dx $$

3. $$ \int \sqrt{x}\,dx $$

4. $$ \int \frac{1}{x}\,dx $$

5. $$ \int \frac{1}{x^2}\,dx $$

6. $$ \int (2x+1)^5\,dx $$

7. $$ \int \frac{dx}{2x+3} $$

8. $$ \int \sin x\,dx $$

9. $$ \int \cos x\,dx $$

10. $$ \int \tan x\,dx $$

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11. $$ \int \sec^2 x\,dx $$

12. $$ \int \csc^2 x\,dx $$

13. $$ \int \sec x\tan x\,dx $$

14. $$ \int \csc x\cot x\,dx $$

15. $$ \int \sin^2 x\,dx $$

16. $$ \int \cos^2 x\,dx $$

17. $$ \int \sin x\cos x\,dx $$

18. $$ \int e^x\,dx $$

19. $$ \int e^{2x}\,dx $$

20. $$ \int a^x\,dx $$

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21. $$ \int \ln x\,dx $$

22. $$ \int \frac{\ln x}{x}\,dx $$

23. $$ \int \frac{x}{x^2+1}\,dx $$

24. $$ \int \frac{dx}{x^2+1} $$

25. $$ \int \frac{dx}{\sqrt{1-x^2}} $$

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26. $$ \int \frac{dx}{\sqrt{x^2-1}} $$

27. $$ \int \frac{dx}{x^2-a^2} $$

28. $$ \int \frac{x}{\sqrt{x^2+1}}\,dx $$

29. $$ \int \sqrt{x^2+a^2}\,dx $$

30. $$ \int \sqrt{a^2-x^2}\,dx $$

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31. $$ \int \frac{dx}{x\sqrt{x^2-1}} $$

32. $$ \int \frac{dx}{x\sqrt{a^2-x^2}} $$

33. $$ \int \frac{x^2}{x^3+1}\,dx $$

34. $$ \int \frac{dx}{x^3} $$

35. $$ \int \frac{dx}{x(x+1)} $$

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36. $$ \int \frac{dx}{x(x-1)} $$

37. $$ \int \frac{dx}{x^2-1} $$

38. $$ \int \frac{dx}{(x+1)^2} $$

39. $$ \int \frac{dx}{\sqrt{x}+1} $$

40. $$ \int x\sqrt{x}\,dx $$

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41. $$ \int \sin(ax)\,dx $$

42. $$ \int \cos(ax)\,dx $$

43. $$ \int e^{ax+b}\,dx $$

44. $$ \int \frac{dx}{ax+b} $$

45. $$ \int \tan^2 x\,dx $$

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46. $$ \int \sec^3 x\,dx $$

47. $$ \int \csc^3 x\,dx $$

48. $$ \int \frac{dx}{\sin x} $$

49. $$ \int \frac{dx}{\cos x} $$

50. $$ \int \sin^3 x\,dx $$

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51. $$ \int \cos^3 x\,dx $$

52. $$ \int xe^x\,dx $$

53. $$ \int x\sin x\,dx $$

54. $$ \int x\cos x\,dx $$

55. $$ \int x\ln x\,dx $$

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56. $$ \int \frac{x}{\sqrt{1+x^2}}\,dx $$

57. $$ \int \frac{dx}{1+\tan^2 x} $$

58. $$ \int \frac{dx}{1+\cot^2 x} $$

59. $$ \int \frac{\sec x}{\tan x}\,dx $$

60. $$ \int \frac{\csc x}{\cot x}\,dx $$

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61. $$ \int \frac{x^2}{\sqrt{x^2+1}}\,dx $$

62. $$ \int \sqrt{1+\sin x}\,dx $$

63. $$ \int \sqrt{1-\cos x}\,dx $$

64. $$ \int \frac{dx}{\sqrt{1+\sin x}} $$

65. $$ \int \frac{dx}{\sqrt{1-\cos x}} $$

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66. $$ \int \frac{x}{(x^2+1)^2}\,dx $$

67. $$ \int \frac{dx}{(x^2+1)^2} $$

68. $$ \int \frac{x}{x^2-1}\,dx $$

69. $$ \int \frac{dx}{\sqrt{x^2+a^2}} $$

70. $$ \int \frac{dx}{\sqrt{x^2-a^2}} $$

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71. $$ \int \ln(ax+b)\,dx $$

72. $$ \int \frac{\ln x}{x^2}\,dx $$

73. $$ \int \frac{dx}{x\ln x} $$

74. $$ \int \sin(\ln x)\,dx $$

75. $$ \int \cos(\ln x)\,dx $$

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76. $$ \int \frac{x^3}{x^4+1}\,dx $$

77. $$ \int \frac{dx}{x^4} $$

78. $$ \int x^2e^x\,dx $$

79. $$ \int x^2\sin x\,dx $$

80. $$ \int x^2\cos x\,dx $$

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81. $$ \int \frac{dx}{\sqrt{ax^2+bx+c}} $$

82. $$ \int \sqrt{ax^2+bx+c}\,dx $$

83. $$ \int \frac{dx}{x\sqrt{ax+b}} $$

84. $$ \int \frac{x}{\sqrt{ax+b}}\,dx $$

85. $$ \int \frac{dx}{(ax+b)^2} $$

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86. $$ \int \frac{dx}{ax^2+bx+c} $$

87. $$ \int \frac{x}{ax^2+bx+c}\,dx $$

88. $$ \int \sin(ax+b)\,dx $$

89. $$ \int \cos(ax+b)\,dx $$

90. $$ \int e^{ax^2}\,dx $$

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91. $$ \int \frac{dx}{\sqrt{1+x^4}} $$

92. $$ \int \sqrt{1+x^4}\,dx $$

93. $$ \int \frac{dx}{x^2\sqrt{x^2-1}} $$

94. $$ \int \frac{dx}{x^2\sqrt{1-x^2}} $$

95. $$ \int \frac{\sqrt{x^2-1}}{x}\,dx $$

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96. $$ \int \frac{\sqrt{1-x^2}}{x}\,dx $$

97. $$ \int \frac{dx}{\sqrt{x^2+x+1}} $$

98. $$ \int \sqrt{x^2+x+1}\,dx $$

99. $$ \int \frac{x}{\sqrt{x^2+x+1}}\,dx $$

100. $$ \int \frac{dx}{x^2+x+1} $$

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Next 100

Mathematics Mathematics

📘 INTEGRATION – NEXT 100 LEVEL QUESTIONS

Class 11 • Class 12 • IIT-JEE Main & Advanced

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A. Algebraic & Rational Integrals

1. \( \int \frac{x^3+1}{x^2+1}\,dx \)

2. \( \int \frac{x^4+1}{x^2+1}\,dx \)

3. \( \int \frac{x^2}{(x^2+1)^2}\,dx \)

4. \( \int \frac{x^3}{(x^2+1)^2}\,dx \)

5. \( \int \frac{x^5}{x^2+1}\,dx \)

6. \( \int \frac{x}{x^4+1}\,dx \)

7. \( \int \frac{x^2}{x^4+1}\,dx \)

8. \( \int \frac{x^3}{x^4+1}\,dx \)

9. \( \int \frac{dx}{x^4+4} \)

10. \( \int \frac{dx}{x^4+1} \)

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B. Trigonometric Integrals

11. \( \int \frac{\sin x}{1+\cos x}\,dx \)

12. \( \int \frac{\cos x}{1+\sin x}\,dx \)

13. \( \int \frac{dx}{\sin x+\cos x} \)

14. \( \int \frac{dx}{\sin x-\cos x} \)

15. \( \int \tan^3 x \sec^2 x\,dx \)

16. \( \int \sin^5 x \cos^3 x\,dx \)

17. \( \int \frac{dx}{\sin^3 x} \)

18. \( \int \frac{dx}{\cos^3 x} \)

19. \( \int \sec x \tan^2 x\,dx \)

20. \( \int \csc x \cot^2 x\,dx \)

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C. Exponential & Logarithmic

21. \( \int x e^{x^2}\,dx \)

22. \( \int x^2 e^x\,dx \)

23. \( \int e^x \sin x\,dx \)

24. \( \int e^x \cos x\,dx \)

25. \( \int x e^x \cos x\,dx \)

26. \( \int \ln(x^2+1)\,dx \)

27. \( \int x\ln x\,dx \)

28. \( \int \ln(\ln x)\,dx \)

29. \( \int \frac{\ln x}{x^2}\,dx \)

30. \( \int \frac{\ln x}{x}\,dx \)

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D. Radical & Special Forms

31. \( \int \sqrt{x^2+1}\,dx \)

32. \( \int \sqrt{x^2-1}\,dx \)

33. \( \int \frac{dx}{\sqrt{x^2+1}} \)

34. \( \int \frac{dx}{\sqrt{x^2-1}} \)

35. \( \int \frac{x}{\sqrt{x^2+1}}\,dx \)

36. \( \int \frac{x^2}{\sqrt{x^2+1}}\,dx \)

37. \( \int \frac{dx}{x\sqrt{x^2-1}} \)

38. \( \int \frac{dx}{x\sqrt{1-x^2}} \)

39. \( \int \sqrt{1+\sin x}\,dx \)

40. \( \int \sqrt{1-\cos x}\,dx \)

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E. Substitution Based

41. \( \int \frac{dx}{x^2\sqrt{x^2-1}} \)

42. \( \int \frac{\sqrt{x^2-1}}{x}\,dx \)

43. \( \int \frac{x}{\sqrt{x^2+x+1}}\,dx \)

44. \( \int \sqrt{x^2+x+1}\,dx \)

45. \( \int \frac{dx}{\sqrt{x^2+x+1}} \)

46. \( \int \frac{dx}{x^2+x+1} \)

47. \( \int \frac{x^2}{x^2+x+1}\,dx \)

48. \( \int \frac{dx}{\sqrt{ax^2+bx+c}} \)

49. \( \int \sqrt{ax^2+bx+c}\,dx \)

50. \( \int \frac{x}{\sqrt{ax+b}}\,dx \)

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F. By Parts

51. \( \int x\sin x\,dx \)

52. \( \int x\cos x\,dx \)

53. \( \int x^2\sin x\,dx \)

54. \( \int x^2\cos x\,dx \)

55. \( \int x\ln x\,dx \)

56. \( \int x^2\ln x\,dx \)

57. \( \int \ln x\,dx \)

58. \( \int x^3 e^x\,dx \)

59. \( \int x^2 e^{2x}\,dx \)

60. \( \int x^3 \cos x\,dx \)

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G. Tricky / Olympiad Type

61. \( \int \frac{dx}{1+\sin x} \)

62. \( \int \frac{dx}{1-\cos x} \)

63. \( \int \frac{\sin x}{1+\cos x}\,dx \)

64. \( \int \frac{\cos x}{1-\sin x}\,dx \)

65. \( \int \tan x \sec x\,dx \)

66. \( \int \frac{dx}{\tan x+\sec x} \)

67. \( \int \frac{dx}{\tan x-\sec x} \)

68. \( \int \frac{\sec x}{\tan x}\,dx \)

69. \( \int \frac{\csc x}{\cot x}\,dx \)

70. \( \int \sin(\ln x)\,dx \)

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H. Expression Type

71. \( \int \cos(\ln x)\,dx \)

72. \( \int x\sin(\ln x)\,dx \)

73. \( \int x\cos(\ln x)\,dx \)

74. \( \int \frac{dx}{x\ln x} \)

75. \( \int \frac{dx}{x(\ln x)^2} \)

76. \( \int \frac{x^3}{x^4+1}\,dx \)

77. \( \int \frac{dx}{x^4} \)

78. \( \int x^2 e^{x^2}\,dx \)

79. \( \int x^3 \sin x\,dx \)

80. \( \int x^3 \cos x\,dx \)

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81. \( \int \frac{dx}{\sqrt{1+x^4}} \)

82. \( \int \sqrt{1+x^4}\,dx \)

83. \( \int \frac{dx}{x^2\sqrt{1-x^2}} \)

84. \( \int \frac{\sqrt{1-x^2}}{x}\,dx \)

85. \( \int \frac{dx}{x^2\sqrt{x^2-1}} \)

86. \( \int \frac{\sqrt{x^2-1}}{x^2}\,dx \)

87. \( \int \frac{dx}{\sqrt{x^4+x^2+1}} \)

88. \( \int \sqrt{x^4+x^2+1}\,dx \)

89. \( \int \frac{x}{\sqrt{x^4+x^2+1}}\,dx \)

90. \( \int \frac{dx}{x^4+x^2+1} \)

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91. \( \int \ln(x^2+x+1)\,dx \)

92. \( \int x\ln(x^2+1)\,dx \)

93. \( \int \ln(\sin x)\,dx \)

94. \( \int \ln(\cos x)\,dx \)

95. \( \int \ln(\tan x)\,dx \)

96. \( \int \frac{dx}{\sqrt{a^2-x^2}} \)

97. \( \int \sqrt{a^2-x^2}\,dx \)

98. \( \int \frac{x}{\sqrt{a^2-x^2}}\,dx \)

99. \( \int \frac{dx}{x^2+a^2} \)

100. \( \int \frac{x^2}{x^2+a^2}\,dx \)

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Author: GrandMaster Bikram Sutradhar
Institute: bAstronautWay

Written By

Full Stack Developer and 5-Time World Record Holder, Grandmaster Bikram Sutradhar

  bAstronautWay :  A Government-Approved Trademark Brand

    SirBikramSutradhar on YouTube

    SirBikramSutradhar is also a Government-Approved Trademark  Brand.                                                               

Written By

Full Stack Developer and 5-Time World Record Holder, Grandmaster Bikram Sutradhar

bAstronautWay

SirBikramSutradhar on YouTube                                                               

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📚 Class 9 Science – Complete Table of Contents (विषय-सूची)

CBSE | NCERT Curriculum | Bilingual (English + Hindi)
By Grandmaster Bikram Sutradhar | SirBikramSutradhar | BASTRONAUTWAY

🔬 PHYSICS (भौतिक विज्ञान)

🔢	Chapter Title (English)	अध्याय का नाम (हिंदी)	Page No.
1️⃣	Motion	गति
2️⃣	Force and Laws of Motion	बल तथा गति के नियम
3️⃣	Gravitation	गुरुत्वाकर्षण
4️⃣	Work and Energy	कार्य तथा ऊर्जा
5️⃣	Sound	ध्वनि

🧪 CHEMISTRY (रसायन विज्ञान)

🔢	Chapter Title (English)	अध्याय का नाम (हिंदी)	Page No.
1️⃣	Matter in Our Surroundings	हमारे आस-पास के पदार्थ
2️⃣	Is Matter Around Us Pure?	क्या हमारे आस-पास के पदार्थ शुद्ध हैं?
3️⃣	Atoms and Molecules	परमाणु एवं अणु