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๐Ÿ“˜ INTEGRATION โ€“ 200 QUESTIONS Easy to Pro

SirBikramSutradhar
๐Ÿ“˜ INTEGRATION โ€“ 200 QUESTIONS Easy to Pro

๐Ÿ“˜ INTEGRATION โ€“ 200 QUESTIONS Easy to Pro

INTEGRATION Grand Master Bikram Sutradhar GRAND MASTER BIKRAM SUTRADHAR

๐Ÿ“˜ INTEGRATION โ€“ 200 QUESTIONS (Easy to Pro)

Class 11 โ€ข Class 12 โ€ข JEE Main โ€ข JEE Advanced

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Next 100

Mathematics Mathematics

๐Ÿ“˜ INTEGRATION โ€“ NEXT 100 LEVEL QUESTIONS

Class 11 โ€ข Class 12 โ€ข IIT-JEE Main & Advanced

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

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

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

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

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

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

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

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

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

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

Author: GrandMaster Bikram Sutradhar
Institute: bAstronautWay

๐Ÿ“˜ INTEGRATION โ€“ 200 QUESTIONS Easy to Pro
๐Ÿ“˜ INTEGRATION โ€“ 200 QUESTIONS Easy to Pro

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

  bAstronautWay :  A Government-Approved Trademark Brand

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    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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๐Ÿ“š Class 9 Science โ€“ Complete Table of Contents (เคตเคฟเคทเคฏ-เคธเฅ‚เคšเฅ€)

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

๐Ÿ”ฌ PHYSICS (เคญเฅŒเคคเคฟเค• เคตเคฟเคœเฅเคžเคพเคจ)

๐Ÿ”ขChapter Title (English)เค…เคงเฅเคฏเคพเคฏ เค•เคพ เคจเคพเคฎ (เคนเคฟเค‚เคฆเฅ€)Page No.
1๏ธโƒฃMotionเค—เคคเคฟ
2๏ธโƒฃForce and Laws of Motionเคฌเคฒ เคคเคฅเคพ เค—เคคเคฟ เค•เฅ‡ เคจเคฟเคฏเคฎ
3๏ธโƒฃGravitationเค—เฅเคฐเฅเคคเฅเคตเคพเค•เคฐเฅเคทเคฃ
4๏ธโƒฃWork and Energyเค•เคพเคฐเฅเคฏ เคคเคฅเคพ เคŠเคฐเฅเคœเคพ
5๏ธโƒฃSoundเคงเฅเคตเคจเคฟ

๐Ÿงช CHEMISTRY (เคฐเคธเคพเคฏเคจ เคตเคฟเคœเฅเคžเคพเคจ)

๐Ÿ”ขChapter Title (English)เค…เคงเฅเคฏเคพเคฏ เค•เคพ เคจเคพเคฎ (เคนเคฟเค‚เคฆเฅ€)Page No.
1๏ธโƒฃMatter in Our Surroundingsเคนเคฎเคพเคฐเฅ‡ เค†เคธ-เคชเคพเคธ เค•เฅ‡ เคชเคฆเคพเคฐเฅเคฅ
2๏ธโƒฃIs Matter Around Us Pure?เค•เฅเคฏเคพ เคนเคฎเคพเคฐเฅ‡ เค†เคธ-เคชเคพเคธ เค•เฅ‡ เคชเคฆเคพเคฐเฅเคฅ เคถเฅเคฆเฅเคง เคนเฅˆเค‚?
3๏ธโƒฃAtoms and Moleculesเคชเคฐเคฎเคพเคฃเฅ เคเคตเค‚ เค…เคฃเฅ
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