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About Integral Calculus AI

An AI solver for integral calculus can help solve various types of integration problems, including standard integration, definite integrals, and integration using different substitutions such as algebraic, trigonometric, and hyperbolic. It can also solve problems involving trigonometric functions like sin, cos, tan, and cot, as well as products and powers of these functions.

The AI can assist with integration using partial fractions, reduction formulae, and techniques like integration by parts. It can also help with double and triple integrals, numerical integration methods like the trapezoidal rule and Simpson's rule, and finding areas under and between curves.

Moreso, the AI can calculate volumes of solids of revolution, centroids of shapes, and solve first-order differential equations using techniques like separation of variables. With the ability to handle a wide range of integral calculus problems, this AI solver can be a valuable tool for students and professionals working in mathematics and related fields.

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1. \int x^2 dx

2. \int 5x dx

3. \int \frac{1}{x} dx

4. \int e^x dx

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

6. \int \sin(x) dx

7. \int \cos(x) dx

8. \int \sin(2x) dx

9. \int \cos(2x) dx

10. \int \tan(3x) dx

11. \int \cot(2x) dx

12. \int x^3 dx

13. \int \frac{1}{x^3} dx

14. \int e^{2x} dx

15. \int \sin^2(x) dx

16. \int \cos^2(x) dx

17. \int \sin(x) \cos(x) dx

18. \int \sin(3x) dx

19. \int \cos(4x) dx

20. \int \sin(2x) \cos(2x) dx

21. \int \sin(\theta) d\theta

22. \int \cos(\theta) d\theta

23. \int \sin^2(\theta) d\theta

24. \int \cos^2(\theta) d\theta

25. \int \sin(\theta) \cos(\theta) d\theta

26. \int \tan(\theta) d\theta

27. \int \cot(\theta) d\theta

28. \int \sin(3\theta) d\theta

29. \int \cos(4\theta) d\theta

30. \int \sin(2\theta) \cos(2\theta) d\theta

31. \int \sinh(x) dx

32. \int \cosh(x) dx

33. \int \sinh(2x) dx

34. \int \cosh(3x) dx

35. \int \sinh(x) \cosh(x) dx

36. \int \sinh(\theta) d\theta

37. \int \cosh(\theta) d\theta

38. \int \sinh^2(\theta) d\theta

39. \int \cosh^2(\theta) d\theta

40. \int \sinh(\theta) \cosh(\theta) d\theta

41. \int e^{3x} dx

42. \int 2x^2 dx

43. \int \frac{1}{x^4} dx

44. \int e^{-x} dx

45. \int \cos(3x) dx

46. \int \tan^2(x) dx

47. \int \cot^3(x) dx

48. \int x^4 dx

49. \int \sin^3(x) dx

50. \int \cos(5x) dx

1. Integral calculus
2. Standard integration
   The process of integration
3. The general solution of integrals of the
   form ax n
4. Standard integrals
5. Definite integrals
6. Integration using algebraic substitutions
7. Change of limits
8. Integration using trigonometric and hyperbolic
   substitutions
9. Worked problems on integration of sin 2 x,
   cos2 x, tan 2 x and cot 2 x
10. Worked problems on integration of powers
    of sines and cosines
11. Worked problems on integration of
    products of sines and cosines
12. Worked problems on integration using the
    sin θ substitution
13. Worked problems on integration using the
    tan θ substitution
14. Worked problems on integration using the
    sinh θ substitution
15. Worked problems on integration using the
    cosh θ substitution
16. Integration using partial fractions
17. Worked problems on integration using
    partial fractions with linear factors
18. Worked problems on integration using
    partial fractions with repeated linear factors
19. Worked problems on integration using
    partial fractions with quadratic factors
20. The t = tan θ/2 substitution
21. Integration by parts
22. Reduction formulae
23. Using reduction formulae for integrals of
    the form ∫ x n ex dx
24. Using reduction formulae for integrals of
    the form ∫ x n cos x dx and ∫ x n sin x dx
25. Using reduction formulae for integrals of
    the form ∫ sinn x dx and ∫ cosn x dx
26. Double and triple integrals
27. Numerical integration
28. The trapezoidal rule
29. The mid-ordinate rule
30. Simpson’s rule
31. Areas under and between curves
32. Area under a curve
33. The area between curves
34. Mean and root mean square values
35. Mean or average values
36. Root mean square values
37. Volumes of solids of revolution
38. Centroids of simple shapes
39. Solution of first-order differential equations
    by separation of variables
40. Family of curves
41. Differential equations