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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

- Integral calculus
- Standard integration

The process of integration - The general solution of integrals of the

form ax n - Standard integrals
- Definite integrals
- Integration using algebraic substitutions
- Change of limits
- Integration using trigonometric and hyperbolic

substitutions - Worked problems on integration of sin 2 x,

cos2 x, tan 2 x and cot 2 x - Worked problems on integration of powers

of sines and cosines - Worked problems on integration of

products of sines and cosines - Worked problems on integration using the

sin θ substitution - Worked problems on integration using the

tan θ substitution - Worked problems on integration using the

sinh θ substitution - Worked problems on integration using the

cosh θ substitution - Integration using partial fractions
- Worked problems on integration using

partial fractions with linear factors - Worked problems on integration using

partial fractions with repeated linear factors - Worked problems on integration using

partial fractions with quadratic factors - The t = tan θ/2 substitution
- Integration by parts
- Reduction formulae
- Using reduction formulae for integrals of

the form ∫ x n ex dx - Using reduction formulae for integrals of

the form ∫ x n cos x dx and ∫ x n sin x dx - Using reduction formulae for integrals of

the form ∫ sinn x dx and ∫ cosn x dx - Double and triple integrals
- Numerical integration
- The trapezoidal rule
- The mid-ordinate rule
- Simpson’s rule
- Areas under and between curves
- Area under a curve
- The area between curves
- Mean and root mean square values
- Mean or average values
- Root mean square values
- Volumes of solids of revolution
- Centroids of simple shapes
- Solution of first-order differential equations

by separation of variables - Family of curves
- Differential equations

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