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Integral Table

Integrator
Indefinite Integrals
1. Basic integrals
2. Integrals involving $int$ a+b x
3. Integrals involving $a+b x^n$
4. Integrals involving $a+b x+c x^n$
5. Integrals involving $sqrt(a+b x)$
6. Integrals involving $sqrt(x^2+-a^2)$
7. Integrals involving $sqrt(a+b x+c x^2)$
8. Integrals involving $sqrt((a+-x)/(b+-x)) and sqrt((x-a)(b-x))$
9. Integrals involving $a^4+-x^4$
10. Integrals involving trig function $int$ sin(x)
11. Integrals involving inverse trig function $int$ asin(x)
12. Integrals involving $int$ exp(x) and $int$ log(x)
13. Integrals involving $int$ exp(x)*sin(x)
14. Integrals involving hyperbolic function $int$ sinh(x) and its inverse $int$ asinh(x)
15. Table of Integrals - Basic Forms and Common Integrals
  The integrals below are very common and are used in a great many calculus problems. We include basic polynomial rules, integrals of the exponential function, integrals of basic trig functions, a... View the lesson
16. Table of Integrals - Forms Involving $ax + b$
  The integrals below involve $ax + b$ , including forms where $ax + b$ is raised to an exponent or in the denominator of a fraction.... View the lesson
17. Table of Integrals - Forms Involving $sqrt(ax+b)$
  The integrals below involve $sqrt(ax+b)$ .... View the lesson
18. Table of Integrals - Forms Involving $ax+b$ and $px+q$
  The integrals below involve $ax+b$ and $px+q$ .... View the lesson
19. Table of Integrals - Forms Involving $sqrt(ax+b)$ and $px+q$
  The integrals below involve $sqrt(ax+b)$ and $px+q$ occurring together in the integrand.... View the lesson
20. Table of Integrals - Forms involving $sqrt(ax+b)$ and $sqrt(px+q)$
  The integrals below involve $sqrt(ax+b)$ and $sqrt(px+q)$ appearing together in the integrand.... View the lesson
21. Table of Integrals - Forms involving $x^2+a^2$
  The integrals below involve $x^2+a^2$ ... View the lesson
22. Table of Integrals - Forms Involving $x^2-a^2$ , $x^2>a^2$
  The integrals below involve $x^2-a^2$ where $x^2>a^2$ ... View the lesson
23. Table of Integrals - Forms Involving $a^2-x^2, x^2lta^2$
  The integrals below involve $a^2-x^2$ where $x^2 < a^2$ ... View the lesson
24. Table of Integrals - Forms Involving $sqrt(x^2+a^2)$
  The integrals below involve $sqrt(x^2+a^2)$ ... View the lesson
25. Table of Integrals - Forms Involving $sqrt(x^2-a^2)$
  The integrals below involve $sqrt(x^2-a^2)$ ... View the lesson
26. Table of Integrals - Forms Involving $sqrt(a^2-x^2)$
  The integrals below involve $sqrt(a^2-x^2)$ ... View the lesson
27. Table of Integrals - Forms Involving $ax^2+bx+c$
  The integrals below involve $ax^2+bx+c$ ... View the lesson
28. Table of Integrals - Forms Involving $sqrt(ax^2+bx+c)$
  The integrals below involve $sqrt(ax^2+bx+c)$ ... View the lesson
29. Table of Integrals - Forms Involving $x^3+a^3$
  The following integrals involve $x^3+a^3$ ... View the lesson
30. Table of Integrals - Forms Involving $x^4+-a^4$
  The integrals below involve $x^4+-a^4$ ... View the lesson
31. Table of Integrals - Forms Involving $x^n+-a^n$
  The integrals below involve $x^n+-a^n$ ... View the lesson
32. Table of Integrals - Forms Involving $sin ax$
  The integrals below involve $sin ax$ ... View the lesson
33. Table of Integrals - Forms Involving $cos ax$
  The integrals below involve $cos ax$ .... View the lesson
34. Table of Integrals - Forms Involving $sin ax$ and $cos ax$
  The integrals below involve $sin ax$ and $cos ax$ . *****Special Note: In integrals #12, #15, and #24 you will see this symbol ${-+}$ . This is to be read as "minus or plus". Treat this as you... View the lesson
35. Table of Integrals - Forms Involving $tan ax$
  The integrals below involve $tan ax$ ... View the lesson
36. Table of Integrals - Forms Involving $cot ax$
  The integrals below involve $cot ax$ .... View the lesson
37. Table of Integrals - Forms Involving $sec ax$
  The integrals below involve $sec ax$ .... View the lesson
38. Table of Integrals - Forms Involving $csc ax$
  The integrals below involve $csc ax$ .... View the lesson
39. Table of Integrals - Forms Involving Inverse Trigonometric Functions
  The integrals below involve inverse trigonometric functions.... View the lesson
40. Table of Integrals - Forms Involving $e^(ax)$
  The integrals below involve $e^(ax)$ ... View the lesson
41. Table of Integrals - Forms Involving $ln x$
  The integrals below involve $ln x$ ... View the lesson
42. Table of Integrals - Forms Involving $sinh ax$
  The integrals below involve $sinh ax$ .... View the lesson
43. Table of Integrals - Forms Involving $cosh ax$
  The integrals below involve $cosh ax$ .... View the lesson
44. Table of Integrals - Forms Involving $sinh ax$ and $cosh ax$
  The integrals below involve $sinh ax$ and $cosh ax$ .... View the lesson
45. Table of Integrals - Forms Involving $tanh ax$
  The integrals below involve $tanh ax$ .... View the lesson
46. Table of Integrals - Forms Involving $coth ax$
  The integrals below involve $coth ax$ .... View the lesson
47. Table of Integrals - Forms Involving $sech ax$
  The integrals below involve $sech ax$ .... View the lesson
48. Table of Integrals - Forms Involving $csch ax$
  The integrals below involve $csch ax$ .... View the lesson
49. Table of Integrals - Forms Involving Inverse Hyperbolic Functions
  The integrals below involve inverse hyperbolic functions.... View the lesson
Integral table
Handbook - Indefinite Integrals Table
Source
Integrator
Definite Integrals
Handbook - Definite Integrals Table

See Also

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Elementary Math - Higher Math
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Function - Formula - equation - graphics
Fractional Calculus - differential equation
Tests - Example :

$(d^0.5y)/dx^0.5 = sin(x-1)sin(y-1)$ == ? $(d^0.5y)/dx^0.5 -cosh(y)-sinh(y)=0$ == ? $(d^1.6y)/(dx^1.6)-int y(x) (dx)^(0.8)-y-exp(x)=0$ == ? $int y(x) (dx)^0.5 -y-exp(x)$ =0 == ? $(d^0.5y)/dx^0.5-exp(y)x=0$ == ? $(d^0.5y)/dx^0.5-exp(y)y=0$ == ? $(d^0.5y)/dx^0.5=cos(x)/xy$ == ? $y(dy^0.5)/dx^0.5-sqrt(x)-1=0$ == ? $(d^1.2y)/(dx^1.2)-2(d^0.6y)/dx^0.6+y-exp(x)=0$ == ? $(d^0.5y)/dx^0.5=cos(y)exp(x)x$ == ? $(d^1.6y)/(dx^1.6)-2(d^0.8y)/dx^0.8+y-exp(x)=0$ == ? $(d^0.5y)/dx^0.5-exp(y)sqrt(x)=0$ == ? $(d^1.6y)/(dx^1.6)-3 (d^0.8y)/dx^0.8+2y-exp(x)=0$ == ? $(d^0.5y)/dx^0.5$ +log(y-1)-exp(x)-x=0 == ? $(d^0.5y)/dx^0.5-exp(y)sin(x)=0$ == ? $(d^0.5y)/dx^0.5 = ysin(x)/x$ == ? $y^((0.5))(x) -4 exp(x)y-exp(x)=0$ == ? $(dy^0.5)/dx^0.5 = 1/(x-y)$ == ? $dy/dx-(d^0.5y)/dx^0.5$ - y - exp(x)=0 == ? $(dy)/dx -exp(y-1)-x-x^2=0$ == ? $(d^1.2y)/(dx^1.2)-3dy^0.6/dx^0.6+2y-exp(x)=0$ == ? $dy/dx-(d^0.5y)/dx^0.5-y-1$ =0 == ? $(d^0.5y)/dx^0.5-cos(y)sin(x)=0$ == ? $(d^1.6y)/(dx^1.6)-(d^0.8y)/dx^0.8-y-exp(4x)=0$ == ? $dy/dx-exp(y-1)-exp(x)=0$ == ? $(dy)/dx - 2(d^0.5y)/dx^0.5-y-exp(x)=0$ == ? $(d^1.6y)/(dx^1.6)-(d^0.8y)/dx^0.8-y-exp(x)=0$ == ? $(d^0.5y)/dx^0.5 -e^(4x)-y$ =0 == ? $y^((0.5))(x) - exp(x)y-exp(x)=0$ == ? $y^((0.5))(x) - exp(x)y-4exp(x)=0$ == ? $(dy)/dx -3(d^0.5y)/dx^0.5 +2y-exp(x)=0$ == ? $y(d^0.5y)/dx^0.5-sqrt(x)-1=0$ == ? $y^((1))(x)-exp(y-1)-x=0$ == ? $(d^1.6y)/(dx^1.6)-(d^0.8y)/dx^0.8-2y-exp(x)=0$ == ? $(d^1.6y)/(dx^1.6)-(d^0.8y)/dx^0.8-y-exp(4x)=0$ == ? $(d^0.5y)/dx^0.5 - log(y-1) - exp(x) + x=0$ == ? $(dy)/dx +asin(y-1) - cos(x)-x=0$ == ? $(d^1.6y)/(dx^1.6)-3(d^0.8y)/dx^0.8+2y-exp(x)=0$ == ? $(dy)/(dx) -sqrt(y-1)-x-1 =0$ == ? $(dy)/(dx) -exp(y-1)-exp(x) = 0$ == ? $(dy)/dx$ +asinh(y-1)-cosh(x)-x =0 == ? $((d^(1/2)y)/dx^(1/2))^2 -3y (dy^0.5)/dx^0.5 + 2y^2 = 0$ == ? $(dy^0.5)/dx^0.5 = cos(x)cos(y-1)$ == ? $(d^0.5y)/dx^0.5 +log(y-1)-exp(x)-x=0$ == ? $(dy^0.5)/dx^0.5 = sin(x-1)exp(y-1)$ == ? $y(d^2y)/dx^2-(dy/dx)^2+1=0$ == ? $y^((1))(x)-exp(y-1)-log(x)=0$ == ? $(d^2y)/dx^2 exp(x)- exp(y-1)=0$ == ? $(d^1.6y)/(dx^1.6)-2 (d^0.8y)/dx^0.8-y-exp(x)=0$ == ? $(d^1.6y)/(dx^1.6)-2 (d^0.8y)/dx^0.8+y-exp(x)=0$ == ? $(dy)/dx -3 (d^0.5y)/dx^0.5+2y-exp(x)=0$ == ? $y^((0.5))(x) - xy-x=0$ == ? $y(dy^3)/dx^3-x^3-3x^2-3x-1=0$ == ? $y^((1.8))(x)-2y^((0.9))(x) +y-1=0$ == ? $y^((0.5))(x)=1/(xy-1)$ == ? $y^((2))(x)y^2-x^2-2x-1=0$ == ? $((d^0.5y)/dx^0.5)^2 -5(d^0.5y)/dx^0.5 +6=0$ == ? $y^((0.5))(x) -2 exp(x)y-4exp(x)=0$ == ? $(d^1.6y)/(dx^1.6)-(d^0.8y)/dx^0.8-y-exp(x)=0$ == ? $y^(0.5)(x)=2yexp(x)$ == ? $y^((0.5))(x)-exp(x)y^2=0$ == ? $(d^1.6y)/(dx^1.6)-2(d^0.8y)/dx^0.8+y-exp(x)=0$ == ? $y^((1))(x)-y^2-xy=0$ == ? $y^((1))(x)-y^((0.5))(x) -y-1=0$ == ? $y^((2))(x) -y^2-x^2=0$ == ? $y^((2))(x) -y^2-x^2-2xy=0$ == ? $y^((0.5))(x) -int y(x) (dx)^0.5-y-exp(x)=0$ == ? $d^0.5/dx^0.5 y -2cos(y)exp(x)=0$ == ? $d^0.5/dx^0.5 y -4sin(y)exp(x)=0$ == ? $(d^0.5y)/dx^0.5=sin(x^2)y$ == ? $(d^0.5y)/dx^0.5-sin(x)sin(y)=0$ == ? $(d^0.5y)/dx^0.5-sinh(x)sinh(y)=0$ == ? $y^((1))(x)=exp(x-y)-x$ == ? $x(d^0.5y)/dx^0.5-y-2x=0$ == ? $(d^0.5y)/dx^0.5=sinh(x-1)sinh(y-1)$ == ? $y^((0.5))(x)-exp(-x)y^2=0$ == ? $(d^0.5y)/dx^0.5=y/xsin(x)$ == ? $(dy)/dx-sin(x-y)-1=0$ == ? $(d^2.5y)/dx^2.5=y(d^0.5y)/dx^0.5$ == ? $(d^0.5y)/dx^0.5=y(dy)/dx$ == ? $(d^(2-i)y)/dx^(2-i)- y+x=0$ == ? $(d^2y)/dx^2=y^3x^2$ == ? $y(d^2y)/dx^2-x^2-3x-1=0$ == ? $y(d^2y)/dx^2-2x^2-3x-1=0$ == ? $(y-x-1)(d^2y)/dx^2-3x-1=0$ == ? $y^2(d^2y)/dx^2-x^2-4x-4=0$ == ? $(y-x-1)(d^2y)/dx^2-x^2-4x-4=0$ == ? $y(d^2y)/dx^2-2x^2-2x-1=0$ == ? $y(d^3y)/dx^3-6x^3-3x^2-3x-1=0$ == ? $y^((0))(x)y^((1))(x)y^((2))(x)=x^2$ == ? $y^((3))(x)y^((2))(x)=y^((1/2))(x)$ == ? $y^((3))(x)=exp(x)y^((1))(x)y^((1/2))(x)$ == ? $y^((1/2))(x)y^((3))(x)=exp(x)$ == ? $y^((1/2))(x)y^((2))(x)=exp(x)$ == ? $(d^0.5y)/dx^0.5-2xy-1=0$ == ? $y^2(d^0.5y)/dx^0.5-x^2-4x-4=0$ == ? $exp(y-1)(d^0.5y)/dx^0.5-x=0$ == ? $y(d^2y)/dx^2-(x-2)(2x-4)=0$ == ? $y(d^3y)/dx^3-6x^3-4x^2-4x-1=0$ == ? $exp(y-1)(d^2y)/dx^2-exp(x)=0$ == ? $y^2(d^2y)/dx^2-x^2-1=0$ == ? $1/y^2(d^2y)/dx^2-x^2-1=0$ == ? $(y-x-1)(d^3y)/dx^3-(x-2)(2x-4)(3x-1)=0$ == ? $(d^0.5y)/dx^0.5-2x^2y^2-8x^2=0$ == ? $(d^0.5y)/dx^0.5-2xy^2-8x=0$ == ? $(d^0.5y)/dx^0.5-y^2-2y-2=0$ == ? $(d^0.5y)/dx^0.5-log(y-1)exp(x)=0$ == ? $y(d^2y)/dx^2-(dy/dx)^2-1=0$ == ? $(d^2y)/dx^2-asin(y-1)-sin(x)-x=0$ == ? $dy/dx(x--y)-x--y-1 = 0$ == ?