ContributeAsk a Question
  1. Home
  2. Math Notes
  3. Calculus II
  4. Antiderivative and Indefinite Integral

Table of Antiderivatives

Related Calculator: Integral (Antiderivative) Calculator with Steps

Below is a short list of functions and their general antiderivatives (we will give more complete table later).

Note that `int f(x)dx=F(x)+A` and `int g(x)dx=G(x)+B` where `A` and `B` are arbitrary constant.

Attention! When we integrate two functions we actually obtain 2 constants:

`int (f(x)+-g(x))dx=int f(x)dx+-int g(x)dx=F(x)+A+-(G(x)+B)`.

If we denote `C=A+-B` then `C` will be new arbitrary constant and `int (f(x)+-g(x))dx=F(x)+-G(x)+C`.

Function General Antiderivative
`int af(x)dx` `aF(x)+C`
`int (f(x)+-g(x))dx` `F(x)+-G(x)+C`
`int 0*dx` `C`
`int 1*dx` `x+C`
`int x^ndx` `{((x^(n+1))/(n+1)+C if n!=-1),(ln|x|+C if n=-1):}`
`int a^xdx` `(a^x)/(ln(a))+C`
`int e^xdx` `e^x+C`
`int cos(x)dx` `sin(x)+C`
`int sin(x)dx` `-cos(x)+C`
`int sec^2(x)dx` `tan(x)+C`
` int csc^2(x)dx` `-cot(x)+C`
`int sec(x)tan(x)dx` `sec(x)+C`
`int 1/sqrt(1-x^2)dx` `arcsin(x)+C`
`int 1/(1+x^2)dx` `arctan(x)+C`