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` |