Table of Integrals

The format is \int f(x) dx = F(x) + c and occasionally I’ve seen F(x) called the antiderivative.

\int x^b dx = \dfrac {1}{b+1} x^{b+1} + C (n \neq -1

\int sin(x) dx = - cos(x) + C

\int cos(x) dx = sin(x) + C

\int e^x dx = e^x + C

\int \dfrac {1} {x} dx = ln |x| + C

Below is the idea that if a function includes a constant, that constant can be taken out of the function and then you integrate the function and the answer is the constant multiplied by the result that you calculated.

\int a f(x) dx = a \int f(x) dx