Integration

\int f'(x) \, dx = f(x) + C

\int x^n \, dx = \frac{x^{n+1}}{n+1} + C, \quad n \neq -1

\int \frac{1}{x} \, dx = \log|x| + C

\int \sin x \, dx = -\cos x + C

\int \cos x \, dx = \sin x + C

\int \sec^2 x \, dx = \tan x + C

\int \csc^2 x \, dx = -\cot x + C

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

\int [f(x) \pm g(x)] \, dx = \int f(x) \, dx \pm \int g(x) \, dx

\int k f(x) \, dx = k \int f(x) \, dx

\int f(ax+b) \, dx = \frac{1}{a} \int f(u) \, du, \quad u = ax+b

\int \frac{f'(x)}{f(x)} \, dx = \log|f(x)| + C