Integration — Formula Sheet

\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

The indefinite integral ∫f(x)dx represents a family of functions differing by a constant.

If F'(x) = f(x), then ∫f(x)dx = F(x) + C.

∫x^n dx = x^(n+1)/(n+1) + C, n ≠ -1

∫1/x dx = log|x| + C

∫sin x dx = -cos x + C

∫[f(x) ± g(x)]dx = ∫f(x)dx ± ∫g(x)dx

∫k f(x)dx = k∫f(x)dx, where k is a constant