Table for direct integrals

Table for direct integrals

\int k x^{n} d x = k \frac{x^{n} + 1}{n + 1} + C

\int k \frac{1}{x} d x = k \int x^{- 1} d x = k \ln | x | + C

\int \frac{1}{x \ln a} d x = \log_{a} | x | + C

\int e^{x} d x = e^{x} + C

\int a^{x} d x = \frac{a^{x}}{\ln a} + C

\int \sin x d x = - \cos x + C

\int \cos x d x = \sin x + C

\int \frac{1}{\cos^{2} x} d x = \tan x + C

\int \frac{1}{\sqrt{1 - x^{2}}} d x = \arcsin x + C

\int \frac{- 1}{\sqrt{1 - x^{2}}} d x = \arccos x + C

\int \frac{1}{a + x^{2}} d x = \arctan x + C