| Table for direct integrals |
| $$$\displaystyle \int k x^n \ dx =k \frac{x^n+1}{n+1} +C$$$ $$$\displaystyle \int k \frac{1}{x} \ dx = k \int x^{-1} \ dx = k\ln |x|+C$$$ $$$\displaystyle \int \frac{1}{x \ln a} \ dx =\log_{a}|x|+C$$$ $$$\displaystyle \int e^x \ dx= e^x+C$$$ $$$\displaystyle \int a^x \ dx = \frac{a^x}{\ln a}+C$$$ $$$\displaystyle \int \sin x \ dx = -\cos x + C$$$ $$$\displaystyle \int \cos x \ dx= \sin x +C$$$ $$$\displaystyle \int \frac{1}{\cos^2 x} \ dx = \tan x +C$$$ $$$\displaystyle \int \frac{1}{\sqrt{1-x^2}} \ dx= \arcsin x+C$$$ $$$\displaystyle \int \frac{-1}{\sqrt{1-x^2}} \ dx= \arccos x +C$$$ $$$\displaystyle \int \frac{1}{a+x^2} \ dx = \arctan x +C$$$ |
