\[ \int dx=x+C \] \[ \int x^{b}dx=\frac{x^{b+1}}{b+1}+C\;,\; b\neq-1 \] \[ \int\frac{1}{x}dx=\ln\left|x\right|+C \] \[ \int\sin xdx=-\cos x+C \] \[ \int\cos xdx=\sin x+C \] \[ \int\tan xdx=-\ln\left|\cos x\right|+C \] \[ \int\frac{1}{\cos^{2}x}dx=\tan x+C \] \[ \int\frac{1}{\sqrt{1-x^{2}}}dx=\arcsin x+C \] \[ \int\frac{1}{1+x^{2}}dx=\arctan x+C \] \[ \int e^{x}dx=e^{x}+C \] \[ \int a^{x}dx=\frac{a^{x}}{\ln a}+C \]