5.11 Standard indefinite integrals.

The following are worth remembering:

$$\int x^{n}\,dx={{x^{n+1}}\over{n+1}}+C\qquad(n\neq-1);$$

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

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

$$\int{{1}\over{x}}dx=\log|x|+C;$$

$$\int e^{x}dx=e^{x}+C;$$

$$\int{{dx}\over{1+x^{2}}}=\tan^{-1}x+C.$$

An indefinite integral can always be checked by differentiating.