$\int k d x=k x+c$ $\int x^{n} d x=\frac{1}{n+1} x^{n+1}+c, n \neq-1$ $\int x^{-1} d x=\int \frac{1}{x} d x=\ln |x|+c$ $\int \frac{1}{a x+b} d x=\frac{1}{a} \ln |a x+b|+c$ $\int \ln u d u=u \ln (u)-u+c$ $\int \mathbf{e}^{u} d u=\mathbf{e}^{u}+c$ $\int \cos u d u=\sin u+c$ $\int \sin u d u=-\cos u+c$ $\int \sec ^{2} u d u=\tan u+c$ $\int \sec u \tan u d u=\sec u+c$ $\int \csc u \cot u d u=-\csc u+c$ $\int \csc ^{2} u d u=-\cot u+c$ $\int \tan u d u=\ln |\sec u|+c$ $\int \sec u d u=\ln |\sec u+\tan u|+c$ $\int \frac{1}{a^{2}+u^{2}} d u=\frac{1}{a} \tan ^{-1}\left(\frac{u}{a}\right)+c$ $\int \frac{1}{\sqrt{a^{2}-u^{2}}} d u=\sin ^{-1}\left(\frac{u}{a}\right)+c$