$\int{kf(u)\,du}=k\int{f(u)\,du}$

$\int{[f(u)\pm g(u)]\,du}=\int{f(u)\,du}\pm\int{g(u)\, du}$

$\int{du}=u+C$

$\int{u^n\,du}=\frac{u^{n+1}}{n+1}+C, n\neq -1$

$\int{\frac{du}{u}}=\ln{|u|}+C$

$\int{e^u\,du}=e^u+C$

$\int{a^u\,du}=(\frac{1}{\ln a})a^u+C$

$\int{\sin u\,du}=-\cos u+C$

$\int{\cos{u}\,du}=\sin{u}+C$

$\int{\tan{u}\,du}=-\ln|\cos{u}|+C$

$\int{\cot{u}\,du}=\ln|\sin{u}|+C$

$\int{\sec{u}\,du}=\ln|\sec{u}+\tan u|+C$

$\int{\csc{u}\,du}=-\ln|\csc{u}+\cot{u}|+C$

$\int{\sec^2{u}\,du}=\tan{u}+C$

$\int{\csc^2{u}\,du}=-\cot{u}+C$

$\int{\sec{u}\tan{u}\,du}=\sec{u}+C$

$\int{\csc{u}\cot{u}\,du}=-\csc{u}+C$

$\int{\frac{du}{\sqrt{a^2-u^2}}}=\arcsin{\frac{u}{a}}+C$

$\int{\frac{du}{a^2+u^2}}=\frac{1}{a}\arctan{\frac{u}{a}}+C$

$\int{\frac{du}{u\sqrt{u^2-a^2}}}=\frac{1}{a}\operatorname{arcsec}{\frac{|u|}{a}}+C$