Derivatives and Integrals for Trig Functions

d/dx [arcsin u]

\frac{u^{\prime}}{\sqrt{1-u^2}}

d/dx [arctan u]

\frac{u^{\prime}}{1+u^2}

d/dx [arcsec u]

\frac{u^{\prime}}{\left|u\right|\sqrt{u^2-1}}

d/dx [arccos u]

\frac{-u^{\prime}}{\sqrt{1-u^2}}

d/dx [arccot u]

\frac{-u^{\prime}}{1+u^2}

d/dx [arccsc u]

\frac{-u^{\prime}}{\left|u\right|\sqrt{u^2-1}}

\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}{\left|u\right|\sqrt{u^2-a^2}}

\frac{1}{a}\operatorname{arcsec}\frac{\left|u\right|}{a}+C