List of integrals of inverse trigonometric functions

It has been suggested that this article or section be merged into List of integrals of arc functions. (Discuss)

Substitution or other forms of algebraic manipulation are used to arrive at integrals listed in the table.

$\int \arcsin x \,dx = x\arcsin x+ \sqrt{1-x^2}$

$\int \arccos x \,dx = x\arccos x- \sqrt{1-x^2}$

$\int \arctan x \,dx = x\arctan x- \frac{1}{2}\ln|1+x^2|$

$\int \arccsc x \,dx = x\arccsc x+ \ln\left| x+x\sqrt{{x^2-1}\over x^2}\right|$

$\int \arcsec x \,dx = x\arcsec x- \ln\left| x+x\sqrt{{x^2-1}\over x^2}\right|$

$\int \arccot x \,dx = x\arccot x+ \frac{1}{2} \ln|1+x^2|$