Inverse Regular & Hyperbolic Trig Integrals

$\int \frac{1}{\sqrt{1-x^{2}}}\:dx$

$\sin^{-1}(x) + C$

$\int\frac{1}{\sqrt{1+x^{2}}}\:dx$

$\sinh^{-1}(x) + C$

$\int \frac{1}{\sqrt{1-x^{2}}}\:dx$

$\sin^{-1}(x) + C$

$\int\frac{1}{\sqrt{1+x^{2}}}\:dx$

$\sinh^{-1}(x) + C$

$\int -\frac{1}{\sqrt{1-x^{2}}}\:dx$

$\cos^{-1}(x) + C$

$\int\frac{1}{\sqrt{x^{2}-1}}\:dx$

$\cosh^{-1}(x) + C$

$\int \frac{1}{1+x^{2}}\:dx$

$\tan^{-1}(x) + C$

$\int \frac{1}{1-x^{2}}\:dx$

$\tanh^{-1}(x) + C$