Inverse Regular & Hyperbolic Trig Integrals

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

\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