Question

Solve :- $\int ({\sin }^{-1}x+{\cos }^{-1}x)dx$= ?

Answer 1

Indentity: ${\sin }^{-1}x+{\cos }^{-1}x=\frac{\pi }{2}$ $(|x|\le 1)$
$\int ({\sin }^{-1}x+{\cos }^{-1}x)dx=\int \frac{\pi }{2}dx$
$=\frac{\pi }{2}x+C$