Question

sin^{-1}cosx.dx
Integrate the function

Answer 1

HELLO DEAR,


GIVEN FUNCTION IS:- $\bold{sin^{-1}cosx}$

now, the first solution is in attachment and next
step is there

$\sf{\int{sin^{-1}cosx}\,dx = \frac{-[\frac{\pi}{2} - x]^2}{2} + c}$

$\sf{-\frac{1}{2}(\frac{\pi^2}{4} + x^2 - \pi x)}$

$\sf{-\frac{1}{8}\pi^2 - \frac{x^2}{2} + \frac{\pi x}{2} + c}$

$\sf{\frac{\pi x}{2} - \frac{x^2}{2} + (c - \frac{\pi}{8})}$

$\sf{\frac{\pi x}{2} - \frac{x^2}{2} + C_1}$


I HOPE ITS HELP YOU DEAR,
THANKS