Question

Solve :
$\int {\cos }^{3}x{e}^{\log \sin x}dx$

Answer 1

$\int {\cos }^{3}x{e}^{\log \sin x}dx$

$Usinglogproperties{a}^{logb}=b^{loga}$

$e^{\log \sin x}=sin{x}^{loge}=sinx$

$Sointegralchangesto$

$\int {\cos }^{3}x.\sin x.dx$

$Letcosx=t⟹-sinxdx=dt$

$=-\int t^3.dt=\frac{-t^4}{4}+c$
$=\frac{-{\cos }^{4}x}{4}+c$