Question

Integrate the function: ${\cos }^{3}x{e}^{\log \sin x}$

Answer 1

${\cos }^{3}x{e}^{\log \sin x}={\cos }^{3}x\times \sin x$
Let $\cos x=t\Rightarrow -\sin xdx=dt$
$\Rightarrow \int {\cos }^{3}x{e}^{\log \sin x}dx=\int {\cos }^{3}x\sin xdx$
$=-\int t^3\cdot dt=-\frac{t^4}{4}+C=-\frac{{\cos }^{4}x}{4}+C$