Question

Evaluate: $\int {\cos }^{3}x{e}^{\log \left(\sin x\right)}dx$

Answer 1

$\int {\cos }^{3}x{e}^{\log \left(\sin x\right)}dx$

$=\int {\cos }^{3}x\sin xdx$

Let $t=\cos x\Rightarrow dt=-\sin xdx$

$=-\int t^{3}dt$

$=-\frac{t^4}{4}+c$

$=-\frac{{\cos }^{4}x}{4}+c$ where $t=\cos x$