Question

Evaluate: $\int {\sin }^{3}xdx$

Answer 1

$\int {\sin }^{3}xdx$

$\int {\sin }^{2}x\sin xdx$

$\int (1-{\cos }^{2}x)\sin xdx$

substitute $u=\cos x\to du=-\sin xdx$

$\int (-1+u^2)du$

$=-u+\frac{u^3}{3}$

$=-\cos x+\frac{{\cos }^{3}x}{3}+c$