Question

Write a value of $\int {\sin }^{3}x\cos xdx$.

Answer 1

Let I=$\int$ sin³ x . cos x dx
Let sin x = t
⇒​ cos x dx = dt
$\therefore I=$​ $\int$ t³ . dt
$$\begin{gathered} =\frac{t^4}{4}+C \\ =\frac{{\sin }^{4}x}{4}+C\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\left(\mathit{\because }t=\sin x\right) \end{gathered}$$