Question

Write a value of $\int x^2\sin x^{3}dx$.

Answer 1

Let I=$\int$x².sin x³ dx
Let x³ = t
⇒ ​3x²dx = dt
$$\begin{gathered} \Rightarrow x^{2}dx=\frac{dt}{3} \\ \therefore I=\frac{1}{3}\int \sin tdt \\ =\frac{1}{3}\left[-\cos t\right]+C \\ =-\frac{1}{3}\cos x^3+C\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\left(\because t=x^{\mathit{3}}\right) \end{gathered}$$