Question

integrate the following with respect to $x$
$\left(i\right)$ $x\sin x^2$

Answer 1

$I=\int x\sin x^{2}dx$

Let $x^2=t$, then, $2xdx=dt$

$I=\frac{1}{2}\int \sin tdt$

$=-\frac{1}{2}\cos t+C$

$=-\frac{1}{2}\cos \left(x^2\right)+C$