Question

Integrate with respect to x:

$x\sin x^2$

Answer 1

$\int x\sin x^{2}dx=\frac{1}{2}\int \sin x^2\left(2xdx\right)$

$=\frac{1}{2}\int \sin x^{2}d\left(x^2\right)$

$=\frac{-\cos x^2}{2}+C$

$\therefore \int x\sin x^{2}dx=\frac{-\cos x^2}{2}+C$