Question

Integrate with respect to $x$:
$x\sin x^2$

Answer 1

$I=\int xsin\left(x^2\right)dx$

put $x^2=t$

2x. dx = dt

$=\int \frac{sin\left(t\right)}{2}dt$

$=-\frac{cos\left(t\right)}{2}+c$

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