Question

integration x ×sinxsqure

Answer 1

Answer:

−12cosx2+C

Explanation:

Let t=x2, then
dt=2xdx,xdx=dt2
∫xsinx2dx=∫sintdt2=12∫sintdt=
=−12cost+C=−12cosx2+C

Answer 2

$= \int \: (x \sin{x}^{2} )dx \\ \\ = \int \: xdx \: \: \:. \: \: \int \sin {x}^{2} dx \\ \\ = \frac{ {x}^{2} }{2} . \frac{( - {x}^{3} \cos {x}^{2})}{3}$