# Math Help - Integral xsin^2(x)cos(x)ds

1. ## Integral xsin^2(x)cos(x)ds

I tried u=sin(x)
du=cos(x)dx
but that doesn't work

2. Originally Posted by khuezy
I tried u=sin(x)
du=cos(x)dx
but that doesn't work
This isnt fun

Seeing that $\sin^2(x)=1-\cos^2(x)$

we have $\int{x\cos(x)-x\cos^3(x)}dx$

Use parts

and on the second one see that $\cos^3(x)=\cos(x)(1-\sin^2(x))$

3. Let: $\int_0^x\sin^2(t)\cos(t)dt=\int_0^{\sin(x)}u^2du=\ frac{\sin^3(x)}{3}=P(x)$

$\int{x\sin^2(x)\cos(x)dx}=\int{x\cdot{P'(x)}dx}$ now apply parts

$\int{x\cdot{P'(x)}dx}=x\cdot{P(x)}-\int{P(x)dx}$

And remember that: $\sin(3x)=-4\sin^3(x)+3\sin(x)$ for your last integral