Set up an integral that is obtained by rotating the given curve about the $x$ axis and find the surface area.
$$ \begin{aligned} x &= t\sin(t) & y &= t\cos(t) & 0 &\leq t \leq \frac{\pi}{2} \end{aligned} \\ \int_{0}^{\pi/2} 2 \pi t\cos\left(t\right) \sqrt{\left(\sin\left(t\right)+t\cos\left(t\right)\right)^2+\left(\cos(t)-t\sin\left(t\right)\right)^2}\;dt $$
Is my integral set up correctly and from what I see it looks like integration by parts inside of integration by parts with u- substitution, and there is no way, unless I use some identities or tricks. How do I simplify this?