u = 2x \\

du = 2dx \\

\end{array} \right\} \Rightarrow \frac{\pi }{8}\int {u^3 \sin u\,du} = \frac{\pi }{8}\left( { - u^3 \cos u + \int {u^2 \cos u\,du} } \right) = \frac{\pi }{8}\left( { - u^3 \cos u + u^2 \sin u - \int {u\sin u\,du} } \right) = \frac{\pi }{8}\left( { - u^3 \cos u + u^2 \sin u + u\cos u - \sin u} \right) = \frac{{\pi \left[ { - 8x^3 \cos \left( {2x} \right) + 4x^2 \sin \left( {2x} \right) + 2x\cos x - \sin x} \right]}}{8} [\tex]

How can I do this faster? Are there things I can skip or connect--etc--?