Exercise
$\int_0^{\pi}\left(\sin^5\left(\frac{1}{2}x\right)\cos^7\left(\frac{1}{2}x\right)\right)dx$
Step-by-step Solution
Final answer to the exercise
$2\cdot \left(\frac{- \sin\left(\pi \left(\frac{1}{2}\right)\right)^{4}\cdot \cos\left(\pi \left(\frac{1}{2}\right)\right)^{8}}{12}+\frac{- \sin\left(\pi \left(\frac{1}{2}\right)\right)^{2}\cdot \cos\left(\pi \left(\frac{1}{2}\right)\right)^{8}}{30}+\frac{- \cos\left(\pi \left(\frac{1}{2}\right)\right)^{8}}{120}- \left(\frac{- \sin\left(0\left(\frac{1}{2}\right)\right)^{4}\cdot \cos\left(0\left(\frac{1}{2}\right)\right)^{8}}{12}+\frac{- \sin\left(0\left(\frac{1}{2}\right)\right)^{2}\cdot \cos\left(0\left(\frac{1}{2}\right)\right)^{8}}{30}+\frac{- \cos\left(0\left(\frac{1}{2}\right)\right)^{8}}{120}\right)\right)$