How to integrate sin^2(x)cos^2(x)

 

\begin{array}{l} \smallint si{n^2}xco{s^2}x{\rm{d}}x\\\\ \smallint \left( {\frac{{{\bf{1}} - {\bf{cos2}}x}}{{\bf{2}}}} \right)\left( {\frac{{{\bf{1}} + {\bf{cos2}}x}}{{\bf{2}}}} \right){\rm{d}}x\\ \;\;\smallint \frac{{1 - {{\cos }^2}2x}}{4}{\rm{d}}x\;\;\\ \;\;\smallint \frac{{1 - \left( {\frac{{1 + \cos 4x}}{2}} \right)}}{4}{\rm{d}}x\\ \;\;\smallint \frac{1}{8}\; - \;\;\frac{{\cos 4x}}{8}{\rm{d}}x\\ \Rightarrow \frac{x}{8} - \frac{{\sin 4x}}{{4 * \left( 8 \right)}}\; + \;C \end{array}