\[\begin{array}{l} \smallint {\sin ^4}x{\rm{d}}x\\\\ \smallint {\left( {{{\sin }^2}{\rm{x}}} \right)^2}{\rm{dx}}\\ \smallint {\left( {\frac{{1 - \cos 2x}}{2}} \right)^2}{\rm{d}}x\\ \smallint \frac{{1 - 2\cos 2x + \cos 2x}}{4}{\rm{d}}x\\ \frac{1}{4}\smallint 1 - 2\cos 2x + \frac{1}{2} + \frac{{\cos 4x}}{2}{\rm{d}}x\;\\ \Rightarrow \frac{1}{4}\left( {x - \frac{{2\sin 2x}}{2} + \frac{x}{2} + \frac{{\sin 4x}}{{4\left( 2 \right)}}} \right) \end{array}\]
Tags:
integration