How To Integrate sin^4(x)
Published On :2020-12-06 20:42:00
[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 - 2cos 2x + cos 2x}}{4}{rm{d}}x\ frac{1}{4}smallint 1 - 2cos 2x + frac{1}{2} + frac{{cos 4x}}{2}{rm{d}}x;\ Rightarrow frac{1}{4}left( {x - frac{{2sin 2x}}{2} + frac{x}{2} + frac{{sin 4x}}{{4left( 2 right)}}} right) end{array}]