How to integrate sin^2(x)cos^2(x)
Published On :2020-12-06 20:35:00
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}