How to integrate 1/( sin x + cos x)^2
Published On :2021-01-27 17:30:00
begin{array}{l} smallint frac{{bf{1}}}{{{{left( {sinx + cosx} right)}^{bf{2}}}}}{rm{d}}x\\ smallint frac{1}{{{{sin }^2}x + 2sin xcos x + {{cos }^2}x}}{rm{d}}x\\ smallint frac{1}{{1 + sin 2x}}{rm{d}}x\\ smallint frac{1}{{1 + sin 2x}} cdot frac{{1 - sin 2x}}{{1 - sin 2x}}{rm{d}}x\\ smallint frac{{1 - sin 2x}}{{1 - {{sin }^2}2x}}{rm{d}}x\\ smallint frac{1}{{{{cos }^2}2x}} - frac{{sin 2x}}{{{{cos }^2}2x}}{rm{d}}x\\ smallint {sec ^2}2x; - tan 2xsec 2x{rm{d}}x\\ frac{{tan 2x}}{2} - frac{{sec 2x}}{2} + c\ end{array}