Integrate: (sin x -cos x) / 1+sin 2x

Answers (1)

Solution: 

          I=int frac(sin x -cos x)1+sin 2xdx \ \ Rightarrow hspace1cm I=int frac(sin x -cos x)sin^2x+cos^2x+2sin x cdot cos xdx \ \ Rightarrow hspace1cmI=int frac(sin x-cos x)(sin x-cos x)^2dx hspace0.5cmLet hspace0.5cmsin x+cos x=t \ \ Rightarrow hspace1cm(cos x-sin x)dx=dt \ \ Rightarrow hspace1cmI=-int frac1t^2dt=frac1t+c=frac1sin x+cos x+c

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