Question

Exl. Evaluate dx or sin xdx 1+ cotx sin x + COS X

SSC CGL

Maths

Solution

113

4.0 (1 ratings)

( begin{aligned} I &=int frac{sin x d x}{sin x+cos x}=frac{1}{2} int frac{2 sin x d x}{sin x+cos x} &=frac{1}{2} intleft(frac{(sin x+cos x)-(cos x-sin x)) d x}{sin x+cos x}right. &=frac{1}{2} intleft(1-frac{cos x-sin x}{sin x+cos x}right) d x &=frac{x}{2}-frac{1}{2} int frac{cos x-sin x}{sin x+cos x} d x Rightarrow & Rightarrow frac{x}{2} sin x+cos x=t &=frac{x}{2}-frac{1}{2} log _{e}(t mid+c &=frac{x}{2}-frac{1}{2} log _{e}|sin x+cos x|+c end{aligned} )