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Question

0π/2sin x cos xcos2 x+3 cos x+2 dx

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Solution

Let I=0π2sin x cos xcos2 x+3 cos x+2 dx. Then,Let cos x =t. Then, - sin x dx= dtWhen x=0, t=1 and x =π2, t=0 I=-10t dtt2+3t+2I=10-t dtt+2t+1I=101t+1-2t+2 dtI=log t+1-2 log t+210I=log t+1t+2201I=log 14-log 2901I=log 98

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