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Question

π20(2logsinxlogsin2x)dx

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Solution

I=π20(2logsinxlogsin2x)dx

we have f(x)=2logsinxlogsin2x

f(x)=logsin2xsin2x

=logtanxlog2

I1=π20logtanx dx

Let y=π2x,dy=dx,tanx=coty

I1=π20logcoty dy=π20logtanx dx=I

2I1=0

I1=0

Now I=π20logtanxdxπ20log2 dx

I=π2log2

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