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-int_(0)^( pi)log(1+cos x)dx

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Find I=int_(0)^( pi)ln(1+cos x)dx

int_(0)^(pi)log(1+cosx)dx=-pi(log2)

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Prove that int_(0)^(pi//2)log (sinx)dx=int_(0)^(pi//2) log (cosx)dx=-(pi)/(2) log 2 .

Prove that int_(0)^(pi//2)log (sinx)dx=int_(0)^(pi//2) log (cosx)dx=-(pi)/(2) log 2 .

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If int_(0)^(pi//2) log cos x dx =(pi)/(2)log ((1)/(2)), then int_(0)^(pi//2) log sec x dx =