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[*38.log(log i)=],[[" 1) "log(pi)/(2)," ...

[*38.log(log i)=],[[" 1) "log(pi)/(2)," 2) "(pi)/(2)log i],[" ,"x," 3) "log(pi)/(2)+(i pi)/(2)," 4) "log(pi)/(2)-1(pi)/(2)]]

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[int_(0)^(0)cot^(-1)(1-x+x^(2))dx=],[[" (A) "(pi)/(2)-ln2," (B) "(pi)/(2)+ln2],[" (C) "(pi)/(2)-ln sqrt(2)," (D) "(pi)/(2)+ln sqrt(2)]]

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int_(0)^((pi)/(2))log sin xdx=int_(0)^((pi)/(2))log cos xdx=(1)/(2)(pi)log((1)/(2))

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Show that int_(0)^((pi)/(2))log(sin2x)dx=-(pi)/(2)(log2)

Show that int_(0)^((pi)/(2))logsinxdx=(pi)/(2)log((1)/(2))=(-pi)/(2)log2