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Question

Solve: logx(1+logx)2dx

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Solution

logx(1+logx)2dxLet,logx=tx=etdx=xdtI=t(1+t)2xdt=et.t(1+t)2dt=et.(t+11)(1+t)2dt=et.(t+1)(1+t)2dtet(1+t2)dt=et[11+t11+t2]dx=et[f(x)+f(x)]x=etf(x)+C=et11+t+C=x1+logx+C

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