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What is the integration of: logx/((1+logx)^2 ) ? (Type: Class 12th, Indefinite Integrals)

What is the integration of: logx/((1+logx)^2 ) ? (Type: Class 12th, Indefinite Integrals)

Grade:12

2 Answers

Sourabh Singh IIT Patna
askIITians Faculty 2104 Points
6 years ago
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mycroft holmes
272 Points
6 years ago
Setting log x = t, we can rewrite the integral as \int \frac{e^tt}{(1+t)^2} \ dt = \int e^t \left(\frac{1}{1+t} - \frac{1}{(1+t)^2)} \right ) \ dt
 
which by the formula for integration of ex [f(x)+f’(x)] is simply ex f(x)
 
and hence is et/ 1+t i.e. x/(1+log x)

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