Evaluate the following integral: `int_1^2 1/(x(1+logx)^2)dx`

Explanation

Given,`int_1^2 1/(x(1+logx)^2)dx...(1)`

Let`(1+logx)=y`

`dy=dx/x...(2)`

Lower limit for Definite Integral:
⇒ x = 1 ⇒ y = 1 + log 1 ⇒ y = 1 ……(3)

Upper limit for Definite Integral
: ⇒ x = 2 ⇒ y = 1 + log2 ⇒ y = 1 + log2 ……(4)

Substituting (2),(3),(4) in the eq(1) we get,

`int_1^(1+log2) 1/(y^2)dy...(1)`

=`(-1/y)_1 ^(1+log2)`

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