Mathematics

# Evaluate :$\int \dfrac{(1+\log x)^2}{x} \ dx$

##### SOLUTION
Let $I=\int \dfrac{(1+\log x)^2}{x} \ dx$

Let $1+\log x=t$
$\dfrac{1}{x} \ dx=dt$

Putting $1+\log x =t$ and $dx = x \ dt$, we get,
Therefore,
$I=\int \dfrac{t^2}{x} \times x \ dt$

$I=\dfrac{t^3}{3}+C$

$I=\dfrac{(1+\log x)^3}{3}+C$

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Subjective Medium Published on 17th 09, 2020
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 84

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