Mathematics

# Integrate $\int x\log 2x \, dx$

##### SOLUTION
$I=\displaystyle\int{x\log{2x}dx}$
Let $u=\log{2x}\Rightarrow\,du=\dfrac{1}{2x}\times 2\,dx=\dfrac{dx}{x}$
$dv=x\,dx\Rightarrow\,v=\dfrac{{x}^{2}}{2}$
$I=\dfrac{{x}^{2}}{2}\log{2x}-\displaystyle\int{\dfrac{{x}^{2}}{2}\dfrac{dx}{x}}$
$=\dfrac{{x}^{2}}{2}\log{2x}-\dfrac{1}{2}\displaystyle\int{x\,dx}$
$=\dfrac{{x}^{2}}{2}\log{2x}-\dfrac{{x}^{2}}{4}+c$

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Subjective Medium Published on 17th 09, 2020
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 86

#### Realted Questions

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Q2 Subjective Medium
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