Mathematics

# Solve:-$\int {\dfrac{{{e^x}}}{x}} \left( {1 + x.\ln x} \right)dx$

##### SOLUTION
$\displaystyle\int \dfrac{e^{x}}{x}(1+x\ln x)\ dx$

$=\displaystyle\int e^{x}\left(\dfrac{1}{x}+\ln x\right)\ dx$

We know that $\displaystyle\int e^{x}(f(x)+f(x))\ dx=e^{x}f(x)+c$

$=\dfrac{e^{x}}{x}+c$  because   $\dfrac{d(\ln x)}{dx}=\dfrac{1}{x}$

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

#### Realted Questions

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1 Verified Answer | Published on 17th 09, 2020

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1 Verified Answer | Published on 17th 09, 2020

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