Mathematics

# Evaluate the following integral$\int { \cfrac { { e }^{ x }+1 }{ { e }^{ x }+x } } dx$

##### SOLUTION
Let
$t={e}^{x}+x\Rightarrow\,dt=\left({e}^{x}+1\right)dx$

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

$=\displaystyle\int{\dfrac{dt}{t}}$

$=\log{\left|t\right|}+c$

$=\log{\left|{e}^{x}+x\right|}+c$ where $t={e}^{x}+x$

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

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