Mathematics

# Evaluate the following integral$\displaystyle\int{\dfrac{{e}^{3x}}{{e}^{3x}+1}dx}$

##### SOLUTION
$\displaystyle\int{\dfrac{{e}^{3x}}{{e}^{3x}+1}dx}$

$t={e}^{3x}+1\Rightarrow\,dt=3{e}^{3x}\,dx$

$\Rightarrow\,{e}^{3x}\,dx=\dfrac{dt}{3}$

$=\dfrac{1}{3}\displaystyle\int{\dfrac{dt}{t}}$

$=\dfrac{1}{3}\log{\left|{e}^{3x}+1\right|}+c$

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

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