Mathematics

# $\displaystyle \int { \cfrac { dx }{ \sqrt { { e }^{ 2x } } -1 } }$ equals to

$\ln \left|e^x-1\right|-x+C$

##### SOLUTION
Given,

$\displaystyle \int \dfrac{1}{\sqrt{e^{2x}}-1}dx$

$\displaystyle=\int \dfrac{1}{e^x-1}dx$

$\displaystyle=\int \dfrac{e^x}{e^x-1}-1dx$

as $\displaystyle\dfrac{1}{e^x-1}=\dfrac{e^x}{e^x-1}-1$

$\displaystyle=\int \dfrac{e^x}{e^x-1}dx-\int \:1dx$

$=\ln \left|e^x-1\right|-x+C$

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

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