Mathematics

# Integrate $\dfrac{dx}{[1-e^{2x}]^(1/2)}$

##### SOLUTION
Let $e^{2x}=t$
$2e^{2x}dx=dt$
$\displaystyle dx=\frac{dt}{2e^{2x}}$
Now putting the value of $dx$ in gven question we get
$\displaystyle \int\frac{dt}{(1-t)t}=\int\frac{dt}{t}+\int\frac{dt}{1-t}$
$\displaystyle \int\frac{dt}{(1-t)t}=$ $\displaystyle \ln{t+ln{(1-t)}}$
Now putting the value of t we get
$\displaystyle \int\frac{2dx}{(1-e^{2x})}=$ $\displaystyle 2x+ln{(1-e^{2x})}$

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

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