Mathematics

# Integrate with respect to x:$\dfrac{e^{2x}}{e^{2x}-2}$.

$\dfrac{ln(e^{2x}-2)}{2}+C$

##### SOLUTION

Consider the given integral.

$I=\int{\dfrac{{{e}^{2X}}}{{{e}^{2X}}-2}}dx$

$t={{e}^{2X}}-2$

$dx=\dfrac{dt}{2{{e}^{2X}}}$

$=\dfrac{1}{2}\int{\dfrac{1}{t}}dt$

$=\dfrac{1}{2}\ln \left( t \right)+C$

$=\dfrac{1}{2}\ln \left( {{e}^{2X}}-2 \right)+C$

Hence, this is the required result

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Single Correct Medium Published on 17th 09, 2020
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 86

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