Mathematics

# Evaluate $\int \dfrac{e^x-e^{-x}}{e^x+e^{-x}}dx$

##### SOLUTION
Let $e^x + e^{-x} = t$
Then $e^x - e^{-x} = dt$

Therefore, required integral = $\int \dfrac{1}{t} dt$
$=\ln|t| + C$
$=\boxed{\ln(e^x + e^{-x}) + C}$

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Subjective Easy Published on 17th 09, 2020
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 111

#### Realted Questions

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If $I_{1}=\displaystyle \int_{0}^{\pi/2}\dfrac{\cos^{2}x}{1+\cos^{2}x}dx, I_{2}=\int_{0}^{\pi/2}\dfrac{\sin^{2}x}{1+\sin^{2}x}dx, I_{3}=\int_{0}^{\pi/2}\dfrac{1+2 \cos^{2} x \sin^{2}x}{4+2 \cos^{2}x \sin^{2}x}dx$ then
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