Mathematics

# Evaluate: $\displaystyle \overset{2}{\underset{0}{\int}} \dfrac{e^x }{e^{2x} + 1}dx$.

##### SOLUTION
Now,
$\displaystyle \overset{2}{\underset{0}{\int}} \dfrac{e^x }{e^{2x} + 1}dx$
$=\displaystyle \overset{2}{\underset{0}{\int}} \dfrac{e^x }{(e^{x})^2 + 1}dx$
$=\displaystyle \overset{2}{\underset{0}{\int}} \dfrac{d(e^x) }{(e^{x})^2 + 1}$
$=\left[\tan^{-1} e^x\right]_{x=0}^{x=2}$
$=\tan^{-1}e^2-\dfrac{\pi}{4}$.

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

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