Evaluate the integral. \int_{0}^{1}\frac{e^{x}}{1+e^{2x}}dx

opatovaL

opatovaL

Answered question

2021-10-19

Evaluate the integral.
01ex1+e2xdx

Answer & Explanation

Cristiano Sears

Cristiano Sears

Skilled2021-10-20Added 96 answers

Step 1: Given that
01ex1+e2xdx
We need to evaluate the integral
Step 2: Solving the integral
We have,
I=01ex1+e2xdx
Substitute.
ex=t
exdx=dt
dxdt=ex
Plugging all the values into the integral we obtain,
01ex1+e2xdx=0111+t2dt
=[tan1(ex)]01
=tan1(e1)tan1(e0)
=tan1(e)tan1(1)
=tan1(e)tan1tanπ4
=tan1(e)π4

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