Use substitution to convert the integrals to integrals of rational functions. Then use partial fractions to evaluate the integrals. \int \frac{1}{2+e^

Armorikam

Armorikam

Answered question

2021-06-16

Use substitution to convert the integrals to integrals of rational functions. Then use partial fractions to evaluate the integrals.
12+exdx

Answer & Explanation

Jaylen Fountain

Jaylen Fountain

Skilled2021-06-17Added 169 answers

12+exdx
Apply the negative exponent rule 1an=an
12+exdx=12+1exdx=ex2ex+1dx
Let u=2exdu=2exdx12du=exdx
ex2ex+1dx=12duu=12duu
Integrate
12duu=12ln|u|+C
Putting the answer back in terms of x, u=2ex+1
12ln(2ex+1)+C

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