The following integrals require a preliminary step such as a change of variables

ediculeN

ediculeN

Answered question

2021-10-10

The following integrals require a preliminary step such as a change of variables before using the method of partial fractions. Evaluate these integrals.
dx1+ex

Answer & Explanation

smallq9

smallq9

Skilled2021-10-11Added 106 answers

Given:
dx1+ex
Explanation:
dx1+ex
Multiplying ex to numerator and denominator, we get
exdxex(1+ex)
Put u=ex
du=exdx
=duu(u+1)
=[1u1u+1]du
=1udu1u+1du
=ln(u)ln(u+1)+C
=ln(ex)ln(ex+1)+C
=xln(ex+1)+C
Answer: =xln(ex+1)+C

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