Evaluate the following integrals. \int e^{x}\tan(e^{x})dx

Lorraine Harvey

Lorraine Harvey

Answered question

2021-12-16

Evaluate the following integrals.
extan(ex)dx

Answer & Explanation

kalupunangh

kalupunangh

Beginner2021-12-17Added 29 answers

Step 1
The given integral is extan(ex)dx
Step 2
Let u=ex.
Then du=exdx
extan(ex)dx=tanudu
=sinucosudu
=1vdv   [Asev=cosu Then dv=sinudu]
=ln|v|
=ln|cosu|
=ln|cos(ex)|+C
Cheryl King

Cheryl King

Beginner2021-12-18Added 36 answers

extanexdx
Let u=exdu=exexdx=du
Apply the substitution
tanexexdxtanudu
Integrate, apply tanudu=ln|cosu|+C
tanudu=(ln|cosu|)+C
=ln|cosu|+C
Back - substitute u=ex
=lncosex+C
Result:
lncosex+C

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