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

Lorraine Harvey 2021-12-16 Answered
Evaluate the following integrals.
extan(ex)dx
You can still ask an expert for help

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Solve your problem for the price of one coffee

  • Available 24/7
  • Math expert for every subject
  • Pay only if we can solve it
Ask Question

Expert Answer

kalupunangh
Answered 2021-12-17 Author has 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
Not exactly what you’re looking for?
Ask My Question
Cheryl King
Answered 2021-12-18 Author has 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
Not exactly what you’re looking for?
Ask My Question

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more