Evaluate the following integrals. intfrac{e^{sin x}}{sec x}dx

nicekikah 2021-02-14 Answered
Evaluate the following integrals.
esinxsecxdx
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

Alix Ortiz
Answered 2021-02-15 Author has 109 answers
The given integral is,
I=esinxsecxdx
Using trigonometric identity, cosθ=1secθ
I=cosx(esinx)dx
Using substitution method,
esinx=t
ddx(esinx)=dtdx
Let[dd(sinx)(esinx)][ddx(sinx)]=dtdx
(esinx)(cosx)=dtdx
(esinx)(cosx)dx=dt
Then the given integral gets transformed as, 
I=dt=t+C
Putting back the value of t, we get
I=esinx+C
Therefore, the value of the given integral is esinx+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

New questions