Evaluate the following integrals. intfrac{4^{cot x}}{sin^2x}dx

banganX 2020-11-20 Answered
Evaluate the following integrals.
4cotxsin2xdx
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

lamusesamuset
Answered 2020-11-21 Author has 93 answers
Given integral is 4cotxsin2x
Rewrite the above integrtal as 4cotxsin2x=4cotxcsc2(x)dx
Consider u=cotx.
Then,
dudx=csc2x
dx=ducsc2x
Substitute u=cotx and dx=ducsc2x in 4cotxcsc2(x)dx.
4cotxcsc2(x)dx=4ucsc2(x)(ducsc2x)
=4udu
=4uln(4)+C
=4cotxln(4)+C
=22cotxln(2)2+C
=22cotx2ln(2)+C
=22cotx1ln(2)+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