Evaluate: \int_2^4\frac{\sqrt{\ln(9-x)}dx}{\sqrt{\ln(9-x)}+\sqrt{\ln(x+3)}}

Pamela Meyer 2021-12-13 Answered
Evaluate:
24ln(9x)dxln(9x)+ln(x+3)
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

zurilomk4
Answered 2021-12-14 Author has 35 answers
Let
L=24ln(9x)ln(9x)+ln(3+x)dx
Now, use that
abf(x)dx=abf(a+bx)dx
Then
I=24ln(3+x)ln(3+x)+ln(9x)dx
Add up these two integrals to get
2I=24ln(9x)+ln(3+x)ln(9x)+ln(3+x)dx
Thus,
I=1
In order to prove (1), write the integral using another variable, say, t:
abf(a+bx)dx=abf(a+bt)dt
In the latter one, set x=a+bt and dt=dx and change the limits of integration to obtain
abf(a+bt)dt=baf(x)dx
=abf(x)dx
Not exactly what you’re looking for?
Ask My Question
Mason Hall
Answered 2021-12-15 Author has 36 answers

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