Solve the integral

  • #1

Homework Statement


∫sqrt((x+1)/(x-1))

Homework Equations




The Attempt at a Solution


t=sqrt((x+1)/(x-1)), t^2=(x+1)/(x-1)⇒x=(-t^2-1)/(-t^2+1) dx=dt⇒ -4t/((t^2-1)^2)
∫t*-4t/((t^2-1)^2)=-4∫t^2+1-1/((t^2+1)^2)=-4∫dt/t^2+1-4∫dt/((t^2-1)^2)
 

Answers and Replies

  • #2
SteamKing
Staff Emeritus
Science Advisor
Homework Helper
12,796
1,668
Please post calculus HW problems in the Calculus HW forum.
 
  • #3
SammyS
Staff Emeritus
Science Advisor
Homework Helper
Gold Member
11,358
1,031

Homework Statement


∫sqrt((x+1)/(x-1))

Homework Equations




The Attempt at a Solution


t=sqrt((x+1)/(x-1)), t^2=(x+1)/(x-1)⇒x=(-t^2-1)/(-t^2+1) dx=dt⇒ -4t/((t^2-1)^2)
∫t*-4t/((t^2-1)^2)=-4∫t^2+1-1/((t^2+1)^2)=-4∫dt/t^2+1-4∫dt/((t^2-1)^2)
Hello Alex235123. Welcome to PF !

It's really not proper to leave the dx out of the integral. It's especially important when using substitution.

Consider multiplying the numerator and denominator by x+1, then simplifying the integrand.

The substitution x = cosh(t) looks like it works well.
 

Related Threads on Solve the integral

  • Last Post
Replies
13
Views
978
  • Last Post
Replies
5
Views
587
Replies
3
Views
657
Replies
11
Views
919
  • Last Post
Replies
3
Views
641
Replies
2
Views
603
Replies
10
Views
2K
Replies
4
Views
1K
Replies
11
Views
412
Replies
6
Views
518
Top