Please give any hints about this integral

  • Thread starter bLaf
  • Start date
  • #1
2
0
Hi guys, I and my colleague have been struggling with this integral for over 2 hours. :D

Any hints about solving it are welcome.

[tex]\int \frac{\sqrt{x^2 - 4}}{x^4}[/tex]


Thanks in advance :)
 

Answers and Replies

  • #2
Dick
Science Advisor
Homework Helper
26,260
619
Looks like a trig substitution to me. Try u=2*sec(x).
 
  • #3
2
0
Hi Dick,

thanks for your reply.

Unfortunately, in some countries(like mine) the secant and cosecant trig functions are not taught(not even in mathematical schools).

Aren't there any alternative approaches? Isn't there a way to use sin/cos/tg/cotg substitutions?

Thanks!
 
  • #4
205
0
You could try [tex]u=2*sin^{-1}(x)[/tex]
 
  • #5
arildno
Science Advisor
Homework Helper
Gold Member
Dearly Missed
9,970
134
The simplest is to use the hyperbolic cosine substitution, x=2Cosh(u).

Using this, you'll readily find a proper anti-derivative, namely:
[tex]A(x)=\frac{1}{12}(\frac{\sqrt{x^{2}-4}}{x})^{3}[/tex]
 
  • #6
34,988
6,739
Unfortunately, in some countries(like mine) the secant and cosecant trig functions are not taught(not even in mathematical schools).
Thanks!
I find it difficult to believe that these functions aren't presented in some countries. If that's the case, though, here is how they're defined:
secant(x) = sec(x) = 1/cos(x)
cosecant(x) = csc(x) = 1/sin(x)
 
  • #7
34,988
6,739
You could try [tex]u=2*sin^{-1}(x)[/tex]
Dagda, did you mean this as u = 2/sin(x)? That's different from 2*sin^(-1)(x), which is the same as 2*arcsin(x).
 
  • #8
205
0
Dagda, did you mean this as u = 2/sin(x)? That's different from 2*sin^(-1)(x), which is the same as 2*arcsin(x).

I think my brain exploded and I accidentally read the wrong trig sub off the table, whatever happened you are of course correct. :smile:
 

Related Threads on Please give any hints about this integral

  • Last Post
Replies
6
Views
2K
  • Last Post
Replies
1
Views
2K
  • Last Post
Replies
2
Views
3K
  • Last Post
Replies
6
Views
2K
  • Last Post
Replies
1
Views
2K
  • Last Post
Replies
3
Views
1K
  • Last Post
Replies
5
Views
2K
Replies
1
Views
857
  • Last Post
Replies
11
Views
2K
Top