Integration Problem

  • Thread starter nova1989
  • Start date
  • #1
nova1989
2
0
Trying to integrate:

((arcsin((x^2 + a) / (b*x))) - c) / x dx

where a, b, c are constants.

No success so far. I've tried integration by parts, but the resulting integral is more complex than the starting integral above!

The free Wolfram online integrator doesn't even read the syntax correctly!

Any assistance appreciated. It's been many years since I last looked at a problem like this.

nova
 
Last edited:

Answers and Replies

  • #2
CRGreathouse
Science Advisor
Homework Helper
2,842
0
I doubt that there is a closed form solution in 'usual' functions.
 
  • #3
CompuChip
Science Advisor
Homework Helper
4,309
49
Mathematica gives something like
[tex]-\frac{\sin ^{-1}\left(x^2+a\right)}{b x}-\frac{2 i \sqrt{\frac{x^2}{a-1}+1} \sqrt{\frac{x^2}{a+1}+1} F\left(i \sinh ^{-1}\left(\sqrt{\frac{1}{a+1}}
x\right)|\frac{a+1}{a-1}\right)}{\sqrt{\frac{1}{a+1}} b \sqrt{-\left(x^2+a-1\right) \left(x^2+a+1\right)}}-c \log (x)[/tex]
where [itex]F(\phi, m)[/itex] is some elliptic integral "of the first kind".

In short, I share CRGreathouse's doubts :smile:
 
  • #4
ssd
268
6
I believe it does not have a solution in terms of simple functions.
 
  • #5
nova1989
2
0
Many thanks to everyone for the replies. Seems I'm out of luck for a closed form solution.

However, if you do think of a possible solution at some point, I would be most grateful for your advice.

Best regards.
 
  • #6
CompuChip
Science Advisor
Homework Helper
4,309
49
Yes, there is a solution. I posted it. I'm thinking of it now. If you insist, you can copy it. Or write n(x) and call it nova's function.
 

Suggested for: Integration Problem

  • Last Post
Replies
0
Views
323
Replies
0
Views
296
  • Last Post
Replies
4
Views
568
  • Last Post
Replies
1
Views
267
  • Last Post
Replies
4
Views
777
Replies
16
Views
276
  • Last Post
Replies
12
Views
620
Replies
3
Views
527
  • Last Post
Replies
2
Views
650
  • Last Post
Replies
4
Views
482
Top