Integrating - solution involves asinh (x)

  • Thread starter Kuryakin
  • Start date
  • #1
10
0

Homework Statement



Context is cosmology but not really relevant to the integration.
I've managed to integrate it using substitution but it didn't seem that neat. Coming back after two-years off and I'm a bit rusty at spotting the best substitutions (wasn't great to start with :)).

Homework Equations



[tex]\int^x_0\frac{1}{\sqrt{1 + x^2/R^2}}dx = Rsinh^{-1} x/R[/tex]

The Attempt at a Solution



I've got to the solution using atan substitution and then integrating sec(x), was wondering whether there were any simpler methods as it was alot more work than a far easier question with the same amount of marks.
 

Answers and Replies

  • #2
dextercioby
Science Advisor
Homework Helper
Insights Author
13,076
640
No, the simplest method requires the substitution [itex] \sinh t = \frac{x}{R} [/itex]. The integration is immediate.

And the [itex] \tan t =\frac{x}{R} [/itex] leads to a lenghthier calculation.
 

Related Threads on Integrating - solution involves asinh (x)

Replies
3
Views
1K
Replies
2
Views
6K
Replies
1
Views
729
Replies
5
Views
8K
  • Last Post
Replies
2
Views
2K
  • Last Post
Replies
1
Views
1K
Replies
2
Views
3K
  • Last Post
Replies
3
Views
454
Top