You are Here: Home >< Maths

# Integration sinh watch

1. I've been working on

Integrating by parts, I've come across

Which according to wolframalpha is

However I can't prove it, so:
Could anyone of you prove to me why

It may be a bit lame, as I have never been properly introduced to hyperbolic functions. I only now what sinhx, and coshx are.

Looking hopefully to your replies ^^
2. cause it's in your formula book?
3. (Original post by Papkin)
I've been working on

Integrating by parts, I've come across

Which according to wolframalpha is

However I can't prove it, so:
Could anyone of you prove to me why

It may be a bit lame, as I have never been properly introduced to hyperbolic functions. I only now what sinhx, and coshx are.

Looking hopefully to your replies ^^
would have been better from the start... Then tidy it up and use IBP. No need for hyperbolics for this integral. If you want the explanation about arcsinh, read Mr M's post.
4. (Original post by Papkin)
Could anyone of you prove to me why

Can you form an expression for in terms of ?

Remember cosh is a positive function.
5. Substitution. Try substituting x with sinhy
6. (Original post by Mr M)

.
Yep, that was lame, I did not know that^^

(Original post by Farhan.Hanif93)
would have been better from the start... Then tidy it up and use IBP. No need for hyperbolics for this integral. If you want the explanation about arcsinh, read Mr M's post.
How is it relevant?
7. (Original post by Papkin)
Yep, that was lame, I did not know that^^
You might like to prove it by using the exponential definitions of sinh and cosh.

If you are interested, Google Osborne's Rule.

http://everything2.com/title/Osborne%2527s+rule
8. (Original post by Papkin)
Yep, that was lame, I did not know that^^

How is it relevant?

Therefore:

.
Now do IBP with and .
9. (Original post by Mr M)
You might like to prove it by using the exponential definitions of sinh and cosh.

If you are interested, Google Osborne's Rule.

http://everything2.com/title/Osborne%2527s+rule
Thanks, done that. Also, the Osborne's rule is pretty cool.
10. (Original post by Farhan.Hanif93)

Therefore:

.
Now do IBP with and .
I didn't imply it was wrong. I implied it was irrelevant to the question I asked.
11. (Original post by Papkin)
I didn't imply it was wrong. I implied it was irrelevant to the question I asked.
Apologies, I offered you an alternative path since you implied you weren't comfortable with a fact about hyperbolics... That was all.

### Related university courses

TSR Support Team

We have a brilliant team of more than 60 Support Team members looking after discussions on The Student Room, helping to make it a fun, safe and useful place to hang out.

This forum is supported by:
Updated: September 25, 2010
Today on TSR

### He lied about his age

Thought he was 19... really he's 14

### University open days

Wed, 25 Jul '18
2. University of Buckingham
Wed, 25 Jul '18
3. Bournemouth University
Wed, 1 Aug '18
Poll
Useful resources

### Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here

### How to use LaTex

Writing equations the easy way

### Study habits of A* students

Top tips from students who have already aced their exams