# Wicked Substitution Integral

1. Aug 29, 2015

### AKJ1

1. The problem statement, all variables and given/known data

(x+ln(x+sqrt(x^2-1)))^3 / (sqrt(x^2-1))

3. The attempt at a solution

I have tried so many different things with this integral but cannot seem to get anywhere with it. Its almost so nicely an inverse coshx but not quite.

Any help?

2. Aug 29, 2015

### Dr. Courtney

Have you tried MMa or Wolfram Alpha?

3. Aug 29, 2015

### Ray Vickson

Have you tried Maple?

4. Aug 29, 2015

### AKJ1

I have tried putting it in various forms into wolfram but returned nothing for step by step results. I tried taking the derivative of the said solution, but couldn't make any sense of it.

5. Aug 29, 2015

### ehild

Try the substitution x=cosh(y).

6. Aug 29, 2015

### AKJ1

Thank you! This worked out quite nicely!

7. Aug 29, 2015

### SammyS

Staff Emeritus
It makes sense that ehild's suggested substitution worked.

After all: $\ \text{arcosh} (x) = \ln \left(x + \sqrt{x^{2} - 1} \right); x \ge 1 \$

8. Aug 30, 2015

### ehild

and AKJ1 has noticed it...