## anonymous 5 years ago how to find the integration int (sinh^-1x)dx

1. amistre64

it equals ln(x+sqrt(x^2+1))

2. amistre64

thats the derivative...lol

3. anonymous

i need the procedure.......whatever be the ans...

4. anonymous

i have books where the ans is given but not the procedure......

5. amistre64

ack!!...sinh^-1x = ln(x+sqrt(x^2+1))

6. amistre64

integrate the ln function; is that possible?

7. nowhereman

There is a better way, substitute x = sinh(z). Then you can integrate by hand, because only terms of the form exp(z) and z exp(z) remain.

8. nowhereman

I get $z\cosh z - \sinh z = \sqrt{1+x^2}\sinh^{-1} x - x$ can that be correct?

9. nowhereman

oh wait, you have to exchange sinh and cosh there ;-) but then it's correct. Yeah that substitution works :-)