# Difficult cosh integral using Leibniz rule?

• A
• Kavorka

#### Kavorka

I was wondering if I could get some pointers on how to at least start on this. In quantum mechanics we are using the WKB approximation, and we end up with a definite integral that looks like this:

∫(1 - a(cosh(x))-2)1/2 dx = ∫(1/cosh(x)) (1 - a(cosh(x))2)1/2 dx

where a is a positive constant. I've tried everything I can think of to no avail, the answer on wolfram isn't pretty but it seems like if I can figure out what process to use I could reach it eventually. I asked the professor and he suggested Leibnitz rule, but not sure how differentiation under the integral sign would help here.

definite integral

But it does not have limits on it. Do you mean indefinite ? I am asking because some indefinite integrals are easy to evalute with limits.

Are you just interested in final result ?

But it does not have limits on it. Do you mean indefinite ? I am asking because some indefinite integrals are easy to evalute with limits.

Are you just interested in final result ?

From how my professor was describing it it seemed like the limits wouldn't be too helpful, but yes it is a definite integral from -cosh-1(a0.5 to cosh-1(a0.5 (inverse hyperbolic cosh, not cosh^-1 )

From how my professor was describing it it seemed like the limits wouldn't be too helpful, but yes it is a definite integral from -cosh-1(a0.5 to cosh-1(a0.5 (inverse hyperbolic cosh, not cosh^-1 )

I tried to integrate it and I was unable to do so except for ##a = 1## (which you can do easily). I think it is not integratable but I am no expert, I don't have any clue about gamma function, airy functions ...