Help with Integral Homework: Can't Solve with MAPLE

[garydia1]

Homework Statement

I have the next integral:
$$\int\frac{dx}{x*arcsin(a/x)}$$
between g0 and R2, assuming that R2,g0>0 and R2>x>g0
I'm using MAPLE but it seams that the problem is not the software, can you assist me to understand why is MAPLE unable to solve the integral.
I've tryed to add assuming that g0/x is between -1 and 1.
No result...

 

[fzero]

This integral is not expressible in terms of elementary functions, so it's not surprising that MAPLE can't give you an answer. If we make a change of variables to

$$y=\sin^{-1}\frac{a}{x},$$

we get

$$-\int \frac{\cot y}{y} dy.$$

It might be possible to relate this to one of the trigonometric integrals, or else, after integration by parts, to Clausen's integral, which might allow you to express it in terms of a dilogarithm.

Otherwise, you'd want to resort to numerical methods to solve this. A power series expansion might work if there is a small enough parameter to expand in.