Solve Indefinite Integral (x/c) arcsin dx/tan(x)

[Gmen]

I would like to know the following indefinite integral:

(INTEGRAL)arcsin(x/c) dx / tan(x). c is a constant.
This is not homework...I found it in fron of me while trying to make a 3d model of an enveloped worm gear. I can explain to anyone who isn't bored.
PLEASE tell me there is a solution...I so feel not :(

 

[chiro]

Hey Gmen.

I guess you should probably ask whether you need it in a closed form using elementary, trig, and transcendental functions or whether you could do something like say a series expansion (like a Taylor series) and integrate it term by term.

You can use this and depending on how much error you can tolerate just find the cut-off term and compute all terms till that term.

 

[Gmen]

This was a really helpful idea. Differentiating is always easier (and possible!) than integrating, and it becomes just a matter of loveable polynomial integration! Thanks! I shall remember this in difficult integrals to come.