Question

Question : Integrate [x/(1+(sin a*sin x))] from 0 to pi

My first thought was to apply integrate f(x) dx= f(a-x) dx method

Which simplified the integral into;
2I = integrate [pi/(1+(sin a*sin x))] dx , cancelling out x

Then I made the integral into the form of the following by making necessary changes;
2I* sin a = integrate [pi*((sin a*cos x)*sec x)/(1+ (sin a* sin x))]

Then integration by parts,
2I*sin a = pi*(ln| 1+(sina* cos x)|*sec x ) - integrate [pi*(ln|(1 +(sin a*sin x))|*(sec x*tan x) dx

How do I simplify ln|(1+(sin a*sin x))| to finish integrating this?

Answer 1

I don't think I can help you on this but hopefully Ms. Sue will come soon.