"I am back" says Integration - Part 2

Calculus Level 5

cos(2x)sin(x)dx \large \int \frac{\sqrt{\cos(2x)}}{\sin(x)} \, dx

If the integral above can be expressed as alog(bcosx+cos(cx))log(dcotx+((cotx)eg)f)\sqrt{a}\log(\sqrt{b}\cos{x} + \sqrt{\cos(cx)}) - \log(d\cot{x} + ((\cot{x})^e - g)^f), for constants a,b,c,d,e,ga,b,c,d,e,g and ff, evaluate abcdg+ef+11\frac{abc}{dg} + ef + 11.

Note: ff is not an integer. And all these constants may not be distinct.

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