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Why all the if's the answer


Suppose I start with :

f = -Log[y*(1 + Cos[alpha])] + Log[(b*c - b*y + c*y*Cos[alpha] +
Sqrt[b^2*(c - y)^2 + c^2*y^2 + 2*b*c*(c - y)*y*Cos[alpha]])/c];

which I think is relatively innocent. I then integrate over y:

Assuming[y > 0 &&  c > 0 && b > 0 && alpha > 0 && alpha < Pi/2,
Integrate[y/c*f, {y, 0, c}]]

After a few hours get a humongous answer with many If's, etc. What else
can I assume or otherwise do to get an analytical answer?

Many thanks in advance!

Aaron Fude


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