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I'm having a bit of trouble evaluating this integral: (This is not a homework problem btw)

Integral between Pi and 0 (x sin x)/(1 + cos^2 x) d x

I don't even know where to begin with the substitutions or anything...... I was thinking the denominator could be sin^2 x..... only when I realized this is trig and not hyperbolic. :(

Also, something in my book:

Integral (2t^2 + 3t*t^3) d(t^2)

This was after the substitution of dy to d(t^2) when dealing with a line integral; I don't understand... how do you integrate this?

Thanks for any ideas.