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I've been having difficulty with this integral for some time now and any help would be gratly appreciated.

[tex]\int\frac{x^2 \sin x}{1+x^6}dx[/tex]

this is a definite integral from -pi/2 to pi/2

The sinx has been giving me problems because if I set u = to any part of the equation I can't write sin(u)

for example

u = x^2 du/2 = xdx

u = 1+x^6 du/6 = x^5dx

u = 1+x^3 du/2 = x^2dx

in all these cases I still get stuck with the sinx..

hints on how to approach this equation would be ideal becasue I need to learn how to do this myself.

Thank you!!