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How does one integrate $\int xf(ax)f(bx) dx$?

I think it cries out for integration by parts, but I don't know how to split the integrand.

Thanks.

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    There is certainly no way to evaluate the integral is terms of anything that brings us any closer to actually finding the integral. If we could work out this integral, then we could find the definite or indefinite integral of any function $g$ we desired simply by setting $a=b=1$, defining $ f = \sqrt{g/x} $ for definite integrals over $[0,1]$ and then scaling/translating the function for other intervals.2011-09-27

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