# Math Help - easiest way to integrate f(x)*g(x) product specifically: x^2 * (1-x)^3 dx

1. ## easiest way to integrate f(x)*g(x) product specifically: x^2 * (1-x)^3 dx

I've solved this properly by expanding the term in paranthesis then multiplying by x^2, and I think this would also be able to be solved via integration by parts, although not necessary.

Is there an easier way, or rules, to integrating products of the same integrating variable?

2. You can integrate by substitution, although I'm not sure if it will work for your example.

3. Letting $u = 1-x$ will give you $\int (u-1)^2u^3\;{du}$. You will expand a quadratic instead of a cubic. I think that's a fair simplification.

4. fair enough, I wanted to make sure there wasn't a nifty chain rule like there is for differentiation that exists. Thanks guys.

PS - how do I set this thread as solved