Hey guys

Needed some help with this question

a) Find the derivative of x^{2}e^{kx}

b) Hence find an anti-derivative of xe^{kx}

I tried using Integration by Recognition on this question, since this is the only method my teacher will teach, but could never get the right answer. I sorta got stuck in a loop where to find one of the integrals I needed to find the integral of the other one.

Was wondering if any of you guys knew how to do it?

Thanks

Hi, ialsohavenolife!

Thank you very much for posting your working out, and good job on attempting the question!

As far as I can see, there is absolutely no issue with your working out and it's actually unsolvable in the scope of VCE Methods.

To be able to solve this you would need to know what \(\int \:x^2e^{kx}dx\), which you do not know (as you pointed out).

EDIT: Response below is better, and is in the scope of methods, however, the question mentioned 'hence' which is why I didn't go with that approach, although it's valid.