QUESTION #1:

Suppose we have a partial fraction as follows:

$\displaystyle \frac{Ax^2+Bx+C}{(Dx+E)(Fx+G)(Hx+I)}$

Can we break that up into partial fractions like so:

$\displaystyle \frac{J}{Dx+E}+\frac{K}{Fx+G}+\frac{L}{Hx+I}$

Where A,B,C,D,E,F,G,H,I,J,K,L are all constants? Or does the whole numerator of the original equation have to be a constant?

QUESTION #2:

How in the world would I go about integrating the following function?

$\displaystyle \int\frac{x^5}{e^x-1}dx$

Thanks!