Integration by Parts Example: int 8/(x^2-x) dx

[BigNate]

Hello,

I'm trying to evaluate an integral by integrating by parts, but am stuggling to see how to setup the integration.

Can someone please point me on the right track? I am trying to do integration by parts on the following:
8/(x^2-x)

I know it needs to be A/(x-r)+ B/(x-r) for second linear function, but the x^2 and x alone are throwing me off.

Again, if someone could help point me in the right direction, that would be much appreciated. Thanks!

 

[lookagain]

It's not integration by parts. It's integration using partial fractions.

\(\displaystyle \dfrac{8}{x^2 - x} \ = \ \dfrac{8}{x(x - 1)}.\)


Your integrand can found by solving for A and B here:


\(\displaystyle \dfrac{A}{x} \ + \ \dfrac{B}{x - 1} \ = \ \dfrac{8}{x(x - 1)} \ \implies\)

A(x - 1) + Bx = 8

 

[Steven G]

I know it needs to be A/(x-r)+ B/(x-r) for second linear function, but the x^2 and x alone are throwing me off.

No, not A/(x-r)+ B/(x-r). Possibly you mean A/(x-r₁)+ B/(x-r₂) or A/(x-r)+ B/(x-s). You should know that the denominators should be different.