Integral of type 'derivative over function' with a twist

[BalintRigo]

Homework Statement

Find the integral

[(2x - 3) / (x^2 - 3x - 5)^2] dx

Homework Equations

I noticed that if I differentiate the denominator I get the nominator, which would be a simple problem. The denominator, however is raised to the power 2.

Can I still somehow use the rule for integrals where the nominator is the derivative of the denominator? Or do I need to take a different approach?

Thank you

 

[Dick]

The 'approach' you are talking about is integration by substitution, I hope. You've observed that if u=x^2-3x-5, then du=u'dx=(2x-3)dx. That's great. That turns the integral into du/u^2 in terms of u. Can you integrate that?

 

[BalintRigo]

I got it, thanks an awful lot!