if anyone could help me with the integration of this quotient it would be greatly appreciated.
i have tried and tried but just cant get the right integral
$\displaystyle
\int \frac{x+2}{x^2-7x+12}dx
$
thanks a lot
Well, in that case:
Multiply by 2 and divide by 2: $\displaystyle \frac{1}{2} \int \frac{2x+4}{x^2-7x+12}dx$
Add 11 and subtract 11: $\displaystyle \frac{1}{2} \int \frac{2x+4+11-11}{x^2-7x+12}dx$
The reason why I did this is to get one integral to be of the form:
$\displaystyle \int \frac{f'(x)}{f(x)} dx$
Simplify and split the integrals: $\displaystyle \frac{1}{2} \int \frac{2x-7}{x^2-7x+12}dx + \frac{11}{2} \int \frac{1}{x^2-7x+12}dx$
The first integral should be easy. In the second one, complete the square, then try to get it in the form of:
$\displaystyle \frac{1}{u^2+1}$
which should be a familiar standard form to you.