# Thread: Integration with partial fractions

1. ## Integration with partial fractions

$\displaystyle \int \frac {5x^{2}-3} {x^2-9}$

Since nominator and denominator are x^2 I have to divide them, right?
I am not sure how to do that.

Thanks for any help.

2. Originally Posted by DBA
$\displaystyle \int \frac {5x^{2}-3} {x^2-9}$

Since nominator and denominator are x^2 I have to divide them, right?
I am not sure how to do that.

Thanks for any help.
Yes start by Long Division.
Actually, there is another solutions without devide.

3. Hello, thanks for answering. Can you please explain how to do so?
That was my problem, actually...

4. Originally Posted by DBA
Hello, thanks for answering. Can you please explain how to do so?
That was my problem, actually...
Ohhh..You do not know to do the long division ?

5. You could do it this way:

$\displaystyle \int \frac {5x^{2}-3} {x^2-9} dx =$

$\displaystyle \int \frac {5x^{2}-45 + 42} {x^2-9} dx =$

$\displaystyle \int \frac {5(x^2 - 9)}{x^2 - 9} dx + \int \frac {42}{x^2 - 9} dx=$

$\displaystyle \int 5 dx + \int \frac {42}{x^2 - 9} dx$

Then use an appropriate substitution on the second integral.