1. ## partial fraction decomposition

x^2 / (x^2 + 5^2)

what do i do since the power of the numerator is the same as the power of the denominator ... ??

2. If the power in the numerator is not smaller than the denominator, use long divison to fix the problem. You should get: $\frac{x^2}{x^2 + 25} = 1 - {\color{blue}\frac{25}{x^2 + 25}}$

But for this example, partial fraction decomposition is not needed. You should recognize the blue as it is in the form of: $\frac{1}{a^2 + x^2}$

Why? Because: $\int \frac{1}{a^2 + x^2} \ dx = \frac{1}{a}\! \tan^{-1} \left(\frac{x}{a}\right) + C$

3. yeah i know i can use trig substitution ... but the question specifically asked for partial fraction decomposition ... maybe thats why i wasnt thinking straight ...

4. But you can't. $x^2 + 25$ is irreducible over the reals (i.e. can't be factored without getting into complex numbers).

5. Originally Posted by razorfever
yeah i know i can use trig substitution ... but the question specifically asked for partial fraction decomposition ... maybe thats why i wasnt thinking straight ...
Are you sure it wasn't asking for

$\int{\frac{x^2}{x^2 - 5^2}\,dx}$?