integral

**acosta0809** · July 30th 2009, 08:20 PM

im not sure how to integrate this

$\int\frac{1}{x^2(x^2+1)}$

i had this on a test and i got it wrong

**VonNemo19** · July 30th 2009, 08:32 PM

Originally Posted by acosta0809

im not sure how to integrate this

$\int\frac{1}{x^2(x^2+1)}$

i had this on a test and i got it wrong

Partial fraction decomp is how I'd do it.

**o_O** · July 30th 2009, 08:34 PM

A couple of ways to do this one.

Notice that: $\frac{1 {\color{red}\ + \ x^2 \ - \ x^2}}{x^2 \left(x^2 + 1\right) } = \frac{1 + {\color{red}x^2}}{x^2 \left(x^2 + 1\right)} - \frac{{\color{red}x^2}}{x^2\left(x^2 + 1\right)} = \frac{1}{x^2} - \frac{1}{1+x^2}$

So your itnegral is the same as: $\int \left( \frac{1}{x^2} - \frac{1}{1+x^2}\right) \ dx$

which is a lot easier. You could've gotten the same thing if you did something along the lines of partial fraction decomposition if you aren't comfortable with the 'adding 0' in the numerator .

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