I have a problem in my book where i have an integral and i have to use complete the square if necessary. I understand how to do the complete the square. However, this problem don't need it but its stumping me. I am not sure how the solutions manual got the second step. It split it up into two integrals and i cant see how it came to that conclusion?

$\displaystyle \int \frac {2x}{x^2+6x+13} dx $

The next step is

$\displaystyle \int \frac {2x + 6} {x^2 + 6x + 13} dx - 6 \int \frac {1}{x^2+6x+13} dx $

How are they splitting up the integral and where is the 2x +6 in the first integral and -6 in the second coming from?

The next step( which i left out) looks like they use complete the square on the second integral.

Thank you so much!!!!!