Problem:

$\displaystyle \int\frac{10x+2}{x^3-5x^2+x-5}dx$

Attempt:

Hint: $\displaystyle x^3 - 5x^2 + x -5 = x^2(x-5) + x - 5$

Can someone tell me how to use partial fractions when there is addition and subtraction in the denominator. My book only covers multiplication. Do I have to use trig substution?

Correct Answer:

$\displaystyle

2ln(x-5)-ln(x^2+1)+C

$