Partial Fractions of integral (10x+2)/(x^3-5x^2+x-5)

**Fallen186** · May 6th 2009, 10:34 AM

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

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

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:
$<br /> 2ln(x-5)-ln(x^2+1)+C<br />$

**Calculus26** · May 6th 2009, 10:39 AM

Look at your hint:

=(x^2+1)(x-5)

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