# Integrating with partial fractions and simpifying the answer

## Homework Statement

the definite integral of (x-1)/(x^3+4x^2+3x) from x=1 to x=3 using partial fraction decomposition. I know the answer should be (5/3)ln2 - ln3.

## The Attempt at a Solution

After integrating, I got -(1/3)ln(3x) - (2/3)ln(x+3) + ln(x+1) . The issue is that after I implement the limits of integration, I cannot seem to simplify it to get the answer (5/3)ln2 - ln3.

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I believe your -(1/3)ln(3x) should be -(1/3)ln(x)

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After integrating, I got -(1/3)ln(x) - (2/3)ln(x+3) + ln(x+1) .
I agree with your result for the antiderivative (after fixing that "3x" ). One of the terms in the evaluation gives (1/3) ln 1 and so can be omitted. Be sure to consider that ln (6) = ln (2) + ln (3) and that ln ( 4 ) = 2 ln ( 2 ) . The stated answer appears to be correct.