# Calc 2 Integration Problem

by Tilted
Tags: calc, integration
 P: 6 1. The problem statement, all variables and given/known data $\int$$(x^2-2x+3)dx/(x^3-x^2-x-2)$ 2. Relevant equations Trig substitution/ partial fractions? 3. The attempt at a solution I used partial fractions to reduce the integral down to: $\int$$dx/(x-2)$+$\int$$(x-1)dx/(x^2+x+1)$ The first integral is easy enough, but the second one I'm not sure where to start. Thanks in advance!
 Sci Advisor HW Helper Thanks P: 25,228 I don't agree with all of your numbers there but the general form is right. For the quadratic part you want to complete the square in the denominator, do substitution for the squared part, then split it up and use a trig substitution.
 P: 4 using partial fractions I obtained (x^2-2x+3) -----------dx ((x-2)(x^2+x+1) A bx+c -- + -------- x-2 x^2+x+1 A=3/7 B=4/7 c=-9/7 this is my attempt, i how it helps somwhat, I'm not sure if it's correct so I apologize early on.
Emeritus
HW Helper
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P: 7,808
Calc 2 Integration Problem

 Quote by jzachey using partial fractions I obtained (x^2-2x+3) -----------dx ((x-2)(x^2+x+1) A Bx+C -- + -------- x-2 x^2+x+1
A                 Bx+C
--       +     --------
x-2           x^2+x+1
 A=3/7 B=4/7 C=-9/7 this is my attempt, i how it helps somwhat, I'm not sure if it's correct so I apologize early on.
Those values for A, B, and C, are correct.
P: 4
 Quote by SammyS A Bx+C -- + -------- x-2 x^2+x+1 Those values for A, B, and C, are correct.
Oh thank you so this means
∫$\frac{3}{7(x-2)}$+$\frac{4x-9}{7(x+x+1)}$
From here you integrate
Emeritus
 Quote by jzachey Oh thank you so this means $\displaystyle \int\left(\frac{3}{7(x-2)}+\frac{4x-9}{7(x^2+x+1)}\right)dx$ From here you integrate