# Improper Integral Check

1. Mar 5, 2013

### B18

Hi guys just want to check my answer for the following improper integral.
∫(2 to ∞) dv/v^2+2v-3. After doing partial fractions, integrating and evaluating I got the following for the answer: 0-(1/4)ln(1/5)=(1/4)ln(1/5)
How does this compare to other answers?
Is there a way I can accurately check this answer myself?

2. Mar 5, 2013

### HallsofIvy

Staff Emeritus
1) How are you handling the limits at infinity?

2) Certainly, -(1/4)ln(1/5) is not equal to (1/4)ln(1/5)!

3. Mar 5, 2013

### B18

I made the natural logs into a quotient by log rules and evaluated that for t approaching infinity. I do agree with you my answer should have been negative.

4. Mar 6, 2013

### HallsofIvy

Staff Emeritus
That's not what I get. After integrating and recombining the logarithms, I get -(1/4)ln(3) at infinity.

5. Mar 6, 2013

### B18

I'm not sure how you got ln of 3 before evaluating I have lim t-> infinity 1/4ln(v-1/v+3) evaluated from 2 to t.
Lim t->infinity [1/4ln((t-1)/(t+3))-1/4ln((2-1)/2+3))
Giving me -1/4ln(1/5)