Improper Integral Solution Check: Is Your Answer Accurate?

[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)

How does this compare to other answers?

Is there a way I can accurately check this answer myself?
Thanks!

 

[AmritpalS]

if I'm not mistaken u= (v+1) is pretty easy and it ends up fitting the arctanh rule. Seems that it'll involve an inverse hyperbolic function

 

[B18]

What exactly do you mean that substituting u=v+1 is easy? I don't see any substitution in this problem

 

[AmritpalS]

What exactly do you mean that substituting u=v+1 is easy? I don't see any substitution in this problem

I meant completing the square so that the denominator is (v+1)^2 -4. Multiply by -1/-1 and you have -dv/(4-(v+1)^2)
which fits the rule ∫du/(a^2-u^2)=1/2a(ln (a+u/a-u)+c

 

[B18]

Alright, that would make sense. Hopefully people get a similar final answer.