# Rational Integral

1. Mar 14, 2013

### whatlifeforme

1. The problem statement, all variables and given/known data
evaluate the integral.

2. Relevant equations
$\displaystyle\int_2^∞ {\frac{2}{v^2 -v} dv}$

3. The attempt at a solution
how does this integrate into:

2 ln| $\frac{v-1}{v}|$

i tried and got 2ln|v^2-v| but not above.

2. Mar 14, 2013

### LCKurtz

Did you try factoring and partial fractions?

3. Mar 14, 2013

### phosgene

Try simplifying the denominator and using the method of partial fractions. Ahhh beaten to the punch!

4. Mar 14, 2013

### epenguin

Also since you know (knew?) the answer, differentiate it and you see what is right and may get some helpful insight and reinforcement.

5. Mar 14, 2013

### Staff: Mentor

Others have shown you the right way - I'll explain what you did that was wrong.

These are correct:
$$\int \frac{dx}{x} = ln|x| + C$$
$$\int \frac{du}{u} = ln|u| + C~$$

BUT, this is NOT correct:
$$\int \frac{dx}{f(x)} = ln|f(x)| + C$$

This is a very common error among students who are learning calculus.