Evaluate Integral: 2 ln| \frac{v-1}{v}|

[whatlifeforme]

Homework Statement

evaluate the integral.

Homework Equations

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

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.

 

[LCKurtz]

Homework Statement

evaluate the integral.

Homework Equations

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

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.

Did you try factoring and partial fractions?

 

[phosgene]

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

 

[epenguin]

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

 

[Mark44]

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

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.

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.