# Thread: the natural logarithmic function?

1. ## the natural logarithmic function?

How do i solve for this using the natural Logarithmic function?

I've tried using u substitution but sort of get lost with how the integra of 2 and 3 get involved.

2. Originally Posted by masterofcheese

How do i solve for this using the natural Logarithmic function?

I've tried using u substitution but sort of get lost with how the integra of 2 and 3 get involved.
You don't need a u substitution.

Note that $\frac{2 + u^2}{u^3} = 2u^{-3} + u^{-1}$.

So $\int_2^3{\frac{2 + u^2}{u^3}\,du} = \int_2^3{2u^{-3} + u^{-1}\,du}$.

Can you go from here?

3. Originally Posted by masterofcheese

How do i solve for this using the natural Logarithmic function?

I've tried using u substitution but sort of get lost with how the integra of 2 and 3 get involved.
$\frac{2+u^2}{u^3}=\frac{2}{u^3}+\frac{1}{u}$, so you can divide your integral in two: the first one is a rational function integral and the second one a logarithmic integral, but immediate.

Tonio

4. so i just do the derivative, then take the integral of 3 minus 2 and that is my solution?

5. No.

$\int{2u^{-3} + u^{-1}\,du} = -u^{-2} + \ln{|u|} + C$.

Go from here.

6. well i tried plugging in 3 and 2 and subtract but i got it wrong. the problem is that i don't have any more tries left for the assignment.

7. Originally Posted by masterofcheese
well i tried plugging in 3 and 2 and subtract but i got it wrong. the problem is that i don't have any more tries left for the assignment.

Well, then all it's lost, ain't it...or not? What do you mean you don't have more tries for the assignment? Is this an online hw and you have to type in the answers in some site? That is, imo, lame, but if that's what you've to do and you only have few trials, why don't you first check thoroughly the deveopment of the problem and the answer?!
You've been given the complete answer, now you have to plug in upper and lower limits, be careful and dp some fractions algebra and a little rules of logarithsm and that's all there is to it.

Tonio