# Thread: Improper Integral's & L'Hopital's Rule

1. ## Improper Integral's & L'Hopital's Rule

Hi. Im having trouble with this improper integral
it is the integral of 5/(z^2+7z+6)dz from 5 to +infinity

I know that you let t=+inf and set it up as the limit of the integral as t approaches +inf and solve

I am stuck at the part after you integrate & plug +inf back in for t & I know that you're supposed to use L'hopitals rule somewhere but am having trouble doing this

2. Did you use partial fractions?

3. Originally Posted by rawkstar
Hi. Im having trouble with this improper integral
it is the integral of 5/(z^2+7z+6)dz from 5 to +infinity

I know that you let t=+inf and set it up as the limit of the integral as t approaches +inf and solve

I am stuck at the part after you integrate & plug +inf back in for t & I know that you're supposed to use L'hopitals rule somewhere but am having trouble doing this

You do not need L'Hopital it is a perfectly ordinary limit problem. Post what you have and we will advise you on how to proceed.

CB

4. If f(z) has only 'simple poles' $\alpha_{1}, \alpha_{2}, ..., \alpha_{n}$ , then is...

$\displaystyle f(z)= \sum_{n=1}^{n} \frac{r_{n}}{z-\alpha_{n}}$ (1)

... where...

$\displaystyle r_{n}= \lim_{z \rightarrow \alpha_{n}} f(z)\ (z-\alpha_{n})$ (2)

Now it is evident that the limits (2) are 'ideterminate forms' of the type $\frac{0}{0}$ so that they can be solved using l'Hopital's rule...

Kind regards

$\chi$ $\sigma$

5. Originally Posted by chisigma
If f(z) has only 'simple poles' $\alpha_{1}, \alpha_{2}, ..., \alpha_{n}$ , then is...

$\displaystyle f(z)= \sum_{n=1}^{n} \frac{r_{n}}{z-\alpha_{n}}$ (1)

... where...

$\displaystyle r_{n}= \lim_{z \rightarrow \alpha_{n}} f(z)\ (z-\alpha_{n})$ (2)

Now it is evident that the limits (2) are 'ideterminate forms' of the type $\frac{0}{0}$ so that they can be solved using l'Hopital's rule...

Kind regards

$\chi$ $\sigma$
Now you are making things more complicated than they need be. You end up with the log of a rational function (from your equation (1)) and that can be handled perfectly well without resort to M. L'Hopital.

CB