Find the result of this integration

[Ali 2]

Hi,
Find the result of this integration::
$$\int_0^\infty \frac { e^ {-3x} - e^ {-4x} }{x} dx$$
The members who know the answer previously please don't answer in order to make the other members think !

Best wishes ,

 

[Tide]

My lips are sealed! :)

 

[benorin]

Hint: use Integration Under the Integral Sign

 

[Ali 2]

Waiting .. :zzz: !

 

[diracbracket]

That is differentiation under the integral sign, actually.

The answer is log(4/3).

How do you do mathematical formulae on the messageboard?

 

[dextercioby]

Neat trick indeed, Benorin, this INTEGRATION under the integral sign. In this problem it involves the function $e^{-ax}$ seen as a function of 2 variables and one may use a theorem which allows changing the order of integration...

Daniel.

 

[saltydog]

Jesus! That's nice. Thanks. With regards to displaying math text, use LaTex code. There is a thread in the Math and Science Tutorials forum that describes it's use or you can just click on the "quote" button to see the code. Here, I'll write the relation suggested above:

$$\int_a^b dx \int_{\alpha_0}^{\alpha} f(x,\alpha)d\alpha=<br /> \int_{\alpha_0}^{\alpha}d\alpha \int_a^b f(x,\alpha)dx$$

 

[diracbracket]

Let me see,

$$\newcommand{\mean}[1]{{<\!\!{#1}\!\!>}}<br /> \newcommand{\braket}[2]{{<\!\!{#1|#2}\!\!>}}<br /> \newcommand{\braketop}[3]{{<\!\!{#1|\hat{#2}|#3}\!\!>}}<br /> \braket{\phi}{\psi} \equiv \int \phi^*(x) \psi(x)\,dx$$This LaTeX code doesn't work when I hit 'preview post'. There's no way to check it's right.

 

[shmoe]

This LaTeX code doesn't work when I hit 'preview post'. There's no way to check it's right.

The preview has been on the fritz for some time now, so this is 'normal'. You can edit after you post of course.