# A nasty integration

• Jan 22nd 2006, 05:54 AM
opcode
A nasty integration
$
\int^1_{0}e^{bx} * sqrt(1+2*x^2)dx
$

Does anybody know how to solve the above integral ? I'm quite out of ideas. Thx in advance.
• Jan 22nd 2006, 11:07 AM
ThePerfectHacker
I do not have time to do this problem now, but the first thing I thought of is using integration by parts.
• Jan 22nd 2006, 01:48 PM
opcode
I thought of that too but that square root won't go away or transform to something easy to integrate.
• Jan 22nd 2006, 02:08 PM
ThePerfectHacker
Are you certain it is possible? Was it in your book?
• Jan 22nd 2006, 02:48 PM
Jameson
Mathematica cannot do it and I know of no method to solve it.
• Jan 22nd 2006, 03:15 PM
ThePerfectHacker
Quote:

Originally Posted by Jameson
Mathematica cannot do it and I know of no method to solve it.

Mathematica is a program it is not creative. It is not able to manipulate the integrand. It propably just checks the Table of Integrals.
• Jan 22nd 2006, 04:15 PM
ThePerfectHacker
Here I graphed it. It looks like an exponential integral,
its regression squared it .9789

Also its equation is:
$1.3905495\times 1.7950946^x$
• Jan 22nd 2006, 09:49 PM
earboth
Quote:

Originally Posted by opcode
$
\int^1_{0}e^{bx} \cdot \sqrt{1+2*x^2}dx
$

Hello,

try this:

$\int^1_{0}e^{bx} \cdot \sqrt{1+2*x^2} \cdot \frac{\sqrt{1+2*x^2}}{\sqrt{1+2*x^2}}dx
$

$\int^1_{0} {\left( e^{bx} \cdot \frac{1}{\sqrt{1+2*x^2}}+e^{bx} \cdot \frac{2*x^2}{\sqrt{1+2*x^2}}} \right) dx$

When integrate this: $\frac{1}{\sqrt{1+2*x^2}}$ you'll get an arsinh-function.

I'm in a hurry now. Hope that this hint is of some help for you.

Bye
• Jan 23rd 2006, 04:53 AM
opcode
First of all I want to thank you all for the help. This integral wasn't in my book. It resulted from a curve integral. I made some changes to the parameters and I managed to avoid it. Anyhow it would be interesting to manage to integrate it. But that might even be impossible with the current means. I don't know.