$\displaystyle

\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.

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- Jan 22nd 2006, 04:54 AMopcodeA nasty integration
$\displaystyle

\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, 10:07 AMThePerfectHacker
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, 12:48 PMopcode
I thought of that too but that square root won't go away or transform to something easy to integrate.

- Jan 22nd 2006, 01:08 PMThePerfectHacker
Are you certain it is possible? Was it in your book?

- Jan 22nd 2006, 01:48 PMJameson
Mathematica cannot do it and I know of no method to solve it.

- Jan 22nd 2006, 02:15 PMThePerfectHackerQuote:

Originally Posted by**Jameson**

- Jan 22nd 2006, 03:15 PMThePerfectHacker
Here I graphed it. It looks like an exponential integral,

its regression squared it .9789

Also its equation is:

$\displaystyle 1.3905495\times 1.7950946^x$ - Jan 22nd 2006, 08:49 PMearbothQuote:

Originally Posted by**opcode**

try this:

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

$

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

When integrate this: $\displaystyle \frac{1}{\sqrt{1+2*x^2}}$ 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, 03:53 AMopcode
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.