1. ## A 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.

2. I do not have time to do this problem now, but the first thing I thought of is using integration by parts.

3. I thought of that too but that square root won't go away or transform to something easy to integrate.

4. Are you certain it is possible? Was it in your book?

5. Mathematica cannot do it and I know of no method to solve it.

6. 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.

7. Here I graphed it. It looks like an exponential integral,
its regression squared it .9789

Also its equation is:
$\displaystyle 1.3905495\times 1.7950946^x$

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

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

9. 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.