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Math Help - A nasty integration

  1. #1
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    A nasty integration

    <br />
\int^1_{0}e^{bx} * sqrt(1+2*x^2)dx<br />

    Does anybody know how to solve the above integral ? I'm quite out of ideas. Thx in advance.
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  2. #2
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    I do not have time to do this problem now, but the first thing I thought of is using integration by parts.
    Last edited by ThePerfectHacker; January 22nd 2006 at 11:29 AM.
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  3. #3
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    I thought of that too but that square root won't go away or transform to something easy to integrate.
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  4. #4
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    Are you certain it is possible? Was it in your book?
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  5. #5
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    Mathematica cannot do it and I know of no method to solve it.
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  6. #6
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    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.
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  7. #7
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    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
    Attached Thumbnails Attached Thumbnails A nasty integration-graph.png  
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  8. #8
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    Quote Originally Posted by opcode
    <br />
\int^1_{0}e^{bx} \cdot \sqrt{1+2*x^2}dx<br />
    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<br />

    \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
    Last edited by ThePerfectHacker; January 23rd 2006 at 12:01 PM.
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  9. #9
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    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.
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