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Math Help - Integration

  1. #1
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    Integration

    Can someone help me with the integration of x/sqrt(1+x^5) ?
    I just do not get it.
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  2. #2
    o_O
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    Doesn't look like it can be done by elementary means.
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  3. #3
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    Thanks for the try. What I actually need to check is if this improper intergral is convergent. As far as I know you have to solve the integral to do this. Or is there another way?
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  4. #4
    MHF Contributor Mathstud28's Avatar
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    Quote Originally Posted by JanW View Post
    Thanks for the try. What I actually need to check is if this improper intergral is convergent. As far as I know you have to solve the integral to do this. Or is there another way?
    Well I assume it is

    \int_0^{\infty}\frac{x}{\sqrt{1+x^5}}dx

    and since \frac{x}{\sqrt{x^5+1}}\sim\frac{x}{x^{\frac{5}{2}}  }=\frac{1}{x^{\frac{3}{2}}}

    therefore this integral is convergent
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  5. #5
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    Great thanks a lot! I forgot the boaders, you are right!
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  6. #6
    Moo
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    Quote Originally Posted by Mathstud28 View Post
    Well I assume it is

    \int_0^{\infty}\frac{x}{\sqrt{1+x^5}}dx

    and since \frac{x}{\sqrt{x^5+1}}\sim\frac{x}{x^{\frac{5}{2}}  }=\frac{1}{x^{\frac{3}{2}}}

    therefore this integral is convergent
    This is only true if the integral goes from 1 to infinity.

    From 0 to 1, the approximation doesn't work
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