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Math Help - integration by parts

  1. #1
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    integration by parts

    Hello
    How do I integrate x^4(1+x^2)^2 I know its: u dv/dx dx=uv- inte v dudx dx
    so I know the integral of x^4 is (x^5)/5 but what the hell is the integral of dv/dx dx?
    please help!
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  2. #2
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    Quote Originally Posted by wolfhound View Post
    Hello
    How do I integrate x^4(1+x^2)^2 I know its: u dv/dx dx=uv- inte v dudx dx
    so I know the integral of x^4 is (x^5)/5 but what the hell is the integral of dv/dx dx?
    please help!
    I wouldn't do this via parts. As the exponent is low expand the binomial and then distribute the x^4

    (1+x^2)^2 = 1+2x^2+x^4

    x^4(1+x^2)^2 = x^4(1+2x^2+x^4) = x^4 + 2x^6 + x^8

    \int (x^4 + 2x^6 + x^8)\, dx = \int x^4\,dx + \int 2x^6\,dx + \int x^8\,dx

    Which is relatively simple to evaluate


    ================================================

    If you want integration by parts anyway prepare for some hard work

    u = (1+x^2)^2  ........ du = 4x(1+x^2) = 4x+4x^3 \, dx

    dv = x^4  .................. v = \frac{x^5}{5}


    \frac{x^5(1+x^2)^2}{5} - \int \frac{x^5(4x+4x^3)}{5}

    and more integration by parts ensues
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  3. #3
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    Thanks,
    I am only new to integration and thought I was expected to use the product/part rule for integration
    Thanks for your help
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  4. #4
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    Can I see how to do it all by parts please?
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