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Math Help - Help with integration

  1. #1
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    Help with integration

    I supposed to integrate (x^2 + x)^(1/2).
    I do it this way

    int (x^2 + x)^(1/2) = x(x^2 + x)^(1/2) - 1/2* int (x(2x + 1))/(x^2 + x)^(1/2) = x (x^2 + x)^(1/2) - 1/2((xln(x^2 +x)) - ln(x^2 + x))

    IF u now take 2pi ((x = 1) - (x = 0)) u are supposed to get
    pi(6(2)^(1/2) - ln(3 + 2(2)^(1/2)) / 4


    And i dont get it, so i wonder what im doing wrong.
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  2. #2
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    Quote Originally Posted by nisse pisse View Post
    I supposed to integrate (x^2 + x)^(1/2).
    (Say that we are integrating on the positive real line).

    \int (x^2+x)^{1/2}dx = \int \frac{2x(x+1)^{1/2}}{2\sqrt{x}}dx
    Let t=\sqrt{x}\implies t' = \frac{1}{2\sqrt{x}} and so,
    \int 2t^2 \sqrt{t^2+1}dt

    Can you finish this?
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  3. #3
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    Now i get 2*(((t^3)/3)*(t^2 + 1)^(1/2)) - (int) (((t^4)/3) * (1/(t^2 + 1)^(1/2)) = 2*(((t^3)/3)*(t^2 + 1)^(1/2)) - ((((t^4)/3) * ln(t + (t^2 + 1)^(1/2))) - (int) (4t/3)*ln(t + (t^2 + 1)^(1/2)))
    I dont see where to go from my last step, becuse i dont the int of
    ln(t + (t^2 + 1)^(1/2))and there got to be an easier way than finding out.
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  4. #4
    Super Member angel.white's Avatar
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    Quote Originally Posted by ThePerfectHacker View Post
    (Say that we are integrating on the positive real line).

    \int (x^2+x)^{1/2}dx = \int \frac{2x(x+1)^{1/2}}{2\sqrt{x}}dx
    Let t=\sqrt{x}\implies t' = \frac{1}{2\sqrt{x}} and so,
    \int 2t^2 \sqrt{t^2+1}dt

    Can you finish this?
    Wow, I really liked that. That was much more elegant that what I would have done.
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  5. #5
    Math Engineering Student
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    But there's no way to avoid a trig. sub. here. You're gonna have to apply it yes or yes. (Integration by parts might work.)
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