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Math Help - Integration using Hyperbolic

  1. #1
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    Integration using Hyperbolic

    \int \frac{x}{\sqrt{x^2+4x}} dx<br />
    use substitution x+2=2cosh\theta

    \int \frac{x}{\sqrt{(x+2)^2-4}} dx

    \int \frac{x}{\sqrt{(2cosh\theta)^2-4}} dx

    \int \frac{x}{\sqrt{(4cosh^2\theta)-4}} dx

    \int \frac{x}{2\sqrt{(cosh^2\theta)-1}} dx

    \int \frac{(2cosh\theta-2)2sinh\theta}{2sinh\theta} d\theta

    \int 2cosh\theta-2 d\theta

    = 2sinh\theta -2\theta + C

    but it doesnt seem right.

    where did i go wrong?

    thanks.
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  2. #2
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    Seems good to me. But is difficult to get \theta =f(x).
    May be more simple is

    <br />
\int \frac{(x+2)-2}{\sqrt{(x+2)^2-4}} dx=\int \frac{x+2}{\sqrt{(x+2)^2-4}} dx-\int \frac{2}{\sqrt{(x+2)^2-4}} dx<br />
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  3. #3
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    Looks wrong to me.
    http://www.wolframalpha.com/input/?i=intg+%28x%29%2F%28x^2%2B4x%29^0.5+0+to+1
    \int \frac{x}{\sqrt{x^2+4x}} dx
    this gives 0.311

    \int 2cosh\theta-2 d\theta
    this gives 0.350

    someone help?

    thanks
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  4. #4
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