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Math Help - Radical-integral

  1. #1
    Super Member dhiab's Avatar
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    Radical-integral

    Calculate :
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  2. #2
    o_O
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    By rationalizing: \frac{x}{x + \sqrt{x^2 - 1}} \cdot {\color{red} \frac{x-\sqrt{x^2 - 1}}{x - \sqrt{x^2-1}}} = \frac{x^2 - x\sqrt{x^2-1}}{x^2 - x^2 + 1} = x^2 - x\sqrt{x^2-1}

    Therefore, your problem is equivalent to: 2\int \left(x^2 - x\sqrt{x^2-1}\right)dx

    The first term is simple. The second one can be done with a u-sub: u = x^2 - 1 \ \Rightarrow \ du = 2x dx
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