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Thread: Indefinite integral?

  1. February 15th 2008, 07:29 AM #1
    TrueToHeart
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    Indefinite integral?

    how do you evaluate the following indefinite integrals?

    (1 + √(2s-1)) /√(2s-1) ds


    i know the answer to this is 1/2(1+√(2s-1))² + c but still don't get it. :S
    and


    (x²+3)^7 (x³-8x) dx
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  2. February 15th 2008, 08:36 AM #2
    Peritus
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    \int {\frac{{1 + \sqrt {2s - 1} }}<br /> {{\sqrt {2s - 1} }}} ds = \int {1 + } \frac{1}<br /> {{\sqrt {2s - 1} }}ds = s + \left( {2s - 1} \right)^{{\raise0.7ex\hbox{$1$} \!\mathord{\left/<br /> {\vphantom {1 2}}\right.\kern-\nulldelimiterspace}<br /> \!\lower0.7ex\hbox{$2$}}} + C

    The answer is given in an equivalent form:

    0.5\left( {1 + \sqrt {2s - 1} } \right)^2 = 0.5\left( {1 + 2\sqrt {2s - 1} + 2s - 1} \right) = \sqrt {2s - 1} + s<br />

    (x²+3)^7 (x³-8x) dx
    I'm not sure how to understand this?
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