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Math Help - Indefinite integral?

  1. #1
    Newbie TrueToHeart's Avatar
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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)) + c but still don't get it. :S
    and


    (x+3)^7 (x-8x) dx
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  2. #2
    Senior Member Peritus's Avatar
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    Nov 2007
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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 />

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