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Math Help - Determine the value of the definate integral

  1. #1
    Junior Member bijosn's Avatar
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    Determine the value of the definate integral

    I = \displaystyle \int_0^{1} \frac{du}{(1+u^2)(1+u)}
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  2. #2
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    Partial Fractions works nicely if you use \displaystyle \frac{Au + B}{1 + u^2} + \frac{C}{1 + u}.

    Once you have the partial fractions, then the first fraction you will need to break up as \displaystyle \frac{Au}{1 + u^2} + \frac{B}{1 + u^2}, the first of which is integrated with substitution, the second is an arctan integral.
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  3. #3
    Member Pranas's Avatar
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    Quote Originally Posted by bijosn View Post
    I = \displaystyle \int_0^{1} \frac{du}{(1+u^2)(1+u)}
    \displaystyle \[\frac{1}{2}\int\limits_0^1 {\left( {\frac{1}{{1 + {u^2}}} - \frac{u}{{1 + {u^2}}} + \frac{1}{{1 + u}}} \right)du} \]

    Partial fraction - Wikipedia, the free encyclopedia
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