# Thread: Determine the value of the definate integral

1. ## Determine the value of the definate integral

$I = \displaystyle \int_0^{1} \frac{du}{(1+u^2)(1+u)}$

2. 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.

3. Originally Posted by bijosn
$I = \displaystyle \int_0^{1} \frac{du}{(1+u^2)(1+u)}$
$\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}$$

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