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x/(x^2-x-3)
Solving integrals/ x/(x^2-x-3)

Integral of x/(x^2-x-3) dx

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The solution

You have entered [src] 
  1              
  /              
 |               
 |      x        
 |  ---------- dx
 |   2           
 |  x  - x - 3   
 |               
/                
0
$$\int\limits_{0}^{1} \frac{x}{x^{2} - x - 3}\, dx$$ 
Integral(x/(x^2 - x - 1*3), (x, 0, 1))
The answer (Indefinite) [src] 
                                                 /     /            ____\      /            ____\\
  /                                         ____ |     |  1       \/ 13 |      |  1       \/ 13 ||
 |                        /      2    \   \/ 13 *|- log|- - + x + ------| + log|- - + x - ------||
 |     x               log\-3 + x  - x/          \     \  2         2   /      \  2         2   //
 | ---------- dx = C + ---------------- + --------------------------------------------------------
 |  2                         2                                      26                           
 | x  - x - 3                                                                                     
 |                                                                                                
/
$$\int \frac{x}{x^{2} - x - 3}\, dx = C + \frac{\sqrt{13} \left(- \log{\left(x - \frac{1}{2} + \frac{\sqrt{13}}{2} \right)} + \log{\left(x - \frac{\sqrt{13}}{2} - \frac{1}{2} \right)}\right)}{26} + \frac{\log{\left(x^{2} - x - 3 \right)}}{2}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
/      ____\    /      ____\   /      ____\ /          /        ____\\   /      ____\    /        ____\   /      ____\ /          /      ____\\
|1   \/ 13 |    |1   \/ 13 |   |1   \/ 13 | |          |  1   \/ 13 ||   |1   \/ 13 |    |  1   \/ 13 |   |1   \/ 13 | |          |1   \/ 13 ||
|- - ------|*log|- + ------| + |- + ------|*|pi*I + log|- - + ------|| - |- - ------|*log|- - + ------| - |- + ------|*|pi*I + log|- + ------||
\2     26  /    \2     2   /   \2     26  / \          \  2     2   //   \2     26  /    \  2     2   /   \2     26  / \          \2     2   //
$$- \left(\frac{1}{2} - \frac{\sqrt{13}}{26}\right) \log{\left(- \frac{1}{2} + \frac{\sqrt{13}}{2} \right)} + \left(\frac{1}{2} - \frac{\sqrt{13}}{26}\right) \log{\left(\frac{1}{2} + \frac{\sqrt{13}}{2} \right)} - \left(\frac{\sqrt{13}}{26} + \frac{1}{2}\right) \left(\log{\left(\frac{1}{2} + \frac{\sqrt{13}}{2} \right)} + i \pi\right) + \left(\frac{\sqrt{13}}{26} + \frac{1}{2}\right) \left(\log{\left(- \frac{1}{2} + \frac{\sqrt{13}}{2} \right)} + i \pi\right)$$ 
=
= 
/      ____\    /      ____\   /      ____\ /          /        ____\\   /      ____\    /        ____\   /      ____\ /          /      ____\\
|1   \/ 13 |    |1   \/ 13 |   |1   \/ 13 | |          |  1   \/ 13 ||   |1   \/ 13 |    |  1   \/ 13 |   |1   \/ 13 | |          |1   \/ 13 ||
|- - ------|*log|- + ------| + |- + ------|*|pi*I + log|- - + ------|| - |- - ------|*log|- - + ------| - |- + ------|*|pi*I + log|- + ------||
\2     26  /    \2     2   /   \2     26  / \          \  2     2   //   \2     26  /    \  2     2   /   \2     26  / \          \2     2   //
$$- \left(\frac{1}{2} - \frac{\sqrt{13}}{26}\right) \log{\left(- \frac{1}{2} + \frac{\sqrt{13}}{2} \right)} + \left(\frac{1}{2} - \frac{\sqrt{13}}{26}\right) \log{\left(\frac{1}{2} + \frac{\sqrt{13}}{2} \right)} - \left(\frac{\sqrt{13}}{26} + \frac{1}{2}\right) \left(\log{\left(\frac{1}{2} + \frac{\sqrt{13}}{2} \right)} + i \pi\right) + \left(\frac{\sqrt{13}}{26} + \frac{1}{2}\right) \left(\log{\left(- \frac{1}{2} + \frac{\sqrt{13}}{2} \right)} + i \pi\right)$$
Упростить
Numerical answer [src] 
-0.157983635931898
-0.157983635931898
The graph
Integral of x/(x^2-x-3) dx

    Use the examples entering the upper and lower limits of integration.

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