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Resolución de integrales/ (x-5)/ x^(2)/ (x-5)/(-2x^(2)+x+4)

Integral de (x-5)/(-2x^(2)+x+4) dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  1                  
  /                  
 |                   
 |      x - 5        
 |  -------------- dx
 |       2           
 |  - 2*x  + x + 4   
 |                   
/                    
0
$$\int\limits_{0}^{1} \frac{x - 5}{\left(- 2 x^{2} + x\right) + 4}\, dx$$ 
Integral((x - 5)/(-2*x^2 + x + 4), (x, 0, 1))
Respuesta (Indefinida) [src] 
                              //             /    ____           \                       \                     
                              ||   ____      |4*\/ 33 *(-1/4 + x)|                       |                     
                              ||-\/ 33 *acoth|-------------------|                       |                     
  /                           ||             \         33        /                 2   33|                     
 |                            ||-----------------------------------  for (-1/4 + x)  > --|      /            2\
 |     x - 5                  ||                132                                    16|   log\-4 - x + 2*x /
 | -------------- dx = C + 38*|<                                                         | - ------------------
 |      2                     ||             /    ____           \                       |           4         
 | - 2*x  + x + 4             ||   ____      |4*\/ 33 *(-1/4 + x)|                       |                     
 |                            ||-\/ 33 *atanh|-------------------|                       |                     
/                             ||             \         33        /                 2   33|                     
                              ||-----------------------------------  for (-1/4 + x)  < --|                     
                              \\                132                                    16/
$$\int \frac{x - 5}{\left(- 2 x^{2} + x\right) + 4}\, dx = C + 38 \left(\begin{cases} - \frac{\sqrt{33} \operatorname{acoth}{\left(\frac{4 \sqrt{33} \left(x - \frac{1}{4}\right)}{33} \right)}}{132} & \text{for}\: \left(x - \frac{1}{4}\right)^{2} > \frac{33}{16} \\- \frac{\sqrt{33} \operatorname{atanh}{\left(\frac{4 \sqrt{33} \left(x - \frac{1}{4}\right)}{33} \right)}}{132} & \text{for}\: \left(x - \frac{1}{4}\right)^{2} < \frac{33}{16} \end{cases}\right) - \frac{\log{\left(2 x^{2} - x - 4 \right)}}{4}$$
Simplificar
Gráfica
Trazar el gráfico f(x)
Respuesta [src] 
/         ____\ /          /      ____\\   /         ____\    /        ____\   /         ____\ /          /        ____\\   /         ____\    /      ____\
|1   19*\/ 33 | |          |1   \/ 33 ||   |1   19*\/ 33 |    |  1   \/ 33 |   |1   19*\/ 33 | |          |  3   \/ 33 ||   |1   19*\/ 33 |    |3   \/ 33 |
|- - ---------|*|pi*I + log|- + ------|| + |- + ---------|*log|- - + ------| - |- - ---------|*|pi*I + log|- - + ------|| - |- + ---------|*log|- + ------|
\4      132   / \          \4     4   //   \4      132   /    \  4     4   /   \4      132   / \          \  4     4   //   \4      132   /    \4     4   /
$$- \left(\frac{1}{4} + \frac{19 \sqrt{33}}{132}\right) \log{\left(\frac{3}{4} + \frac{\sqrt{33}}{4} \right)} + \left(\frac{1}{4} + \frac{19 \sqrt{33}}{132}\right) \log{\left(- \frac{1}{4} + \frac{\sqrt{33}}{4} \right)} + \left(\frac{1}{4} - \frac{19 \sqrt{33}}{132}\right) \left(\log{\left(\frac{1}{4} + \frac{\sqrt{33}}{4} \right)} + i \pi\right) - \left(\frac{1}{4} - \frac{19 \sqrt{33}}{132}\right) \left(\log{\left(- \frac{3}{4} + \frac{\sqrt{33}}{4} \right)} + i \pi\right)$$ 
=
= 
/         ____\ /          /      ____\\   /         ____\    /        ____\   /         ____\ /          /        ____\\   /         ____\    /      ____\
|1   19*\/ 33 | |          |1   \/ 33 ||   |1   19*\/ 33 |    |  1   \/ 33 |   |1   19*\/ 33 | |          |  3   \/ 33 ||   |1   19*\/ 33 |    |3   \/ 33 |
|- - ---------|*|pi*I + log|- + ------|| + |- + ---------|*log|- - + ------| - |- - ---------|*|pi*I + log|- - + ------|| - |- + ---------|*log|- + ------|
\4      132   / \          \4     4   //   \4      132   /    \  4     4   /   \4      132   / \          \  4     4   //   \4      132   /    \4     4   /
$$- \left(\frac{1}{4} + \frac{19 \sqrt{33}}{132}\right) \log{\left(\frac{3}{4} + \frac{\sqrt{33}}{4} \right)} + \left(\frac{1}{4} + \frac{19 \sqrt{33}}{132}\right) \log{\left(- \frac{1}{4} + \frac{\sqrt{33}}{4} \right)} + \left(\frac{1}{4} - \frac{19 \sqrt{33}}{132}\right) \left(\log{\left(\frac{1}{4} + \frac{\sqrt{33}}{4} \right)} + i \pi\right) - \left(\frac{1}{4} - \frac{19 \sqrt{33}}{132}\right) \left(\log{\left(- \frac{3}{4} + \frac{\sqrt{33}}{4} \right)} + i \pi\right)$$ 
(1/4 - 19*sqrt(33)/132)*(pi*i + log(1/4 + sqrt(33)/4)) + (1/4 + 19*sqrt(33)/132)*log(-1/4 + sqrt(33)/4) - (1/4 - 19*sqrt(33)/132)*(pi*i + log(-3/4 + sqrt(33)/4)) - (1/4 + 19*sqrt(33)/132)*log(3/4 + sqrt(33)/4)
Respuesta numérica [src] 
-1.17710438704181
-1.17710438704181

    Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.

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