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Resolución de integrales/ (2*x*x-5)/(x*x*x*x-5*x*x+6)

Integral de (2*x*x-5)/(x*x*x*x-5*x*x+6) dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  1                       
  /                       
 |                        
 |       2*x*x - 5        
 |  ------------------- dx
 |  x*x*x*x - 5*x*x + 6   
 |                        
/                         
0
$$\int\limits_{0}^{1} \frac{x 2 x - 5}{\left(- x 5 x + x x x x\right) + 6}\, dx$$ 
Integral(((2*x)*x - 5)/(((x*x)*x)*x - 5*x*x + 6), (x, 0, 1))
Respuesta (Indefinida) [src] 
                                //            /    ___\             \   //            /    ___\             \
                                ||   ___      |x*\/ 2 |             |   ||   ___      |x*\/ 3 |             |
                                ||-\/ 2 *acoth|-------|             |   ||-\/ 3 *acoth|-------|             |
  /                             ||            \   2   /        2    |   ||            \   3   /        2    |
 |                              ||----------------------  for x  > 2|   ||----------------------  for x  > 3|
 |      2*x*x - 5               ||          2                       |   ||          3                       |
 | ------------------- dx = C + |<                                  | + |<                                  |
 | x*x*x*x - 5*x*x + 6          ||            /    ___\             |   ||            /    ___\             |
 |                              ||   ___      |x*\/ 2 |             |   ||   ___      |x*\/ 3 |             |
/                               ||-\/ 2 *atanh|-------|             |   ||-\/ 3 *atanh|-------|             |
                                ||            \   2   /        2    |   ||            \   3   /        2    |
                                ||----------------------  for x  < 2|   ||----------------------  for x  < 3|
                                \\          2                       /   \\          3                       /
$$\int \frac{x 2 x - 5}{\left(- x 5 x + x x x x\right) + 6}\, dx = C + \begin{cases} - \frac{\sqrt{2} \operatorname{acoth}{\left(\frac{\sqrt{2} x}{2} \right)}}{2} & \text{for}\: x^{2} > 2 \\- \frac{\sqrt{2} \operatorname{atanh}{\left(\frac{\sqrt{2} x}{2} \right)}}{2} & \text{for}\: x^{2} < 2 \end{cases} + \begin{cases} - \frac{\sqrt{3} \operatorname{acoth}{\left(\frac{\sqrt{3} x}{3} \right)}}{3} & \text{for}\: x^{2} > 3 \\- \frac{\sqrt{3} \operatorname{atanh}{\left(\frac{\sqrt{3} x}{3} \right)}}{3} & \text{for}\: x^{2} < 3 \end{cases}$$
Simplificar
Gráfica
Trazar el gráfico f(x)
Respuesta [src] 
    ___ /          /  ___\\     ___    /      ___\     ___ /          /  ___\\     ___    /      ___\     ___ /          /       ___\\     ___    /  ___\     ___ /          /       ___\\     ___    /  ___\
  \/ 2 *\pi*I + log\\/ 2 //   \/ 2 *log\1 + \/ 2 /   \/ 3 *\pi*I + log\\/ 3 //   \/ 3 *log\1 + \/ 3 /   \/ 2 *\pi*I + log\-1 + \/ 2 //   \/ 2 *log\\/ 2 /   \/ 3 *\pi*I + log\-1 + \/ 3 //   \/ 3 *log\\/ 3 /
- ------------------------- - -------------------- - ------------------------- - -------------------- + ------------------------------ + ---------------- + ------------------------------ + ----------------
              4                        4                         6                        6                           4                         4                         6                         6
$$- \frac{\sqrt{2} \log{\left(1 + \sqrt{2} \right)}}{4} - \frac{\sqrt{3} \log{\left(1 + \sqrt{3} \right)}}{6} + \frac{\sqrt{2} \log{\left(\sqrt{2} \right)}}{4} + \frac{\sqrt{3} \log{\left(\sqrt{3} \right)}}{6} - \frac{\sqrt{2} \left(\log{\left(\sqrt{2} \right)} + i \pi\right)}{4} - \frac{\sqrt{3} \left(\log{\left(\sqrt{3} \right)} + i \pi\right)}{6} + \frac{\sqrt{3} \left(\log{\left(-1 + \sqrt{3} \right)} + i \pi\right)}{6} + \frac{\sqrt{2} \left(\log{\left(-1 + \sqrt{2} \right)} + i \pi\right)}{4}$$ 
=
= 
    ___ /          /  ___\\     ___    /      ___\     ___ /          /  ___\\     ___    /      ___\     ___ /          /       ___\\     ___    /  ___\     ___ /          /       ___\\     ___    /  ___\
  \/ 2 *\pi*I + log\\/ 2 //   \/ 2 *log\1 + \/ 2 /   \/ 3 *\pi*I + log\\/ 3 //   \/ 3 *log\1 + \/ 3 /   \/ 2 *\pi*I + log\-1 + \/ 2 //   \/ 2 *log\\/ 2 /   \/ 3 *\pi*I + log\-1 + \/ 3 //   \/ 3 *log\\/ 3 /
- ------------------------- - -------------------- - ------------------------- - -------------------- + ------------------------------ + ---------------- + ------------------------------ + ----------------
              4                        4                         6                        6                           4                         4                         6                         6
$$- \frac{\sqrt{2} \log{\left(1 + \sqrt{2} \right)}}{4} - \frac{\sqrt{3} \log{\left(1 + \sqrt{3} \right)}}{6} + \frac{\sqrt{2} \log{\left(\sqrt{2} \right)}}{4} + \frac{\sqrt{3} \log{\left(\sqrt{3} \right)}}{6} - \frac{\sqrt{2} \left(\log{\left(\sqrt{2} \right)} + i \pi\right)}{4} - \frac{\sqrt{3} \left(\log{\left(\sqrt{3} \right)} + i \pi\right)}{6} + \frac{\sqrt{3} \left(\log{\left(-1 + \sqrt{3} \right)} + i \pi\right)}{6} + \frac{\sqrt{2} \left(\log{\left(-1 + \sqrt{2} \right)} + i \pi\right)}{4}$$ 
-sqrt(2)*(pi*i + log(sqrt(2)))/4 - sqrt(2)*log(1 + sqrt(2))/4 - sqrt(3)*(pi*i + log(sqrt(3)))/6 - sqrt(3)*log(1 + sqrt(3))/6 + sqrt(2)*(pi*i + log(-1 + sqrt(2)))/4 + sqrt(2)*log(sqrt(2))/4 + sqrt(3)*(pi*i + log(-1 + sqrt(3)))/6 + sqrt(3)*log(sqrt(3))/6
Respuesta numérica [src] 
-1.0033982382907
-1.0033982382907

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

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