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Resolución de integrales/ x^2-9/ (x^2-8)/ (x^2-9)/(x^2-8)

Integral de (x^2-9)/(x^2-8) dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  1          
  /          
 |           
 |   2       
 |  x  - 9   
 |  ------ dx
 |   2       
 |  x  - 8   
 |           
/            
0
$$\int\limits_{0}^{1} \frac{x^{2} - 9}{x^{2} - 8}\, dx$$ 
Integral((x^2 - 9)/(x^2 - 8), (x, 0, 1))
Respuesta (Indefinida) [src] 
                       //            /    ___\             \
                       ||   ___      |x*\/ 2 |             |
  /                    ||-\/ 2 *acoth|-------|             |
 |                     ||            \   4   /        2    |
 |  2                  ||----------------------  for x  > 8|
 | x  - 9              ||          4                       |
 | ------ dx = C + x - |<                                  |
 |  2                  ||            /    ___\             |
 | x  - 8              ||   ___      |x*\/ 2 |             |
 |                     ||-\/ 2 *atanh|-------|             |
/                      ||            \   4   /        2    |
                       ||----------------------  for x  < 8|
                       \\          4                       /
$$\int \frac{x^{2} - 9}{x^{2} - 8}\, dx = C + x - \begin{cases} - \frac{\sqrt{2} \operatorname{acoth}{\left(\frac{\sqrt{2} x}{4} \right)}}{4} & \text{for}\: x^{2} > 8 \\- \frac{\sqrt{2} \operatorname{atanh}{\left(\frac{\sqrt{2} x}{4} \right)}}{4} & \text{for}\: x^{2} < 8 \end{cases}$$
Simplificar
Gráfica
Trazar el gráfico f(x)
Respuesta [src] 
      ___ /          /         ___\\     ___    /    ___\     ___ /          /    ___\\     ___    /        ___\
    \/ 2 *\pi*I + log\-1 + 2*\/ 2 //   \/ 2 *log\2*\/ 2 /   \/ 2 *\pi*I + log\2*\/ 2 //   \/ 2 *log\1 + 2*\/ 2 /
1 - -------------------------------- - ------------------ + --------------------------- + ----------------------
                   8                           8                         8                          8
$$- \frac{\sqrt{2} \log{\left(2 \sqrt{2} \right)}}{8} + \frac{\sqrt{2} \log{\left(1 + 2 \sqrt{2} \right)}}{8} + 1 - \frac{\sqrt{2} \left(\log{\left(-1 + 2 \sqrt{2} \right)} + i \pi\right)}{8} + \frac{\sqrt{2} \left(\log{\left(2 \sqrt{2} \right)} + i \pi\right)}{8}$$ 
=
= 
      ___ /          /         ___\\     ___    /    ___\     ___ /          /    ___\\     ___    /        ___\
    \/ 2 *\pi*I + log\-1 + 2*\/ 2 //   \/ 2 *log\2*\/ 2 /   \/ 2 *\pi*I + log\2*\/ 2 //   \/ 2 *log\1 + 2*\/ 2 /
1 - -------------------------------- - ------------------ + --------------------------- + ----------------------
                   8                           8                         8                          8
$$- \frac{\sqrt{2} \log{\left(2 \sqrt{2} \right)}}{8} + \frac{\sqrt{2} \log{\left(1 + 2 \sqrt{2} \right)}}{8} + 1 - \frac{\sqrt{2} \left(\log{\left(-1 + 2 \sqrt{2} \right)} + i \pi\right)}{8} + \frac{\sqrt{2} \left(\log{\left(2 \sqrt{2} \right)} + i \pi\right)}{8}$$ 
1 - sqrt(2)*(pi*i + log(-1 + 2*sqrt(2)))/8 - sqrt(2)*log(2*sqrt(2))/8 + sqrt(2)*(pi*i + log(2*sqrt(2)))/8 + sqrt(2)*log(1 + 2*sqrt(2))/8
Respuesta numérica [src] 
1.13063761434512
1.13063761434512

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

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