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Resolución de integrales/ -12*x/ x^2-1/ dx/(x^2-12*x-3)

Integral de dx/(x^2-12*x-3) dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  1                 
  /                 
 |                  
 |        1         
 |  ------------- dx
 |   2              
 |  x  - 12*x - 3   
 |                  
/                   
0
$$\int\limits_{0}^{1} \frac{1}{\left(x^{2} - 12 x\right) - 3}\, dx$$ 
Integral(1/(x^2 - 12*x - 3), (x, 0, 1))
Respuesta (Indefinida) [src] 
                          //             /  ____         \                     \
                          ||   ____      |\/ 39 *(-6 + x)|                     |
                          ||-\/ 39 *acoth|---------------|                     |
  /                       ||             \       39      /               2     |
 |                        ||-------------------------------  for (-6 + x)  > 39|
 |       1                ||               39                                  |
 | ------------- dx = C + |<                                                   |
 |  2                     ||             /  ____         \                     |
 | x  - 12*x - 3          ||   ____      |\/ 39 *(-6 + x)|                     |
 |                        ||-\/ 39 *atanh|---------------|                     |
/                         ||             \       39      /               2     |
                          ||-------------------------------  for (-6 + x)  < 39|
                          \\               39                                  /
$$\int \frac{1}{\left(x^{2} - 12 x\right) - 3}\, dx = C + \begin{cases} - \frac{\sqrt{39} \operatorname{acoth}{\left(\frac{\sqrt{39} \left(x - 6\right)}{39} \right)}}{39} & \text{for}\: \left(x - 6\right)^{2} > 39 \\- \frac{\sqrt{39} \operatorname{atanh}{\left(\frac{\sqrt{39} \left(x - 6\right)}{39} \right)}}{39} & \text{for}\: \left(x - 6\right)^{2} < 39 \end{cases}$$
Simplificar
Gráfica
Trazar el gráfico f(x)
Respuesta [src] 
    ____ /          /      ____\\     ____    /       ____\     ____ /          /      ____\\     ____    /       ____\
  \/ 39 *\pi*I + log\6 + \/ 39 //   \/ 39 *log\-5 + \/ 39 /   \/ 39 *\pi*I + log\5 + \/ 39 //   \/ 39 *log\-6 + \/ 39 /
- ------------------------------- - ----------------------- + ------------------------------- + -----------------------
                 78                            78                            78                            78
$$\frac{\sqrt{39} \log{\left(-6 + \sqrt{39} \right)}}{78} - \frac{\sqrt{39} \log{\left(-5 + \sqrt{39} \right)}}{78} - \frac{\sqrt{39} \left(\log{\left(6 + \sqrt{39} \right)} + i \pi\right)}{78} + \frac{\sqrt{39} \left(\log{\left(5 + \sqrt{39} \right)} + i \pi\right)}{78}$$ 
=
= 
    ____ /          /      ____\\     ____    /       ____\     ____ /          /      ____\\     ____    /       ____\
  \/ 39 *\pi*I + log\6 + \/ 39 //   \/ 39 *log\-5 + \/ 39 /   \/ 39 *\pi*I + log\5 + \/ 39 //   \/ 39 *log\-6 + \/ 39 /
- ------------------------------- - ----------------------- + ------------------------------- + -----------------------
                 78                            78                            78                            78
$$\frac{\sqrt{39} \log{\left(-6 + \sqrt{39} \right)}}{78} - \frac{\sqrt{39} \log{\left(-5 + \sqrt{39} \right)}}{78} - \frac{\sqrt{39} \left(\log{\left(6 + \sqrt{39} \right)} + i \pi\right)}{78} + \frac{\sqrt{39} \left(\log{\left(5 + \sqrt{39} \right)} + i \pi\right)}{78}$$ 
-sqrt(39)*(pi*i + log(6 + sqrt(39)))/78 - sqrt(39)*log(-5 + sqrt(39))/78 + sqrt(39)*(pi*i + log(5 + sqrt(39)))/78 + sqrt(39)*log(-6 + sqrt(39))/78
Respuesta numérica [src] 
-0.136976287297817
-0.136976287297817

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

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