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Integral de 1/(x^2-4x-4) dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src]
  1                
  /                
 |                 
 |       1         
 |  ------------ dx
 |   2             
 |  x  - 4*x - 4   
 |                 
/                  
0                  
$$\int\limits_{0}^{1} \frac{1}{\left(x^{2} - 4 x\right) - 4}\, dx$$
Integral(1/(x^2 - 4*x - 4), (x, 0, 1))
Respuesta (Indefinida) [src]
                         //            /  ___         \                    \
                         ||   ___      |\/ 2 *(-2 + x)|                    |
                         ||-\/ 2 *acoth|--------------|                    |
  /                      ||            \      4       /               2    |
 |                       ||-----------------------------  for (-2 + x)  > 8|
 |      1                ||              4                                 |
 | ------------ dx = C + |<                                                |
 |  2                    ||            /  ___         \                    |
 | x  - 4*x - 4          ||   ___      |\/ 2 *(-2 + x)|                    |
 |                       ||-\/ 2 *atanh|--------------|                    |
/                        ||            \      4       /               2    |
                         ||-----------------------------  for (-2 + x)  < 8|
                         \\              4                                 /
$$\int \frac{1}{\left(x^{2} - 4 x\right) - 4}\, dx = C + \begin{cases} - \frac{\sqrt{2} \operatorname{acoth}{\left(\frac{\sqrt{2} \left(x - 2\right)}{4} \right)}}{4} & \text{for}\: \left(x - 2\right)^{2} > 8 \\- \frac{\sqrt{2} \operatorname{atanh}{\left(\frac{\sqrt{2} \left(x - 2\right)}{4} \right)}}{4} & \text{for}\: \left(x - 2\right)^{2} < 8 \end{cases}$$
Gráfica
Respuesta [src]
    ___ /          /        ___\\     ___    /         ___\     ___ /          /        ___\\     ___    /         ___\
  \/ 2 *\pi*I + log\2 + 2*\/ 2 //   \/ 2 *log\-1 + 2*\/ 2 /   \/ 2 *\pi*I + log\1 + 2*\/ 2 //   \/ 2 *log\-2 + 2*\/ 2 /
- ------------------------------- - ----------------------- + ------------------------------- + -----------------------
                 8                             8                             8                             8           
$$- \frac{\sqrt{2} \log{\left(-1 + 2 \sqrt{2} \right)}}{8} + \frac{\sqrt{2} \log{\left(-2 + 2 \sqrt{2} \right)}}{8} - \frac{\sqrt{2} \left(\log{\left(2 + 2 \sqrt{2} \right)} + i \pi\right)}{8} + \frac{\sqrt{2} \left(\log{\left(1 + 2 \sqrt{2} \right)} + i \pi\right)}{8}$$
=
=
    ___ /          /        ___\\     ___    /         ___\     ___ /          /        ___\\     ___    /         ___\
  \/ 2 *\pi*I + log\2 + 2*\/ 2 //   \/ 2 *log\-1 + 2*\/ 2 /   \/ 2 *\pi*I + log\1 + 2*\/ 2 //   \/ 2 *log\-2 + 2*\/ 2 /
- ------------------------------- - ----------------------- + ------------------------------- + -----------------------
                 8                             8                             8                             8           
$$- \frac{\sqrt{2} \log{\left(-1 + 2 \sqrt{2} \right)}}{8} + \frac{\sqrt{2} \log{\left(-2 + 2 \sqrt{2} \right)}}{8} - \frac{\sqrt{2} \left(\log{\left(2 + 2 \sqrt{2} \right)} + i \pi\right)}{8} + \frac{\sqrt{2} \left(\log{\left(1 + 2 \sqrt{2} \right)} + i \pi\right)}{8}$$
-sqrt(2)*(pi*i + log(2 + 2*sqrt(2)))/8 - sqrt(2)*log(-1 + 2*sqrt(2))/8 + sqrt(2)*(pi*i + log(1 + 2*sqrt(2)))/8 + sqrt(2)*log(-2 + 2*sqrt(2))/8
Respuesta numérica [src]
-0.180975005724995
-0.180975005724995

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