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Resolución de integrales/ x^2-2/ 2-2*x/ dx/(x^2-2*x-4)

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

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  1                
  /                
 |                 
 |       1         
 |  ------------ dx
 |   2             
 |  x  - 2*x - 4   
 |                 
/                  
0
∫011(x2−2x)−4 dx\int\limits_{0}^{1} \frac{1}{\left(x^{2} - 2 x\right) - 4}\, dx 
Integral(1/(x^2 - 2*x - 4), (x, 0, 1))
Respuesta (Indefinida) [src] 
                         //            /  ___         \                    \
                         ||   ___      |\/ 5 *(-1 + x)|                    |
                         ||-\/ 5 *acoth|--------------|                    |
  /                      ||            \      5       /               2    |
 |                       ||-----------------------------  for (-1 + x)  > 5|
 |      1                ||              5                                 |
 | ------------ dx = C + |<                                                |
 |  2                    ||            /  ___         \                    |
 | x  - 2*x - 4          ||   ___      |\/ 5 *(-1 + x)|                    |
 |                       ||-\/ 5 *atanh|--------------|                    |
/                        ||            \      5       /               2    |
                         ||-----------------------------  for (-1 + x)  < 5|
                         \\              5                                 /
∫1(x2−2x)−4 dx=C+{−5acoth⁡(5(x−1)5)5for (x−1)2>5−5atanh⁡(5(x−1)5)5for (x−1)2<5\int \frac{1}{\left(x^{2} - 2 x\right) - 4}\, dx = C + \begin{cases} - \frac{\sqrt{5} \operatorname{acoth}{\left(\frac{\sqrt{5} \left(x - 1\right)}{5} \right)}}{5} & \text{for}\: \left(x - 1\right)^{2} > 5 \\- \frac{\sqrt{5} \operatorname{atanh}{\left(\frac{\sqrt{5} \left(x - 1\right)}{5} \right)}}{5} & \text{for}\: \left(x - 1\right)^{2} < 5 \end{cases}
Simplificar
Gráfica
0.001.000.100.200.300.400.500.600.700.800.90-0.30-0.15
Trazar el gráfico f(x)
Respuesta [src] 
    ___ /          /      ___\\     ___    /  ___\     ___ /          /  ___\\     ___    /       ___\
  \/ 5 *\pi*I + log\1 + \/ 5 //   \/ 5 *log\\/ 5 /   \/ 5 *\pi*I + log\\/ 5 //   \/ 5 *log\-1 + \/ 5 /
- ----------------------------- - ---------------- + ------------------------- + ---------------------
                10                       10                      10                        10
−5log⁡(5)10+5log⁡(−1+5)10−5(log⁡(1+5)+iπ)10+5(log⁡(5)+iπ)10- \frac{\sqrt{5} \log{\left(\sqrt{5} \right)}}{10} + \frac{\sqrt{5} \log{\left(-1 + \sqrt{5} \right)}}{10} - \frac{\sqrt{5} \left(\log{\left(1 + \sqrt{5} \right)} + i \pi\right)}{10} + \frac{\sqrt{5} \left(\log{\left(\sqrt{5} \right)} + i \pi\right)}{10} 
=
= 
    ___ /          /      ___\\     ___    /  ___\     ___ /          /  ___\\     ___    /       ___\
  \/ 5 *\pi*I + log\1 + \/ 5 //   \/ 5 *log\\/ 5 /   \/ 5 *\pi*I + log\\/ 5 //   \/ 5 *log\-1 + \/ 5 /
- ----------------------------- - ---------------- + ------------------------- + ---------------------
                10                       10                      10                        10
−5log⁡(5)10+5log⁡(−1+5)10−5(log⁡(1+5)+iπ)10+5(log⁡(5)+iπ)10- \frac{\sqrt{5} \log{\left(\sqrt{5} \right)}}{10} + \frac{\sqrt{5} \log{\left(-1 + \sqrt{5} \right)}}{10} - \frac{\sqrt{5} \left(\log{\left(1 + \sqrt{5} \right)} + i \pi\right)}{10} + \frac{\sqrt{5} \left(\log{\left(\sqrt{5} \right)} + i \pi\right)}{10} 
-sqrt(5)*(pi*i + log(1 + sqrt(5)))/10 - sqrt(5)*log(sqrt(5))/10 + sqrt(5)*(pi*i + log(sqrt(5)))/10 + sqrt(5)*log(-1 + sqrt(5))/10
Respuesta numérica [src] 
-0.215204470482002
-0.215204470482002

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

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