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Resolución de integrales/ 6*x-2/ 1/(x^2+6*x-2)

Integral de 1/(x^2+6*x-2) dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  2                
  /                
 |                 
 |       1         
 |  ------------ dx
 |   2             
 |  x  + 6*x - 2   
 |                 
/                  
1
∫121(x2+6x)−2 dx\int\limits_{1}^{2} \frac{1}{\left(x^{2} + 6 x\right) - 2}\, dx 
Integral(1/(x^2 + 6*x - 2), (x, 1, 2))
Respuesta (Indefinida) [src] 
                         //             /  ____        \                    \
                         ||   ____      |\/ 11 *(3 + x)|                    |
                         ||-\/ 11 *acoth|--------------|                    |
  /                      ||             \      11      /              2     |
 |                       ||------------------------------  for (3 + x)  > 11|
 |      1                ||              11                                 |
 | ------------ dx = C + |<                                                 |
 |  2                    ||             /  ____        \                    |
 | x  + 6*x - 2          ||   ____      |\/ 11 *(3 + x)|                    |
 |                       ||-\/ 11 *atanh|--------------|                    |
/                        ||             \      11      /              2     |
                         ||------------------------------  for (3 + x)  < 11|
                         \\              11                                 /
∫1(x2+6x)−2 dx=C+{−11acoth⁡(11(x+3)11)11for (x+3)2>11−11atanh⁡(11(x+3)11)11for (x+3)2<11\int \frac{1}{\left(x^{2} + 6 x\right) - 2}\, dx = C + \begin{cases} - \frac{\sqrt{11} \operatorname{acoth}{\left(\frac{\sqrt{11} \left(x + 3\right)}{11} \right)}}{11} & \text{for}\: \left(x + 3\right)^{2} > 11 \\- \frac{\sqrt{11} \operatorname{atanh}{\left(\frac{\sqrt{11} \left(x + 3\right)}{11} \right)}}{11} & \text{for}\: \left(x + 3\right)^{2} < 11 \end{cases}
Simplificar
Gráfica
1.002.001.101.201.301.401.501.601.701.801.900.5-0.5
Trazar el gráfico f(x)
Respuesta [src] 
    ____    /      ____\     ____    /      ____\     ____    /      ____\     ____    /      ____\
  \/ 11 *log\4 - \/ 11 /   \/ 11 *log\5 + \/ 11 /   \/ 11 *log\4 + \/ 11 /   \/ 11 *log\5 - \/ 11 /
- ---------------------- - ---------------------- + ---------------------- + ----------------------
            22                       22                       22                       22
−11log⁡(11+5)22−11log⁡(4−11)22+11log⁡(5−11)22+11log⁡(11+4)22- \frac{\sqrt{11} \log{\left(\sqrt{11} + 5 \right)}}{22} - \frac{\sqrt{11} \log{\left(4 - \sqrt{11} \right)}}{22} + \frac{\sqrt{11} \log{\left(5 - \sqrt{11} \right)}}{22} + \frac{\sqrt{11} \log{\left(\sqrt{11} + 4 \right)}}{22} 
=
= 
    ____    /      ____\     ____    /      ____\     ____    /      ____\     ____    /      ____\
  \/ 11 *log\4 - \/ 11 /   \/ 11 *log\5 + \/ 11 /   \/ 11 *log\4 + \/ 11 /   \/ 11 *log\5 - \/ 11 /
- ---------------------- - ---------------------- + ---------------------- + ----------------------
            22                       22                       22                       22
−11log⁡(11+5)22−11log⁡(4−11)22+11log⁡(5−11)22+11log⁡(11+4)22- \frac{\sqrt{11} \log{\left(\sqrt{11} + 5 \right)}}{22} - \frac{\sqrt{11} \log{\left(4 - \sqrt{11} \right)}}{22} + \frac{\sqrt{11} \log{\left(5 - \sqrt{11} \right)}}{22} + \frac{\sqrt{11} \log{\left(\sqrt{11} + 4 \right)}}{22} 
-sqrt(11)*log(4 - sqrt(11))/22 - sqrt(11)*log(5 + sqrt(11))/22 + sqrt(11)*log(4 + sqrt(11))/22 + sqrt(11)*log(5 - sqrt(11))/22
Respuesta numérica [src] 
0.116595141798677
0.116595141798677

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

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