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

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

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  1                
  /                
 |                 
 |       1         
 |  ------------ dx
 |       2         
 |  2 - x  + 6*x   
 |                 
/                  
0
$$\int\limits_{0}^{1} \frac{1}{6 x + \left(2 - x^{2}\right)}\, dx$$ 
Integral(1/(2 - x^2 + 6*x), (x, 0, 1))
Respuesta (Indefinida) [src] 
                         //             /  ____         \                     \
                         ||   ____      |\/ 11 *(-3 + x)|                     |
                         ||-\/ 11 *acoth|---------------|                     |
  /                      ||             \       11      /               2     |
 |                       ||-------------------------------  for (-3 + x)  > 11|
 |      1                ||               11                                  |
 | ------------ dx = C - |<                                                   |
 |      2                ||             /  ____         \                     |
 | 2 - x  + 6*x          ||   ____      |\/ 11 *(-3 + x)|                     |
 |                       ||-\/ 11 *atanh|---------------|                     |
/                        ||             \       11      /               2     |
                         ||-------------------------------  for (-3 + x)  < 11|
                         \\               11                                  /
$$\int \frac{1}{6 x + \left(2 - x^{2}\right)}\, dx = C - \begin{cases} - \frac{\sqrt{11} \operatorname{acoth}{\left(\frac{\sqrt{11} \left(x - 3\right)}{11} \right)}}{11} & \text{for}\: \left(x - 3\right)^{2} > 11 \\- \frac{\sqrt{11} \operatorname{atanh}{\left(\frac{\sqrt{11} \left(x - 3\right)}{11} \right)}}{11} & \text{for}\: \left(x - 3\right)^{2} < 11 \end{cases}$$
Simplificar
Gráfica
Trazar el gráfico f(x)
Respuesta [src] 
    ____ /          /      ____\\     ____    /       ____\     ____ /          /      ____\\     ____    /       ____\
  \/ 11 *\pi*I + log\2 + \/ 11 //   \/ 11 *log\-3 + \/ 11 /   \/ 11 *\pi*I + log\3 + \/ 11 //   \/ 11 *log\-2 + \/ 11 /
- ------------------------------- - ----------------------- + ------------------------------- + -----------------------
                 22                            22                            22                            22
$$\frac{\sqrt{11} \log{\left(-2 + \sqrt{11} \right)}}{22} - \frac{\sqrt{11} \log{\left(-3 + \sqrt{11} \right)}}{22} - \frac{\sqrt{11} \left(\log{\left(2 + \sqrt{11} \right)} + i \pi\right)}{22} + \frac{\sqrt{11} \left(\log{\left(3 + \sqrt{11} \right)} + i \pi\right)}{22}$$ 
=
= 
    ____ /          /      ____\\     ____    /       ____\     ____ /          /      ____\\     ____    /       ____\
  \/ 11 *\pi*I + log\2 + \/ 11 //   \/ 11 *log\-3 + \/ 11 /   \/ 11 *\pi*I + log\3 + \/ 11 //   \/ 11 *log\-2 + \/ 11 /
- ------------------------------- - ----------------------- + ------------------------------- + -----------------------
                 22                            22                            22                            22
$$\frac{\sqrt{11} \log{\left(-2 + \sqrt{11} \right)}}{22} - \frac{\sqrt{11} \log{\left(-3 + \sqrt{11} \right)}}{22} - \frac{\sqrt{11} \left(\log{\left(2 + \sqrt{11} \right)} + i \pi\right)}{22} + \frac{\sqrt{11} \left(\log{\left(3 + \sqrt{11} \right)} + i \pi\right)}{22}$$ 
-sqrt(11)*(pi*i + log(2 + sqrt(11)))/22 - sqrt(11)*log(-3 + sqrt(11))/22 + sqrt(11)*(pi*i + log(3 + sqrt(11)))/22 + sqrt(11)*log(-2 + sqrt(11))/22
Respuesta numérica [src] 
0.240825503024632
0.240825503024632

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

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