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

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

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  1                
  /                
 |                 
 |       1         
 |  ------------ dx
 |   2             
 |  x  - 6*x + 6   
 |                 
/                  
0
∫011(x2−6x)+6 dx\int\limits_{0}^{1} \frac{1}{\left(x^{2} - 6 x\right) + 6}\, dx 
Integral(1/(x^2 - 6*x + 6), (x, 0, 1))
Respuesta (Indefinida) [src] 
                         //            /  ___         \                    \
                         ||   ___      |\/ 3 *(-3 + x)|                    |
                         ||-\/ 3 *acoth|--------------|                    |
  /                      ||            \      3       /               2    |
 |                       ||-----------------------------  for (-3 + x)  > 3|
 |      1                ||              3                                 |
 | ------------ dx = C + |<                                                |
 |  2                    ||            /  ___         \                    |
 | x  - 6*x + 6          ||   ___      |\/ 3 *(-3 + x)|                    |
 |                       ||-\/ 3 *atanh|--------------|                    |
/                        ||            \      3       /               2    |
                         ||-----------------------------  for (-3 + x)  < 3|
                         \\              3                                 /
∫1(x2−6x)+6 dx=C+{−3acoth⁡(3(x−3)3)3for (x−3)2>3−3atanh⁡(3(x−3)3)3for (x−3)2<3\int \frac{1}{\left(x^{2} - 6 x\right) + 6}\, dx = C + \begin{cases} - \frac{\sqrt{3} \operatorname{acoth}{\left(\frac{\sqrt{3} \left(x - 3\right)}{3} \right)}}{3} & \text{for}\: \left(x - 3\right)^{2} > 3 \\- \frac{\sqrt{3} \operatorname{atanh}{\left(\frac{\sqrt{3} \left(x - 3\right)}{3} \right)}}{3} & \text{for}\: \left(x - 3\right)^{2} < 3 \end{cases}
Simplificar
Gráfica
0.001.000.100.200.300.400.500.600.700.800.900.02.0
Trazar el gráfico f(x)
Respuesta [src] 
    ___ /          /      ___\\     ___ /          /      ___\\     ___ /          /      ___\\     ___ /          /      ___\\
  \/ 3 *\pi*I + log\2 - \/ 3 //   \/ 3 *\pi*I + log\3 + \/ 3 //   \/ 3 *\pi*I + log\2 + \/ 3 //   \/ 3 *\pi*I + log\3 - \/ 3 //
- ----------------------------- - ----------------------------- + ----------------------------- + -----------------------------
                6                               6                               6                               6
−3(log⁡(3+3)+iπ)6−3(log⁡(2−3)+iπ)6+3(log⁡(3−3)+iπ)6+3(log⁡(3+2)+iπ)6- \frac{\sqrt{3} \left(\log{\left(\sqrt{3} + 3 \right)} + i \pi\right)}{6} - \frac{\sqrt{3} \left(\log{\left(2 - \sqrt{3} \right)} + i \pi\right)}{6} + \frac{\sqrt{3} \left(\log{\left(3 - \sqrt{3} \right)} + i \pi\right)}{6} + \frac{\sqrt{3} \left(\log{\left(\sqrt{3} + 2 \right)} + i \pi\right)}{6} 
=
= 
    ___ /          /      ___\\     ___ /          /      ___\\     ___ /          /      ___\\     ___ /          /      ___\\
  \/ 3 *\pi*I + log\2 - \/ 3 //   \/ 3 *\pi*I + log\3 + \/ 3 //   \/ 3 *\pi*I + log\2 + \/ 3 //   \/ 3 *\pi*I + log\3 - \/ 3 //
- ----------------------------- - ----------------------------- + ----------------------------- + -----------------------------
                6                               6                               6                               6
−3(log⁡(3+3)+iπ)6−3(log⁡(2−3)+iπ)6+3(log⁡(3−3)+iπ)6+3(log⁡(3+2)+iπ)6- \frac{\sqrt{3} \left(\log{\left(\sqrt{3} + 3 \right)} + i \pi\right)}{6} - \frac{\sqrt{3} \left(\log{\left(2 - \sqrt{3} \right)} + i \pi\right)}{6} + \frac{\sqrt{3} \left(\log{\left(3 - \sqrt{3} \right)} + i \pi\right)}{6} + \frac{\sqrt{3} \left(\log{\left(\sqrt{3} + 2 \right)} + i \pi\right)}{6} 
-sqrt(3)*(pi*i + log(2 - sqrt(3)))/6 - sqrt(3)*(pi*i + log(3 + sqrt(3)))/6 + sqrt(3)*(pi*i + log(2 + sqrt(3)))/6 + sqrt(3)*(pi*i + log(3 - sqrt(3)))/6
Respuesta numérica [src] 
0.380172998150473
0.380172998150473

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

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