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Resolución de integrales/ x^2-6/ (x-1)/ -6x-8/ 1/((x-1)*(x^2-6x-8))

Integral de 1/((x-1)*(x^2-6x-8)) dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  1                          
  /                          
 |                           
 |            1              
 |  ---------------------- dx
 |          / 2          \   
 |  (x - 1)*\x  - 6*x - 8/   
 |                           
/                            
0
∫011(x−1)((x2−6x)−8) dx\int\limits_{0}^{1} \frac{1}{\left(x - 1\right) \left(\left(x^{2} - 6 x\right) - 8\right)}\, dx 
Integral(1/((x - 1)*(x^2 - 6*x - 8)), (x, 0, 1))
Respuesta (Indefinida) [src] 
                                     //             /  ____         \                     \                                   
                                     ||   ____      |\/ 17 *(-3 + x)|                     |                                   
                                     ||-\/ 17 *acoth|---------------|                     |                                   
                                     ||             \       17      /               2     |                                   
                                     ||-------------------------------  for (-3 + x)  > 17|                                   
                                     ||               17                                  |                                   
                                   2*|<                                                   |                                   
                                     ||             /  ____         \                     |                                   
                                     ||   ____      |\/ 17 *(-3 + x)|                     |                                   
                                     ||-\/ 17 *atanh|---------------|                     |                                   
  /                                  ||             \       17      /               2     |                                   
 |                                   ||-------------------------------  for (-3 + x)  < 17|                    /      2      \
 |           1                       \\               17                                  /   log(-1 + x)   log\-8 + x  - 6*x/
 | ---------------------- dx = C - -------------------------------------------------------- - ----------- + ------------------
 |         / 2          \                                     13                                   13               26        
 | (x - 1)*\x  - 6*x - 8/                                                                                                     
 |                                                                                                                            
/
∫1(x−1)((x2−6x)−8) dx=C−2({−17acoth⁡(17(x−3)17)17for (x−3)2>17−17atanh⁡(17(x−3)17)17for (x−3)2<17)13−log⁡(x−1)13+log⁡(x2−6x−8)26\int \frac{1}{\left(x - 1\right) \left(\left(x^{2} - 6 x\right) - 8\right)}\, dx = C - \frac{2 \left(\begin{cases} - \frac{\sqrt{17} \operatorname{acoth}{\left(\frac{\sqrt{17} \left(x - 3\right)}{17} \right)}}{17} & \text{for}\: \left(x - 3\right)^{2} > 17 \\- \frac{\sqrt{17} \operatorname{atanh}{\left(\frac{\sqrt{17} \left(x - 3\right)}{17} \right)}}{17} & \text{for}\: \left(x - 3\right)^{2} < 17 \end{cases}\right)}{13} - \frac{\log{\left(x - 1 \right)}}{13} + \frac{\log{\left(x^{2} - 6 x - 8 \right)}}{26}
Simplificar
Gráfica
0.001.000.100.200.300.400.500.600.700.800.9001000
Trazar el gráfico f(x)
Respuesta [src] 
                   /          /                           2            \\       
                   |          |              /       ____\             ||       
                   |          |              |1    \/ 17 |             ||       
     /       ____\ |          |       316030*|-- - ------|         ____||       
     |1    \/ 17 | |          |2049          \26    221  /    39*\/ 17 ||   pi*I
oo - |-- - ------|*|pi*I + log|---- - --------------------- + ---------|| + ----
     \26    221  / \          \298             149               149   //    13
∞−(126−17221)(log⁡(−316030(126−17221)2149+3917149+2049298)+iπ)+iπ13\infty - \left(\frac{1}{26} - \frac{\sqrt{17}}{221}\right) \left(\log{\left(- \frac{316030 \left(\frac{1}{26} - \frac{\sqrt{17}}{221}\right)^{2}}{149} + \frac{39 \sqrt{17}}{149} + \frac{2049}{298} \right)} + i \pi\right) + \frac{i \pi}{13} 
=
= 
                   /          /                           2            \\       
                   |          |              /       ____\             ||       
                   |          |              |1    \/ 17 |             ||       
     /       ____\ |          |       316030*|-- - ------|         ____||       
     |1    \/ 17 | |          |2049          \26    221  /    39*\/ 17 ||   pi*I
oo - |-- - ------|*|pi*I + log|---- - --------------------- + ---------|| + ----
     \26    221  / \          \298             149               149   //    13
∞−(126−17221)(log⁡(−316030(126−17221)2149+3917149+2049298)+iπ)+iπ13\infty - \left(\frac{1}{26} - \frac{\sqrt{17}}{221}\right) \left(\log{\left(- \frac{316030 \left(\frac{1}{26} - \frac{\sqrt{17}}{221}\right)^{2}}{149} + \frac{39 \sqrt{17}}{149} + \frac{2049}{298} \right)} + i \pi\right) + \frac{i \pi}{13} 
oo - (1/26 - sqrt(17)/221)*(pi*i + log(2049/298 - 316030*(1/26 - sqrt(17)/221)^2/149 + 39*sqrt(17)/149)) + pi*i/13
Respuesta numérica [src] 
3.42498788411389
3.42498788411389

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

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