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Resolución de integrales/ x^2-5/ (x+6)/ 1/((x^2-5)*(x+6))

Integral de 1/((x^2-5)*(x+6)) dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  1                    
  /                    
 |                     
 |         1           
 |  ---------------- dx
 |  / 2    \           
 |  \x  - 5/*(x + 6)   
 |                     
/                      
0
∫011(x+6)(x2−5) dx\int\limits_{0}^{1} \frac{1}{\left(x + 6\right) \left(x^{2} - 5\right)}\, dx 
Integral(1/((x^2 - 5)*(x + 6)), (x, 0, 1))
Respuesta (Indefinida) [src] 
                                                           //            /    ___\             \
                                                           ||   ___      |x*\/ 5 |             |
                                                           ||-\/ 5 *acoth|-------|             |
                                                           ||            \   5   /        2    |
                                                           ||----------------------  for x  > 5|
                                                           ||          5                       |
                                                         6*|<                                  |
                                                           ||            /    ___\             |
                                                           ||   ___      |x*\/ 5 |             |
                                                           ||-\/ 5 *atanh|-------|             |
  /                                                        ||            \   5   /        2    |
 |                              /      2\                  ||----------------------  for x  < 5|
 |        1                  log\-5 + x /   log(6 + x)     \\          5                       /
 | ---------------- dx = C - ------------ + ---------- + ---------------------------------------
 | / 2    \                       62            31                          31                  
 | \x  - 5/*(x + 6)                                                                             
 |                                                                                              
/
∫1(x+6)(x2−5) dx=C+6({−5acoth⁡(5x5)5for x2>5−5atanh⁡(5x5)5for x2<5)31+log⁡(x+6)31−log⁡(x2−5)62\int \frac{1}{\left(x + 6\right) \left(x^{2} - 5\right)}\, dx = C + \frac{6 \left(\begin{cases} - \frac{\sqrt{5} \operatorname{acoth}{\left(\frac{\sqrt{5} x}{5} \right)}}{5} & \text{for}\: x^{2} > 5 \\- \frac{\sqrt{5} \operatorname{atanh}{\left(\frac{\sqrt{5} x}{5} \right)}}{5} & \text{for}\: x^{2} < 5 \end{cases}\right)}{31} + \frac{\log{\left(x + 6 \right)}}{31} - \frac{\log{\left(x^{2} - 5 \right)}}{62}
Simplificar
Gráfica
0.001.000.100.200.300.400.500.600.700.800.90-0.040-0.030
Trazar el gráfico f(x)
Respuesta [src] 
                                        /                                          2\                    /          /                             2           \\                       /                                          2\                    /          /                             2           \\
                                        |                          /           ___\ |                    |          |             /           ___\            ||                       |                          /           ___\ |                    |          |             /           ___\            ||
                                        |                          |  1    3*\/ 5 | |                    |          |             |  1    3*\/ 5 |            ||                       |                          |  1    3*\/ 5 | |                    |          |             |  1    3*\/ 5 |            ||
                    /           ___\    |             ___   163370*|- -- - -------| |   /           ___\ |          |      163370*|- -- + -------|         ___||   /           ___\    |             ___   163370*|- -- - -------| |   /           ___\ |          |      163370*|- -- + -------|         ___||
  log(6)   log(7)   |  1    3*\/ 5 |    |  679   31*\/ 5           \  62     155  / |   |  1    3*\/ 5 | |          |679          \  62     155  /    31*\/ 5 ||   |  1    3*\/ 5 |    |  697   31*\/ 5           \  62     155  / |   |  1    3*\/ 5 | |          |697          \  62     155  /    31*\/ 5 ||
- ------ + ------ + |- -- - -------|*log|- --- - -------- + ------------------------| + |- -- + -------|*|pi*I + log|--- - ------------------------ - --------|| - |- -- - -------|*log|- --- - -------- + ------------------------| - |- -- + -------|*|pi*I + log|--- - ------------------------ - --------||
    31       31     \  62     155  /    \   18      3                  9            /   \  62     155  / \          \ 18              9                  3    //   \  62     155  /    \   18      3                  9            /   \  62     155  / \          \ 18              9                  3    //
(−35155−162)log⁡(−67918−3153+163370(−35155−162)29)−log⁡(6)31−(−35155−162)log⁡(−69718−3153+163370(−35155−162)29)+log⁡(7)31−(−162+35155)(log⁡(−3153−163370(−162+35155)29+69718)+iπ)+(−162+35155)(log⁡(−3153−163370(−162+35155)29+67918)+iπ)\left(- \frac{3 \sqrt{5}}{155} - \frac{1}{62}\right) \log{\left(- \frac{679}{18} - \frac{31 \sqrt{5}}{3} + \frac{163370 \left(- \frac{3 \sqrt{5}}{155} - \frac{1}{62}\right)^{2}}{9} \right)} - \frac{\log{\left(6 \right)}}{31} - \left(- \frac{3 \sqrt{5}}{155} - \frac{1}{62}\right) \log{\left(- \frac{697}{18} - \frac{31 \sqrt{5}}{3} + \frac{163370 \left(- \frac{3 \sqrt{5}}{155} - \frac{1}{62}\right)^{2}}{9} \right)} + \frac{\log{\left(7 \right)}}{31} - \left(- \frac{1}{62} + \frac{3 \sqrt{5}}{155}\right) \left(\log{\left(- \frac{31 \sqrt{5}}{3} - \frac{163370 \left(- \frac{1}{62} + \frac{3 \sqrt{5}}{155}\right)^{2}}{9} + \frac{697}{18} \right)} + i \pi\right) + \left(- \frac{1}{62} + \frac{3 \sqrt{5}}{155}\right) \left(\log{\left(- \frac{31 \sqrt{5}}{3} - \frac{163370 \left(- \frac{1}{62} + \frac{3 \sqrt{5}}{155}\right)^{2}}{9} + \frac{679}{18} \right)} + i \pi\right) 
=
= 
                                        /                                          2\                    /          /                             2           \\                       /                                          2\                    /          /                             2           \\
                                        |                          /           ___\ |                    |          |             /           ___\            ||                       |                          /           ___\ |                    |          |             /           ___\            ||
                                        |                          |  1    3*\/ 5 | |                    |          |             |  1    3*\/ 5 |            ||                       |                          |  1    3*\/ 5 | |                    |          |             |  1    3*\/ 5 |            ||
                    /           ___\    |             ___   163370*|- -- - -------| |   /           ___\ |          |      163370*|- -- + -------|         ___||   /           ___\    |             ___   163370*|- -- - -------| |   /           ___\ |          |      163370*|- -- + -------|         ___||
  log(6)   log(7)   |  1    3*\/ 5 |    |  679   31*\/ 5           \  62     155  / |   |  1    3*\/ 5 | |          |679          \  62     155  /    31*\/ 5 ||   |  1    3*\/ 5 |    |  697   31*\/ 5           \  62     155  / |   |  1    3*\/ 5 | |          |697          \  62     155  /    31*\/ 5 ||
- ------ + ------ + |- -- - -------|*log|- --- - -------- + ------------------------| + |- -- + -------|*|pi*I + log|--- - ------------------------ - --------|| - |- -- - -------|*log|- --- - -------- + ------------------------| - |- -- + -------|*|pi*I + log|--- - ------------------------ - --------||
    31       31     \  62     155  /    \   18      3                  9            /   \  62     155  / \          \ 18              9                  3    //   \  62     155  /    \   18      3                  9            /   \  62     155  / \          \ 18              9                  3    //
(−35155−162)log⁡(−67918−3153+163370(−35155−162)29)−log⁡(6)31−(−35155−162)log⁡(−69718−3153+163370(−35155−162)29)+log⁡(7)31−(−162+35155)(log⁡(−3153−163370(−162+35155)29+69718)+iπ)+(−162+35155)(log⁡(−3153−163370(−162+35155)29+67918)+iπ)\left(- \frac{3 \sqrt{5}}{155} - \frac{1}{62}\right) \log{\left(- \frac{679}{18} - \frac{31 \sqrt{5}}{3} + \frac{163370 \left(- \frac{3 \sqrt{5}}{155} - \frac{1}{62}\right)^{2}}{9} \right)} - \frac{\log{\left(6 \right)}}{31} - \left(- \frac{3 \sqrt{5}}{155} - \frac{1}{62}\right) \log{\left(- \frac{697}{18} - \frac{31 \sqrt{5}}{3} + \frac{163370 \left(- \frac{3 \sqrt{5}}{155} - \frac{1}{62}\right)^{2}}{9} \right)} + \frac{\log{\left(7 \right)}}{31} - \left(- \frac{1}{62} + \frac{3 \sqrt{5}}{155}\right) \left(\log{\left(- \frac{31 \sqrt{5}}{3} - \frac{163370 \left(- \frac{1}{62} + \frac{3 \sqrt{5}}{155}\right)^{2}}{9} + \frac{697}{18} \right)} + i \pi\right) + \left(- \frac{1}{62} + \frac{3 \sqrt{5}}{155}\right) \left(\log{\left(- \frac{31 \sqrt{5}}{3} - \frac{163370 \left(- \frac{1}{62} + \frac{3 \sqrt{5}}{155}\right)^{2}}{9} + \frac{679}{18} \right)} + i \pi\right) 
-log(6)/31 + log(7)/31 + (-1/62 - 3*sqrt(5)/155)*log(-679/18 - 31*sqrt(5)/3 + 163370*(-1/62 - 3*sqrt(5)/155)^2/9) + (-1/62 + 3*sqrt(5)/155)*(pi*i + log(679/18 - 163370*(-1/62 + 3*sqrt(5)/155)^2/9 - 31*sqrt(5)/3)) - (-1/62 - 3*sqrt(5)/155)*log(-697/18 - 31*sqrt(5)/3 + 163370*(-1/62 - 3*sqrt(5)/155)^2/9) - (-1/62 + 3*sqrt(5)/155)*(pi*i + log(697/18 - 163370*(-1/62 + 3*sqrt(5)/155)^2/9 - 31*sqrt(5)/3))
Respuesta numérica [src] 
-0.033080786045408
-0.033080786045408

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

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