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Resolución de integrales/ (x^3-3)/ 1/(x^3-3)

Integral de 1/(x^3-3) dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  1          
  /          
 |           
 |    1      
 |  ------ dx
 |   3       
 |  x  - 3   
 |           
/            
0
∫011x3−3 dx\int\limits_{0}^{1} \frac{1}{x^{3} - 3}\, dx 
Integral(1/(x^3 - 3), (x, 0, 1))
Respuesta (Indefinida) [src] 
                            /  ___       6 ___\                                                        
  /                 5/6     |\/ 3    2*x*\/ 3 |                                                        
 |                 3   *atan|----- + ---------|   3 ___    / 2/3    2     3 ___\   3 ___    /    3 ___\
 |   1                      \  3         3    /   \/ 3 *log\3    + x  + x*\/ 3 /   \/ 3 *log\x - \/ 3 /
 | ------ dx = C - ---------------------------- - ------------------------------ + --------------------
 |  3                           9                               18                          9          
 | x  - 3                                                                                              
 |                                                                                                     
/
∫1x3−3 dx=C+33log⁡(x−33)9−33log⁡(x2+33x+323)18−356atan⁡(236x3+33)9\int \frac{1}{x^{3} - 3}\, dx = C + \frac{\sqrt[3]{3} \log{\left(x - \sqrt[3]{3} \right)}}{9} - \frac{\sqrt[3]{3} \log{\left(x^{2} + \sqrt[3]{3} x + 3^{\frac{2}{3}} \right)}}{18} - \frac{3^{\frac{5}{6}} \operatorname{atan}{\left(\frac{2 \sqrt[6]{3} x}{3} + \frac{\sqrt{3}}{3} \right)}}{9}
Simplificar
Gráfica
0.001.000.100.200.300.400.500.600.700.800.90-0.6-0.2
Trazar el gráfico f(x)
Respuesta [src] 
                                       /  ___     6 ___\                                                                                           
                               5/6     |\/ 3    2*\/ 3 |                                                                                           
  3 ___ /          /3 ___\\   3   *atan|----- + -------|   3 ___    /    3 ___    2/3\   3 ___ /          /     3 ___\\   3 ___    / 2/3\       5/6
  \/ 3 *\pi*I + log\\/ 3 //            \  3        3   /   \/ 3 *log\1 + \/ 3  + 3   /   \/ 3 *\pi*I + log\-1 + \/ 3 //   \/ 3 *log\3   /   pi*3   
- ------------------------- - -------------------------- - --------------------------- + ------------------------------ + --------------- + -------
              9                           9                             18                             9                         18            54
−356atan⁡(33+2363)9−33log⁡(1+33+323)18+33log⁡(323)18+356π54−33(log⁡(33)+iπ)9+33(log⁡(−1+33)+iπ)9- \frac{3^{\frac{5}{6}} \operatorname{atan}{\left(\frac{\sqrt{3}}{3} + \frac{2 \sqrt[6]{3}}{3} \right)}}{9} - \frac{\sqrt[3]{3} \log{\left(1 + \sqrt[3]{3} + 3^{\frac{2}{3}} \right)}}{18} + \frac{\sqrt[3]{3} \log{\left(3^{\frac{2}{3}} \right)}}{18} + \frac{3^{\frac{5}{6}} \pi}{54} - \frac{\sqrt[3]{3} \left(\log{\left(\sqrt[3]{3} \right)} + i \pi\right)}{9} + \frac{\sqrt[3]{3} \left(\log{\left(-1 + \sqrt[3]{3} \right)} + i \pi\right)}{9} 
=
= 
                                       /  ___     6 ___\                                                                                           
                               5/6     |\/ 3    2*\/ 3 |                                                                                           
  3 ___ /          /3 ___\\   3   *atan|----- + -------|   3 ___    /    3 ___    2/3\   3 ___ /          /     3 ___\\   3 ___    / 2/3\       5/6
  \/ 3 *\pi*I + log\\/ 3 //            \  3        3   /   \/ 3 *log\1 + \/ 3  + 3   /   \/ 3 *\pi*I + log\-1 + \/ 3 //   \/ 3 *log\3   /   pi*3   
- ------------------------- - -------------------------- - --------------------------- + ------------------------------ + --------------- + -------
              9                           9                             18                             9                         18            54
−356atan⁡(33+2363)9−33log⁡(1+33+323)18+33log⁡(323)18+356π54−33(log⁡(33)+iπ)9+33(log⁡(−1+33)+iπ)9- \frac{3^{\frac{5}{6}} \operatorname{atan}{\left(\frac{\sqrt{3}}{3} + \frac{2 \sqrt[6]{3}}{3} \right)}}{9} - \frac{\sqrt[3]{3} \log{\left(1 + \sqrt[3]{3} + 3^{\frac{2}{3}} \right)}}{18} + \frac{\sqrt[3]{3} \log{\left(3^{\frac{2}{3}} \right)}}{18} + \frac{3^{\frac{5}{6}} \pi}{54} - \frac{\sqrt[3]{3} \left(\log{\left(\sqrt[3]{3} \right)} + i \pi\right)}{9} + \frac{\sqrt[3]{3} \left(\log{\left(-1 + \sqrt[3]{3} \right)} + i \pi\right)}{9} 
-3^(1/3)*(pi*i + log(3^(1/3)))/9 - 3^(5/6)*atan(sqrt(3)/3 + 2*3^(1/6)/3)/9 - 3^(1/3)*log(1 + 3^(1/3) + 3^(2/3))/18 + 3^(1/3)*(pi*i + log(-1 + 3^(1/3)))/9 + 3^(1/3)*log(3^(2/3))/18 + pi*3^(5/6)/54
Respuesta numérica [src] 
-0.368072866710524
-0.368072866710524

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

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