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Resolución de integrales/ (x^3-3)/ 2*x/(x^3-3)

Integral de 2*x/(x^3-3) dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  1          
  /          
 |           
 |   2*x     
 |  ------ dx
 |   3       
 |  x  - 3   
 |           
/            
0
∫012xx3−3 dx\int\limits_{0}^{1} \frac{2 x}{x^{3} - 3}\, dx 
Integral((2*x)/(x^3 - 3), (x, 0, 1))
Respuesta (Indefinida) [src] 
                                                               /  ___       6 ___\                        
  /                                                  6 ___     |\/ 3    2*x*\/ 3 |                        
 |                  2/3    / 2/3    2     3 ___\   2*\/ 3 *atan|----- + ---------|      2/3    /    3 ___\
 |  2*x            3   *log\3    + x  + x*\/ 3 /               \  3         3    /   2*3   *log\x - \/ 3 /
 | ------ dx = C - ----------------------------- + ------------------------------- + ---------------------
 |  3                            9                                3                            9          
 | x  - 3                                                                                                 
 |                                                                                                        
/
∫2xx3−3 dx=C+2⋅323log⁡(x−33)9−323log⁡(x2+33x+323)9+236atan⁡(236x3+33)3\int \frac{2 x}{x^{3} - 3}\, dx = C + \frac{2 \cdot 3^{\frac{2}{3}} \log{\left(x - \sqrt[3]{3} \right)}}{9} - \frac{3^{\frac{2}{3}} \log{\left(x^{2} + \sqrt[3]{3} x + 3^{\frac{2}{3}} \right)}}{9} + \frac{2 \sqrt[6]{3} \operatorname{atan}{\left(\frac{2 \sqrt[6]{3} x}{3} + \frac{\sqrt{3}}{3} \right)}}{3}
Simplificar
Gráfica
0.001.000.100.200.300.400.500.600.700.800.901-2
Trazar el gráfico f(x)
Respuesta [src] 
                                                                                                    /  ___     6 ___\                                  
                                                                                          6 ___     |\/ 3    2*\/ 3 |                                  
     2/3 /          /3 ___\\      6 ___    2/3    /    3 ___    2/3\    2/3    / 2/3\   2*\/ 3 *atan|----- + -------|      2/3 /          /     3 ___\\
  2*3   *\pi*I + log\\/ 3 //   pi*\/ 3    3   *log\1 + \/ 3  + 3   /   3   *log\3   /               \  3        3   /   2*3   *\pi*I + log\-1 + \/ 3 //
- -------------------------- - -------- - -------------------------- + -------------- + ----------------------------- + -------------------------------
              9                   9                   9                      9                        3                                9
−36π9−323log⁡(1+33+323)9+323log⁡(323)9+236atan⁡(33+2363)3−2⋅323(log⁡(33)+iπ)9+2⋅323(log⁡(−1+33)+iπ)9- \frac{\sqrt[6]{3} \pi}{9} - \frac{3^{\frac{2}{3}} \log{\left(1 + \sqrt[3]{3} + 3^{\frac{2}{3}} \right)}}{9} + \frac{3^{\frac{2}{3}} \log{\left(3^{\frac{2}{3}} \right)}}{9} + \frac{2 \sqrt[6]{3} \operatorname{atan}{\left(\frac{\sqrt{3}}{3} + \frac{2 \sqrt[6]{3}}{3} \right)}}{3} - \frac{2 \cdot 3^{\frac{2}{3}} \left(\log{\left(\sqrt[3]{3} \right)} + i \pi\right)}{9} + \frac{2 \cdot 3^{\frac{2}{3}} \left(\log{\left(-1 + \sqrt[3]{3} \right)} + i \pi\right)}{9} 
=
= 
                                                                                                    /  ___     6 ___\                                  
                                                                                          6 ___     |\/ 3    2*\/ 3 |                                  
     2/3 /          /3 ___\\      6 ___    2/3    /    3 ___    2/3\    2/3    / 2/3\   2*\/ 3 *atan|----- + -------|      2/3 /          /     3 ___\\
  2*3   *\pi*I + log\\/ 3 //   pi*\/ 3    3   *log\1 + \/ 3  + 3   /   3   *log\3   /               \  3        3   /   2*3   *\pi*I + log\-1 + \/ 3 //
- -------------------------- - -------- - -------------------------- + -------------- + ----------------------------- + -------------------------------
              9                   9                   9                      9                        3                                9
−36π9−323log⁡(1+33+323)9+323log⁡(323)9+236atan⁡(33+2363)3−2⋅323(log⁡(33)+iπ)9+2⋅323(log⁡(−1+33)+iπ)9- \frac{\sqrt[6]{3} \pi}{9} - \frac{3^{\frac{2}{3}} \log{\left(1 + \sqrt[3]{3} + 3^{\frac{2}{3}} \right)}}{9} + \frac{3^{\frac{2}{3}} \log{\left(3^{\frac{2}{3}} \right)}}{9} + \frac{2 \sqrt[6]{3} \operatorname{atan}{\left(\frac{\sqrt{3}}{3} + \frac{2 \sqrt[6]{3}}{3} \right)}}{3} - \frac{2 \cdot 3^{\frac{2}{3}} \left(\log{\left(\sqrt[3]{3} \right)} + i \pi\right)}{9} + \frac{2 \cdot 3^{\frac{2}{3}} \left(\log{\left(-1 + \sqrt[3]{3} \right)} + i \pi\right)}{9} 
-2*3^(2/3)*(pi*i + log(3^(1/3)))/9 - pi*3^(1/6)/9 - 3^(2/3)*log(1 + 3^(1/3) + 3^(2/3))/9 + 3^(2/3)*log(3^(2/3))/9 + 2*3^(1/6)*atan(sqrt(3)/3 + 2*3^(1/6)/3)/3 + 2*3^(2/3)*(pi*i + log(-1 + 3^(1/3)))/9
Respuesta numérica [src] 
-0.390095539326299
-0.390095539326299

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

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