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  • Integral de d{x}:
  • Integral de e^-y
  • Integral de e^(e^x+x)
  • Integral de e^lnx
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  • Expresiones idénticas

  • uno /((uno -x)^(uno / tres)*(dos -x)^ dos)
  • 1 dividir por ((1 menos x) en el grado (1 dividir por 3) multiplicar por (2 menos x) al cuadrado )
  • uno dividir por ((uno menos x) en el grado (uno dividir por tres) multiplicar por (dos menos x) en el grado dos)
  • 1/((1-x)(1/3)*(2-x)2)
  • 1/1-x1/3*2-x2
  • 1/((1-x)^(1/3)*(2-x)²)
  • 1/((1-x) en el grado (1/3)*(2-x) en el grado 2)
  • 1/((1-x)^(1/3)(2-x)^2)
  • 1/((1-x)(1/3)(2-x)2)
  • 1/1-x1/32-x2
  • 1/1-x^1/32-x^2
  • 1 dividir por ((1-x)^(1 dividir por 3)*(2-x)^2)
  • 1/((1-x)^(1/3)*(2-x)^2)dx

  • Expresiones semejantes

  • 1/((1-x)^(1/3)*(2+x)^2)
  • 1/((1+x)^(1/3)*(2-x)^2)
Resolución de integrales/ (1-x)/ (1/3)/ (2-x)/ 1/((1-x)^(1/3)*(2-x)^2)

Integral de 1/((1-x)^(1/3)*(2-x)^2) dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
 oo                      
  /                      
 |                       
 |          1            
 |  ------------------ dx
 |  3 _______        2   
 |  \/ 1 - x *(2 - x)    
 |                       
/                        
4
∫4∞11−x3(2−x)2 dx\int\limits_{4}^{\infty} \frac{1}{\sqrt[3]{1 - x} \left(2 - x\right)^{2}}\, dx 
Integral(1/((1 - x)^(1/3)*(2 - x)^2), (x, 4, oo))
Respuesta (Indefinida) [src] 
                                                                        /                4*pi*I\                                                /                4*pi*I\                                            2*pi*I                                                    -2*pi*I               /                2*pi*I\                           2*pi*I                                                                 -2*pi*I               /                2*pi*I\                           2*pi*I                                       
  /                                                                     |                ------|                                                |                ------|                                            ------                                                    -------               |                ------|                           ------                                                                 -------               |                ------|                           ------                                       
 |                                        2/3         4/3               |    3 ________    3   |                  2/3         7/3               |    3 ________    3   |                             2/3         2    3                                      2/3         4/3     3                  |    3 ________    3   |          2/3         4/3    3                  /    3 ________  2*pi*I\         2/3         7/3     3                  |    3 ________    3   |          2/3         7/3    3                  /    3 ________  2*pi*I\
 |         1                        2*(-1)   *(-1 + x)   *Gamma(2/3)*log\1 - \/ -1 + x *e      /            2*(-1)   *(-1 + x)   *Gamma(2/3)*log\1 - \/ -1 + x *e      /                       6*(-1)   *(-1 + x) *e      *Gamma(2/3)                  2*(-1)   *(-1 + x)   *e       *Gamma(2/3)*log\1 - \/ -1 + x *e      /    2*(-1)   *(-1 + x)   *e      *Gamma(2/3)*log\1 - \/ -1 + x *e      /   2*(-1)   *(-1 + x)   *e       *Gamma(2/3)*log\1 - \/ -1 + x *e      /    2*(-1)   *(-1 + x)   *e      *Gamma(2/3)*log\1 - \/ -1 + x *e      /
 | ------------------ dx = C - --------------------------------------------------------------------- + --------------------------------------------------------------------- + --------------------------------------------------------------------- - --------------------------------------------------------------------- - --------------------------------------------------------------------- + --------------------------------------------------------------------- + ---------------------------------------------------------------------
 | 3 _______        2                           2*pi*I                             2*pi*I                               2*pi*I                             2*pi*I                               2*pi*I                             2*pi*I                               2*pi*I                             2*pi*I                               2*pi*I                             2*pi*I                               2*pi*I                             2*pi*I                               2*pi*I                             2*pi*I           
 | \/ 1 - x *(2 - x)                            ------                             ------                               ------                             ------                               ------                             ------                               ------                             ------                               ------                             ------                               ------                             ------                               ------                             ------           
 |                                         4/3    3                           7/3    3                             4/3    3                           7/3    3                             4/3    3                           7/3    3                             4/3    3                           7/3    3                             4/3    3                           7/3    3                             4/3    3                           7/3    3                             4/3    3                           7/3    3              
/                              - 9*(-1 + x)   *e      *Gamma(5/3) + 9*(-1 + x)   *e      *Gamma(5/3)   - 9*(-1 + x)   *e      *Gamma(5/3) + 9*(-1 + x)   *e      *Gamma(5/3)   - 9*(-1 + x)   *e      *Gamma(5/3) + 9*(-1 + x)   *e      *Gamma(5/3)   - 9*(-1 + x)   *e      *Gamma(5/3) + 9*(-1 + x)   *e      *Gamma(5/3)   - 9*(-1 + x)   *e      *Gamma(5/3) + 9*(-1 + x)   *e      *Gamma(5/3)   - 9*(-1 + x)   *e      *Gamma(5/3) + 9*(-1 + x)   *e      *Gamma(5/3)   - 9*(-1 + x)   *e      *Gamma(5/3) + 9*(-1 + x)   *e      *Gamma(5/3)
∫11−x3(2−x)2 dx=C+2(−1)23(x−1)73e−2iπ3log⁡(−x−13e2iπ3+1)Γ(23)9(x−1)73e2iπ3Γ(53)−9(x−1)43e2iπ3Γ(53)+2(−1)23(x−1)73log⁡(−x−13e4iπ3+1)Γ(23)9(x−1)73e2iπ3Γ(53)−9(x−1)43e2iπ3Γ(53)+2(−1)23(x−1)73e2iπ3log⁡(−x−13e2iπ+1)Γ(23)9(x−1)73e2iπ3Γ(53)−9(x−1)43e2iπ3Γ(53)−2(−1)23(x−1)43e−2iπ3log⁡(−x−13e2iπ3+1)Γ(23)9(x−1)73e2iπ3Γ(53)−9(x−1)43e2iπ3Γ(53)−2(−1)23(x−1)43log⁡(−x−13e4iπ3+1)Γ(23)9(x−1)73e2iπ3Γ(53)−9(x−1)43e2iπ3Γ(53)−2(−1)23(x−1)43e2iπ3log⁡(−x−13e2iπ+1)Γ(23)9(x−1)73e2iπ3Γ(53)−9(x−1)43e2iπ3Γ(53)+6(−1)23(x−1)2e2iπ3Γ(23)9(x−1)73e2iπ3Γ(53)−9(x−1)43e2iπ3Γ(53)\int \frac{1}{\sqrt[3]{1 - x} \left(2 - x\right)^{2}}\, dx = C + \frac{2 \left(-1\right)^{\frac{2}{3}} \left(x - 1\right)^{\frac{7}{3}} e^{- \frac{2 i \pi}{3}} \log{\left(- \sqrt[3]{x - 1} e^{\frac{2 i \pi}{3}} + 1 \right)} \Gamma\left(\frac{2}{3}\right)}{9 \left(x - 1\right)^{\frac{7}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{5}{3}\right) - 9 \left(x - 1\right)^{\frac{4}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{5}{3}\right)} + \frac{2 \left(-1\right)^{\frac{2}{3}} \left(x - 1\right)^{\frac{7}{3}} \log{\left(- \sqrt[3]{x - 1} e^{\frac{4 i \pi}{3}} + 1 \right)} \Gamma\left(\frac{2}{3}\right)}{9 \left(x - 1\right)^{\frac{7}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{5}{3}\right) - 9 \left(x - 1\right)^{\frac{4}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{5}{3}\right)} + \frac{2 \left(-1\right)^{\frac{2}{3}} \left(x - 1\right)^{\frac{7}{3}} e^{\frac{2 i \pi}{3}} \log{\left(- \sqrt[3]{x - 1} e^{2 i \pi} + 1 \right)} \Gamma\left(\frac{2}{3}\right)}{9 \left(x - 1\right)^{\frac{7}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{5}{3}\right) - 9 \left(x - 1\right)^{\frac{4}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{5}{3}\right)} - \frac{2 \left(-1\right)^{\frac{2}{3}} \left(x - 1\right)^{\frac{4}{3}} e^{- \frac{2 i \pi}{3}} \log{\left(- \sqrt[3]{x - 1} e^{\frac{2 i \pi}{3}} + 1 \right)} \Gamma\left(\frac{2}{3}\right)}{9 \left(x - 1\right)^{\frac{7}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{5}{3}\right) - 9 \left(x - 1\right)^{\frac{4}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{5}{3}\right)} - \frac{2 \left(-1\right)^{\frac{2}{3}} \left(x - 1\right)^{\frac{4}{3}} \log{\left(- \sqrt[3]{x - 1} e^{\frac{4 i \pi}{3}} + 1 \right)} \Gamma\left(\frac{2}{3}\right)}{9 \left(x - 1\right)^{\frac{7}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{5}{3}\right) - 9 \left(x - 1\right)^{\frac{4}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{5}{3}\right)} - \frac{2 \left(-1\right)^{\frac{2}{3}} \left(x - 1\right)^{\frac{4}{3}} e^{\frac{2 i \pi}{3}} \log{\left(- \sqrt[3]{x - 1} e^{2 i \pi} + 1 \right)} \Gamma\left(\frac{2}{3}\right)}{9 \left(x - 1\right)^{\frac{7}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{5}{3}\right) - 9 \left(x - 1\right)^{\frac{4}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{5}{3}\right)} + \frac{6 \left(-1\right)^{\frac{2}{3}} \left(x - 1\right)^{2} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{2}{3}\right)}{9 \left(x - 1\right)^{\frac{7}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{5}{3}\right) - 9 \left(x - 1\right)^{\frac{4}{3}} e^{\frac{2 i \pi}{3}} \Gamma\left(\frac{5}{3}\right)}
Simplificar
Respuesta [src] 
      -pi*I                                   
      ------              _                   
 2/3    3                |_  /1/3, 4/3 |     \
2   *e      *Gamma(4/3)* |   |         | -1/2|
                        2  1 \  7/3    |     /
----------------------------------------------
                 4*Gamma(7/3)
223e−iπ3Γ(43)2F1(13,4373|−12)4Γ(73)\frac{2^{\frac{2}{3}} e^{- \frac{i \pi}{3}} \Gamma\left(\frac{4}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{3}, \frac{4}{3} \\ \frac{7}{3} \end{matrix}\middle| {- \frac{1}{2}} \right)}}{4 \Gamma\left(\frac{7}{3}\right)} 
=
= 
      -pi*I                                   
      ------              _                   
 2/3    3                |_  /1/3, 4/3 |     \
2   *e      *Gamma(4/3)* |   |         | -1/2|
                        2  1 \  7/3    |     /
----------------------------------------------
                 4*Gamma(7/3)
223e−iπ3Γ(43)2F1(13,4373|−12)4Γ(73)\frac{2^{\frac{2}{3}} e^{- \frac{i \pi}{3}} \Gamma\left(\frac{4}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{3}, \frac{4}{3} \\ \frac{7}{3} \end{matrix}\middle| {- \frac{1}{2}} \right)}}{4 \Gamma\left(\frac{7}{3}\right)} 
2^(2/3)*exp(-pi*i/3)*gamma(4/3)*hyper((1/3, 4/3), (7/3,), -1/2)/(4*gamma(7/3))

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

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