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Resolución de integrales/ x*x^2/ e^1/(x*x^2)

Integral de e^1/(x*x^2) dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  1         
  /         
 |          
 |    1     
 |   ----   
 |      2   
 |   x*x    
 |  E     dx
 |          
/           
0
$$\int\limits_{0}^{1} e^{\frac{1}{x x^{2}}}\, dx$$ 
Integral(E^(1/(x*x^2)), (x, 0, 1))
Respuesta (Indefinida) [src] 
  /                -2*pi*I                                     
 |                 -------                       / pi*I   pi*I\
 |   1                3                          |e      e    |
 |  ----          e       *Gamma(-1/3)*lowergamma|-----, -----|
 |     2                                         |  3       3 |
 |  x*x                                          \         x  /
 | E     dx = C - ---------------------------------------------
 |                                 9*Gamma(2/3)                
/
$$\int e^{\frac{1}{x x^{2}}}\, dx = C - \frac{e^{- \frac{2 i \pi}{3}} \Gamma\left(- \frac{1}{3}\right) \gamma\left(\frac{e^{i \pi}}{3}, \frac{e^{i \pi}}{x^{3}}\right)}{9 \Gamma\left(\frac{2}{3}\right)}$$
Simplificar
Respuesta [src] 
   -2*pi*I                                         -2*pi*I                                   
   -------                       / pi*I       \    -------                       / pi*I     \
      3                          |e       pi*I|       3                          |e         |
  e       *Gamma(-1/3)*lowergamma|-----, e    |   e       *Gamma(-1/3)*lowergamma|-----, -oo|
                                 \  3         /                                  \  3       /
- --------------------------------------------- + -------------------------------------------
                   9*Gamma(2/3)                                   9*Gamma(2/3)
-2*pi*I -2*pi*I ------- / pi*I \ ------- / pi*I \ 3 |e pi*I| 3 |e | e *Gamma(-1/3)*lowergamma|-----, e | e *Gamma(-1/3)*lowergamma|-----, -oo| \ 3 / \ 3 / - --------------------------------------------- + ------------------------------------------- 9*Gamma(2/3) 9*Gamma(2/3) 
=
= 
   -2*pi*I                                         -2*pi*I                                   
   -------                       / pi*I       \    -------                       / pi*I     \
      3                          |e       pi*I|       3                          |e         |
  e       *Gamma(-1/3)*lowergamma|-----, e    |   e       *Gamma(-1/3)*lowergamma|-----, -oo|
                                 \  3         /                                  \  3       /
- --------------------------------------------- + -------------------------------------------
                   9*Gamma(2/3)                                   9*Gamma(2/3)
-2*pi*I -2*pi*I ------- / pi*I \ ------- / pi*I \ 3 |e pi*I| 3 |e | e *Gamma(-1/3)*lowergamma|-----, e | e *Gamma(-1/3)*lowergamma|-----, -oo| \ 3 / \ 3 / - --------------------------------------------- + ------------------------------------------- 9*Gamma(2/3) 9*Gamma(2/3) 
-exp(-2*pi*i/3)*gamma(-1/3)*lowergamma(exp_polar(pi*i)/3, exp_polar(pi*i))/(9*gamma(2/3)) + exp(-2*pi*i/3)*gamma(-1/3)*lowergamma(exp_polar(pi*i)/3, -oo)/(9*gamma(2/3))
Respuesta numérica [src] 
3.15480081050419e+431510637999868418905622596197908767125401523991691183391
3.15480081050419e+431510637999868418905622596197908767125401523991691183391

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

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