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Resolución de integrales/ 1/(((5-x)^(1/4))*((x-10)^(1/4)))

Integral de 1/(((5-x)^(1/4))*((x-10)^(1/4))) dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  1                        
  /                        
 |                         
 |           1             
 |  -------------------- dx
 |  4 _______ 4 ________   
 |  \/ 5 - x *\/ x - 10    
 |                         
/                          
0
$$\int\limits_{0}^{1} \frac{1}{\sqrt[4]{5 - x} \sqrt[4]{x - 10}}\, dx$$ 
Integral(1/((5 - x)^(1/4)*(x - 10)^(1/4)), (x, 0, 1))
Respuesta (Indefinida) [src] 
                                                          -3*pi*I                                    
                                                          -------              _                     
  /                              4 ____  3/4         3/4     4                |_  /1/4, 3/4 |      x\
 |                               \/ -1 *5   *(-5 + x)   *e       *Gamma(3/4)* |   |         | -1 + -|
 |          1                                                                2  1 \  7/4    |      5/
 | -------------------- dx = C + --------------------------------------------------------------------
 | 4 _______ 4 ________                                      5*Gamma(7/4)                            
 | \/ 5 - x *\/ x - 10                                                                               
 |                                                                                                   
/
$$\int \frac{1}{\sqrt[4]{5 - x} \sqrt[4]{x - 10}}\, dx = C + \frac{\sqrt[4]{-1} \cdot 5^{\frac{3}{4}} \left(x - 5\right)^{\frac{3}{4}} e^{- \frac{3 i \pi}{4}} \Gamma\left(\frac{3}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{4}, \frac{3}{4} \\ \frac{7}{4} \end{matrix}\middle| {\frac{x}{5} - 1} \right)}}{5 \Gamma\left(\frac{7}{4}\right)}$$
Simplificar
Gráfica
Trazar el gráfico f(x)
Respuesta [src] 
       -3*pi*I                                                 -3*pi*I                                  
       -------              _                                  -------              _                   
  ___     4                |_  /1/4, 3/4 |   \       ___  3/4     4                |_  /1/4, 3/4 |     \
\/ 5 *e       *Gamma(3/4)* |   |         | -1|   2*\/ 2 *5   *e       *Gamma(3/4)* |   |         | -4/5|
                          2  1 \  7/4    |   /                                    2  1 \  7/4    |     /
---------------------------------------------- - -------------------------------------------------------
                  Gamma(7/4)                                           5*Gamma(7/4)
$$\frac{\sqrt{5} e^{- \frac{3 i \pi}{4}} \Gamma\left(\frac{3}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{4}, \frac{3}{4} \\ \frac{7}{4} \end{matrix}\middle| {-1} \right)}}{\Gamma\left(\frac{7}{4}\right)} - \frac{2 \sqrt{2} \cdot 5^{\frac{3}{4}} e^{- \frac{3 i \pi}{4}} \Gamma\left(\frac{3}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{4}, \frac{3}{4} \\ \frac{7}{4} \end{matrix}\middle| {- \frac{4}{5}} \right)}}{5 \Gamma\left(\frac{7}{4}\right)}$$ 
=
= 
       -3*pi*I                                                 -3*pi*I                                  
       -------              _                                  -------              _                   
  ___     4                |_  /1/4, 3/4 |   \       ___  3/4     4                |_  /1/4, 3/4 |     \
\/ 5 *e       *Gamma(3/4)* |   |         | -1|   2*\/ 2 *5   *e       *Gamma(3/4)* |   |         | -4/5|
                          2  1 \  7/4    |   /                                    2  1 \  7/4    |     /
---------------------------------------------- - -------------------------------------------------------
                  Gamma(7/4)                                           5*Gamma(7/4)
$$\frac{\sqrt{5} e^{- \frac{3 i \pi}{4}} \Gamma\left(\frac{3}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{4}, \frac{3}{4} \\ \frac{7}{4} \end{matrix}\middle| {-1} \right)}}{\Gamma\left(\frac{7}{4}\right)} - \frac{2 \sqrt{2} \cdot 5^{\frac{3}{4}} e^{- \frac{3 i \pi}{4}} \Gamma\left(\frac{3}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{4}, \frac{3}{4} \\ \frac{7}{4} \end{matrix}\middle| {- \frac{4}{5}} \right)}}{5 \Gamma\left(\frac{7}{4}\right)}$$ 
sqrt(5)*exp(-3*pi*i/4)*gamma(3/4)*hyper((1/4, 3/4), (7/4,), -1)/gamma(7/4) - 2*sqrt(2)*5^(3/4)*exp(-3*pi*i/4)*gamma(3/4)*hyper((1/4, 3/4), (7/4,), -4/5)/(5*gamma(7/4))
Respuesta numérica [src] 
(0.276787992253102 - 0.276787992253102j)
(0.276787992253102 - 0.276787992253102j)

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

    © Sr Examen