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Resolución de integrales/ (x^2)/ (x^4+4)/ ((x^4+4)^(1/2))/(x^2)

Integral de ((x^4+4)^(1/2))/(x^2) dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
     ___              
 2*\/ 3               
    /                 
   |                  
   |       ________   
   |      /  4        
   |    \/  x  + 4    
   |    ----------- dx
   |          2       
   |         x        
   |                  
  /                   
  2
∫223x4+4x2 dx\int\limits_{2}^{2 \sqrt{3}} \frac{\sqrt{x^{4} + 4}}{x^{2}}\, dx 
Integral(sqrt(x^4 + 4)/x^2, (x, 2, 2*sqrt(3)))
Respuesta (Indefinida) [src] 
  /                       /                                     
 |                       |                                      
 |    ________           |    _______________________________   
 |   /  4                |   / /     2      \ /     2      \    
 | \/  x  + 4            | \/  \2 + x  - 2*x/*\2 + x  + 2*x/    
 | ----------- dx = C +  | ---------------------------------- dx
 |       2               |                  2                   
 |      x                |                 x                    
 |                       |                                      
/                       /
∫x4+4x2 dx=C+∫(x2−2x+2)(x2+2x+2)x2 dx\int \frac{\sqrt{x^{4} + 4}}{x^{2}}\, dx = C + \int \frac{\sqrt{\left(x^{2} - 2 x + 2\right) \left(x^{2} + 2 x + 2\right)}}{x^{2}}\, dx
Simplificar
Gráfica
2.02.12.22.32.42.52.62.72.82.93.03.13.23.33.42-2
Trazar el gráfico f(x)
Respuesta [src] 
                _                                               _                         
               |_  /-1/2, -1/4 |    pi*I\     ___              |_  /-1/2, -1/4 |     pi*I\
  Gamma(-1/4)* |   |           | 4*e    |   \/ 3 *Gamma(-1/4)* |   |           | 36*e    |
              2  1 \   3/4     |        /                     2  1 \   3/4     |         /
- --------------------------------------- + ----------------------------------------------
                4*Gamma(3/4)                                12*Gamma(3/4)
−Γ(−14)2F1(−12,−1434|4eiπ)4Γ(34)+3Γ(−14)2F1(−12,−1434|36eiπ)12Γ(34)- \frac{\Gamma\left(- \frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, - \frac{1}{4} \\ \frac{3}{4} \end{matrix}\middle| {4 e^{i \pi}} \right)}}{4 \Gamma\left(\frac{3}{4}\right)} + \frac{\sqrt{3} \Gamma\left(- \frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, - \frac{1}{4} \\ \frac{3}{4} \end{matrix}\middle| {36 e^{i \pi}} \right)}}{12 \Gamma\left(\frac{3}{4}\right)} 
=
= 
                _                                               _                         
               |_  /-1/2, -1/4 |    pi*I\     ___              |_  /-1/2, -1/4 |     pi*I\
  Gamma(-1/4)* |   |           | 4*e    |   \/ 3 *Gamma(-1/4)* |   |           | 36*e    |
              2  1 \   3/4     |        /                     2  1 \   3/4     |         /
- --------------------------------------- + ----------------------------------------------
                4*Gamma(3/4)                                12*Gamma(3/4)
−Γ(−14)2F1(−12,−1434|4eiπ)4Γ(34)+3Γ(−14)2F1(−12,−1434|36eiπ)12Γ(34)- \frac{\Gamma\left(- \frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, - \frac{1}{4} \\ \frac{3}{4} \end{matrix}\middle| {4 e^{i \pi}} \right)}}{4 \Gamma\left(\frac{3}{4}\right)} + \frac{\sqrt{3} \Gamma\left(- \frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, - \frac{1}{4} \\ \frac{3}{4} \end{matrix}\middle| {36 e^{i \pi}} \right)}}{12 \Gamma\left(\frac{3}{4}\right)} 
-gamma(-1/4)*hyper((-1/2, -1/4), (3/4,), 4*exp_polar(pi*i))/(4*gamma(3/4)) + sqrt(3)*gamma(-1/4)*hyper((-1/2, -1/4), (3/4,), 36*exp_polar(pi*i))/(12*gamma(3/4))
Respuesta numérica [src] 
1.52937226142443
1.52937226142443

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

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