Sr Examen

Otras calculadoras

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

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src]
 1/10              
   /               
  |                
  |       1        
  |  ----------- dx
  |     ________   
  |    /      4    
  |  \/  1 + x     
  |                
 /                 
 0                 
$$\int\limits_{0}^{\frac{1}{10}} \frac{1}{\sqrt{x^{4} + 1}}\, dx$$
Integral(1/(sqrt(1 + x^4)), (x, 0, 1/10))
Respuesta (Indefinida) [src]
                                       _                       
  /                                   |_  /1/4, 1/2 |  4  pi*I\
 |                      x*Gamma(1/4)* |   |         | x *e    |
 |      1                            2  1 \  5/4    |         /
 | ----------- dx = C + ---------------------------------------
 |    ________                        4*Gamma(5/4)             
 |   /      4                                                  
 | \/  1 + x                                                   
 |                                                             
/                                                              
$$\int \frac{1}{\sqrt{x^{4} + 1}}\, dx = C + \frac{x \Gamma\left(\frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{4}, \frac{1}{2} \\ \frac{5}{4} \end{matrix}\middle| {x^{4} e^{i \pi}} \right)}}{4 \Gamma\left(\frac{5}{4}\right)}$$
Gráfica
Respuesta [src]
             _                       
            |_  /1/4, 1/2 |         \
Gamma(1/4)* |   |         | -1/10000|
           2  1 \  5/4    |         /
-------------------------------------
            40*Gamma(5/4)            
$$\frac{\Gamma\left(\frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{4}, \frac{1}{2} \\ \frac{5}{4} \end{matrix}\middle| {- \frac{1}{10000}} \right)}}{40 \Gamma\left(\frac{5}{4}\right)}$$
=
=
             _                       
            |_  /1/4, 1/2 |         \
Gamma(1/4)* |   |         | -1/10000|
           2  1 \  5/4    |         /
-------------------------------------
            40*Gamma(5/4)            
$$\frac{\Gamma\left(\frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{4}, \frac{1}{2} \\ \frac{5}{4} \end{matrix}\middle| {- \frac{1}{10000}} \right)}}{40 \Gamma\left(\frac{5}{4}\right)}$$
gamma(1/4)*hyper((1/4, 1/2), (5/4,), -1/10000)/(40*gamma(5/4))
Respuesta numérica [src]
0.0999990000416643
0.0999990000416643

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