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1/sqrt(1+x^4)
Solving integrals/ 1/sqrt(1+x^4)

Integral of 1/sqrt(1+x^4) dx

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The solution

You have entered [src] 
 10                 
  /                 
 |                  
 |         1        
 |  1*----------- dx
 |       ________   
 |      /      4    
 |    \/  1 + x     
 |                  
/                   
2
∫2101⋅1x4+1 dx\int\limits_{2}^{10} 1 \cdot \frac{1}{\sqrt{x^{4} + 1}}\, dx 
Integral(1/sqrt(1 + x^4), (x, 2, 10))
The answer (Indefinite) [src] 
                                         _                       
  /                                     |_  /1/4, 1/2 |  4  pi*I\
 |                        x*Gamma(1/4)* |   |         | x *e    |
 |        1                            2  1 \  5/4    |         /
 | 1*----------- dx = C + ---------------------------------------
 |      ________                        4*Gamma(5/4)             
 |     /      4                                                  
 |   \/  1 + x                                                   
 |                                                               
/
∫1x4+1  dx\int {{{1}\over{\sqrt{x^4+1}}}}{\;dx}
Simplify
The graph
2.03.04.05.06.07.08.09.010.002
Plot the graph f(x)
The answer [src] 
               _                                         _                          
              |_  /1/4, 1/2 |     pi*I\                 |_  /1/4, 1/2 |        pi*I\
  Gamma(1/4)* |   |         | 16*e    |   5*Gamma(1/4)* |   |         | 10000*e    |
             2  1 \  5/4    |         /                2  1 \  5/4    |            /
- ------------------------------------- + ------------------------------------------
               2*Gamma(5/4)                              2*Gamma(5/4)
∫2101x4+1  dx\int_{2}^{10}{{{1}\over{\sqrt{x^4+1}}}\;dx} 
=
= 
               _                                         _                          
              |_  /1/4, 1/2 |     pi*I\                 |_  /1/4, 1/2 |        pi*I\
  Gamma(1/4)* |   |         | 16*e    |   5*Gamma(1/4)* |   |         | 10000*e    |
             2  1 \  5/4    |         /                2  1 \  5/4    |            /
- ------------------------------------- + ------------------------------------------
               2*Gamma(5/4)                              2*Gamma(5/4)
−Γ(14)2F1(14,1254|16eiπ)2Γ(54)+5Γ(14)2F1(14,1254|10000eiπ)2Γ(54)- \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| {16 e^{i \pi}} \right)}}{2 \Gamma\left(\frac{5}{4}\right)} + \frac{5 \Gamma\left(\frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{4}, \frac{1}{2} \\ \frac{5}{4} \end{matrix}\middle| {10000 e^{i \pi}} \right)}}{2 \Gamma\left(\frac{5}{4}\right)}
Simplify
Numerical answer [src] 
0.39695456316779
0.39695456316779
The graph
Integral of 1/sqrt(1+x^4) dx

    Use the examples entering the upper and lower limits of integration.

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