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Resolución de integrales/ x/(x^4+16)/ dx/(x^4+16)

Integral de dx/(x^4+16) dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  1           
  /           
 |            
 |     1      
 |  ------- dx
 |   4        
 |  x  + 16   
 |            
/             
0
$$\int\limits_{0}^{1} \frac{1}{x^{4} + 16}\, dx$$ 
Integral(1/(x^4 + 16), (x, 0, 1))
Respuesta (Indefinida) [src] 
                                                              /        ___\             /         ___\                                
  /                                                   ___     |    x*\/ 2 |     ___     |     x*\/ 2 |                                
 |                    ___    /     2         ___\   \/ 2 *atan|1 + -------|   \/ 2 *atan|-1 + -------|     ___    /     2         ___\
 |    1             \/ 2 *log\4 + x  - 2*x*\/ 2 /             \       2   /             \        2   /   \/ 2 *log\4 + x  + 2*x*\/ 2 /
 | ------- dx = C - ----------------------------- + ----------------------- + ------------------------ + -----------------------------
 |  4                             64                           32                        32                            64             
 | x  + 16                                                                                                                            
 |                                                                                                                                    
/
$$\int \frac{1}{x^{4} + 16}\, dx = C - \frac{\sqrt{2} \log{\left(x^{2} - 2 \sqrt{2} x + 4 \right)}}{64} + \frac{\sqrt{2} \log{\left(x^{2} + 2 \sqrt{2} x + 4 \right)}}{64} + \frac{\sqrt{2} \operatorname{atan}{\left(\frac{\sqrt{2} x}{2} - 1 \right)}}{32} + \frac{\sqrt{2} \operatorname{atan}{\left(\frac{\sqrt{2} x}{2} + 1 \right)}}{32}$$
Simplificar
Gráfica
Trazar el gráfico f(x)
Respuesta [src] 
            /      ___\                                      /      ___\                         
    ___     |    \/ 2 |                              ___     |    \/ 2 |                         
  \/ 2 *atan|1 - -----|     ___    /        ___\   \/ 2 *atan|1 + -----|     ___    /        ___\
            \      2  /   \/ 2 *log\5 - 2*\/ 2 /             \      2  /   \/ 2 *log\5 + 2*\/ 2 /
- --------------------- - ---------------------- + --------------------- + ----------------------
            32                      64                       32                      64
$$- \frac{\sqrt{2} \log{\left(5 - 2 \sqrt{2} \right)}}{64} - \frac{\sqrt{2} \operatorname{atan}{\left(1 - \frac{\sqrt{2}}{2} \right)}}{32} + \frac{\sqrt{2} \log{\left(2 \sqrt{2} + 5 \right)}}{64} + \frac{\sqrt{2} \operatorname{atan}{\left(\frac{\sqrt{2}}{2} + 1 \right)}}{32}$$ 
=
= 
            /      ___\                                      /      ___\                         
    ___     |    \/ 2 |                              ___     |    \/ 2 |                         
  \/ 2 *atan|1 - -----|     ___    /        ___\   \/ 2 *atan|1 + -----|     ___    /        ___\
            \      2  /   \/ 2 *log\5 - 2*\/ 2 /             \      2  /   \/ 2 *log\5 + 2*\/ 2 /
- --------------------- - ---------------------- + --------------------- + ----------------------
            32                      64                       32                      64
$$- \frac{\sqrt{2} \log{\left(5 - 2 \sqrt{2} \right)}}{64} - \frac{\sqrt{2} \operatorname{atan}{\left(1 - \frac{\sqrt{2}}{2} \right)}}{32} + \frac{\sqrt{2} \log{\left(2 \sqrt{2} + 5 \right)}}{64} + \frac{\sqrt{2} \operatorname{atan}{\left(\frac{\sqrt{2}}{2} + 1 \right)}}{32}$$ 
-sqrt(2)*atan(1 - sqrt(2)/2)/32 - sqrt(2)*log(5 - 2*sqrt(2))/64 + sqrt(2)*atan(1 + sqrt(2)/2)/32 + sqrt(2)*log(5 + 2*sqrt(2))/64
Respuesta numérica [src] 
0.0617447563846798
0.0617447563846798

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

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