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

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

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
 9/10          
   /           
  |            
  |      2     
  |     x      
  |   ------ dx
  |    4       
  |   x  + 1   
  |            
 /             
-9/10
∫−910910x2x4+1 dx\int\limits_{- \frac{9}{10}}^{\frac{9}{10}} \frac{x^{2}}{x^{4} + 1}\, dx 
Integral(x^2/(x^4 + 1), (x, -9/10, 9/10))
Respuesta (Indefinida) [src] 
  /                                                                                                                              
 |                                                                                                                               
 |    2              ___    /     2       ___\     ___     /        ___\     ___     /         ___\     ___    /     2       ___\
 |   x             \/ 2 *log\1 + x  + x*\/ 2 /   \/ 2 *atan\1 + x*\/ 2 /   \/ 2 *atan\-1 + x*\/ 2 /   \/ 2 *log\1 + x  - x*\/ 2 /
 | ------ dx = C - --------------------------- + ----------------------- + ------------------------ + ---------------------------
 |  4                           8                           4                         4                            8             
 | x  + 1                                                                                                                        
 |                                                                                                                               
/
∫x2x4+1 dx=C+2log⁡(x2−2x+1)8−2log⁡(x2+2x+1)8+2atan⁡(2x−1)4+2atan⁡(2x+1)4\int \frac{x^{2}}{x^{4} + 1}\, dx = C + \frac{\sqrt{2} \log{\left(x^{2} - \sqrt{2} x + 1 \right)}}{8} - \frac{\sqrt{2} \log{\left(x^{2} + \sqrt{2} x + 1 \right)}}{8} + \frac{\sqrt{2} \operatorname{atan}{\left(\sqrt{2} x - 1 \right)}}{4} + \frac{\sqrt{2} \operatorname{atan}{\left(\sqrt{2} x + 1 \right)}}{4}
Simplificar
Gráfica
-0.8-0.6-0.4-0.20.00.20.40.60.81.0-0.5
Trazar el gráfico f(x)
Respuesta [src] 
          /        ___\             /        ___\            /          ___\            /          ___\
  ___     |    9*\/ 2 |     ___     |    9*\/ 2 |     ___    |181   9*\/ 2 |     ___    |181   9*\/ 2 |
\/ 2 *atan|1 + -------|   \/ 2 *atan|1 - -------|   \/ 2 *log|--- + -------|   \/ 2 *log|--- - -------|
          \       10  /             \       10  /            \100      10  /            \100      10  /
----------------------- - ----------------------- - ------------------------ + ------------------------
           2                         2                         4                          4
−2log⁡(9210+181100)4+2log⁡(181100−9210)4−2atan⁡(1−9210)2+2atan⁡(1+9210)2- \frac{\sqrt{2} \log{\left(\frac{9 \sqrt{2}}{10} + \frac{181}{100} \right)}}{4} + \frac{\sqrt{2} \log{\left(\frac{181}{100} - \frac{9 \sqrt{2}}{10} \right)}}{4} - \frac{\sqrt{2} \operatorname{atan}{\left(1 - \frac{9 \sqrt{2}}{10} \right)}}{2} + \frac{\sqrt{2} \operatorname{atan}{\left(1 + \frac{9 \sqrt{2}}{10} \right)}}{2} 
=
= 
          /        ___\             /        ___\            /          ___\            /          ___\
  ___     |    9*\/ 2 |     ___     |    9*\/ 2 |     ___    |181   9*\/ 2 |     ___    |181   9*\/ 2 |
\/ 2 *atan|1 + -------|   \/ 2 *atan|1 - -------|   \/ 2 *log|--- + -------|   \/ 2 *log|--- - -------|
          \       10  /             \       10  /            \100      10  /            \100      10  /
----------------------- - ----------------------- - ------------------------ + ------------------------
           2                         2                         4                          4
−2log⁡(9210+181100)4+2log⁡(181100−9210)4−2atan⁡(1−9210)2+2atan⁡(1+9210)2- \frac{\sqrt{2} \log{\left(\frac{9 \sqrt{2}}{10} + \frac{181}{100} \right)}}{4} + \frac{\sqrt{2} \log{\left(\frac{181}{100} - \frac{9 \sqrt{2}}{10} \right)}}{4} - \frac{\sqrt{2} \operatorname{atan}{\left(1 - \frac{9 \sqrt{2}}{10} \right)}}{2} + \frac{\sqrt{2} \operatorname{atan}{\left(1 + \frac{9 \sqrt{2}}{10} \right)}}{2} 
sqrt(2)*atan(1 + 9*sqrt(2)/10)/2 - sqrt(2)*atan(1 - 9*sqrt(2)/10)/2 - sqrt(2)*log(181/100 + 9*sqrt(2)/10)/4 + sqrt(2)*log(181/100 - 9*sqrt(2)/10)/4
Respuesta numérica [src] 
0.388208300640057
0.388208300640057

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

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