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Resolución de integrales/ 2-x^2/ x^2*dx/ x^2*dx/(2-x^2)

Integral de x^2*dx/(2-x^2) dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  1          
  /          
 |           
 |     2     
 |    x      
 |  ------ dx
 |       2   
 |  2 - x    
 |           
/            
0
∫01x22−x2 dx\int\limits_{0}^{1} \frac{x^{2}}{2 - x^{2}}\, dx 
Integral(x^2/(2 - x^2), (x, 0, 1))
Respuesta (Indefinida) [src] 
                         //            /    ___\             \
                         ||   ___      |x*\/ 2 |             |
  /                      ||-\/ 2 *acoth|-------|             |
 |                       ||            \   2   /        2    |
 |    2                  ||----------------------  for x  > 2|
 |   x                   ||          2                       |
 | ------ dx = C - x - 2*|<                                  |
 |      2                ||            /    ___\             |
 | 2 - x                 ||   ___      |x*\/ 2 |             |
 |                       ||-\/ 2 *atanh|-------|             |
/                        ||            \   2   /        2    |
                         ||----------------------  for x  < 2|
                         \\          2                       /
∫x22−x2 dx=C−x−2({−2acoth⁡(2x2)2for x2>2−2atanh⁡(2x2)2for x2<2)\int \frac{x^{2}}{2 - x^{2}}\, dx = C - x - 2 \left(\begin{cases} - \frac{\sqrt{2} \operatorname{acoth}{\left(\frac{\sqrt{2} x}{2} \right)}}{2} & \text{for}\: x^{2} > 2 \\- \frac{\sqrt{2} \operatorname{atanh}{\left(\frac{\sqrt{2} x}{2} \right)}}{2} & \text{for}\: x^{2} < 2 \end{cases}\right)
Simplificar
Gráfica
0.001.000.100.200.300.400.500.600.700.800.9002
Trazar el gráfico f(x)
Respuesta [src] 
       ___ /          /  ___\\     ___    /      ___\     ___ /          /       ___\\     ___    /  ___\
     \/ 2 *\pi*I + log\\/ 2 //   \/ 2 *log\1 + \/ 2 /   \/ 2 *\pi*I + log\-1 + \/ 2 //   \/ 2 *log\\/ 2 /
-1 + ------------------------- + -------------------- - ------------------------------ - ----------------
                 2                        2                           2                         2
−1−2log⁡(2)2+2log⁡(1+2)2−2(log⁡(−1+2)+iπ)2+2(log⁡(2)+iπ)2-1 - \frac{\sqrt{2} \log{\left(\sqrt{2} \right)}}{2} + \frac{\sqrt{2} \log{\left(1 + \sqrt{2} \right)}}{2} - \frac{\sqrt{2} \left(\log{\left(-1 + \sqrt{2} \right)} + i \pi\right)}{2} + \frac{\sqrt{2} \left(\log{\left(\sqrt{2} \right)} + i \pi\right)}{2} 
=
= 
       ___ /          /  ___\\     ___    /      ___\     ___ /          /       ___\\     ___    /  ___\
     \/ 2 *\pi*I + log\\/ 2 //   \/ 2 *log\1 + \/ 2 /   \/ 2 *\pi*I + log\-1 + \/ 2 //   \/ 2 *log\\/ 2 /
-1 + ------------------------- + -------------------- - ------------------------------ - ----------------
                 2                        2                           2                         2
−1−2log⁡(2)2+2log⁡(1+2)2−2(log⁡(−1+2)+iπ)2+2(log⁡(2)+iπ)2-1 - \frac{\sqrt{2} \log{\left(\sqrt{2} \right)}}{2} + \frac{\sqrt{2} \log{\left(1 + \sqrt{2} \right)}}{2} - \frac{\sqrt{2} \left(\log{\left(-1 + \sqrt{2} \right)} + i \pi\right)}{2} + \frac{\sqrt{2} \left(\log{\left(\sqrt{2} \right)} + i \pi\right)}{2} 
-1 + sqrt(2)*(pi*i + log(sqrt(2)))/2 + sqrt(2)*log(1 + sqrt(2))/2 - sqrt(2)*(pi*i + log(-1 + sqrt(2)))/2 - sqrt(2)*log(sqrt(2))/2
Respuesta numérica [src] 
0.246450480280461
0.246450480280461

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

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