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Resolución de integrales/ x^2-1/ 5/x^2/ 1/(x^2-1+(5/x^2))

Integral de 1/(x^2-1+(5/x^2)) dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  1               
  /               
 |                
 |       1        
 |  ----------- dx
 |   2       5    
 |  x  - 1 + --   
 |            2   
 |           x    
 |                
/                 
0
∫011(x2−1)+5x2 dx\int\limits_{0}^{1} \frac{1}{\left(x^{2} - 1\right) + \frac{5}{x^{2}}}\, dx 
Integral(1/(x^2 - 1 + 5/x^2), (x, 0, 1))
Respuesta (Indefinida) [src] 
  /                                                                               
 |                                                                                
 |      1                      /      4       2                /               3\\
 | ----------- dx = C + RootSum\5776*t  + 76*t  + 5, t -> t*log\x + 2*t + 304*t //
 |  2       5                                                                     
 | x  - 1 + --                                                                    
 |           2                                                                    
 |          x                                                                     
 |                                                                                
/
∫1(x2−1)+5x2 dx=C+RootSum⁡(5776t4+76t2+5,(t↦tlog⁡(304t3+2t+x)))\int \frac{1}{\left(x^{2} - 1\right) + \frac{5}{x^{2}}}\, dx = C + \operatorname{RootSum} {\left(5776 t^{4} + 76 t^{2} + 5, \left( t \mapsto t \log{\left(304 t^{3} + 2 t + x \right)} \right)\right)}
Simplificar
Gráfica
0.001.000.100.200.300.400.500.600.700.800.901-1
Trazar el gráfico f(x)
Respuesta [src] 
         /      4       2                /           3\\          /      4       2                /               3\\
- RootSum\5776*t  + 76*t  + 5, t -> t*log\2*t + 304*t // + RootSum\5776*t  + 76*t  + 5, t -> t*log\1 + 2*t + 304*t //
−RootSum⁡(5776t4+76t2+5,(t↦tlog⁡(304t3+2t)))+RootSum⁡(5776t4+76t2+5,(t↦tlog⁡(304t3+2t+1)))- \operatorname{RootSum} {\left(5776 t^{4} + 76 t^{2} + 5, \left( t \mapsto t \log{\left(304 t^{3} + 2 t \right)} \right)\right)} + \operatorname{RootSum} {\left(5776 t^{4} + 76 t^{2} + 5, \left( t \mapsto t \log{\left(304 t^{3} + 2 t + 1 \right)} \right)\right)} 
=
= 
         /      4       2                /           3\\          /      4       2                /               3\\
- RootSum\5776*t  + 76*t  + 5, t -> t*log\2*t + 304*t // + RootSum\5776*t  + 76*t  + 5, t -> t*log\1 + 2*t + 304*t //
−RootSum⁡(5776t4+76t2+5,(t↦tlog⁡(304t3+2t)))+RootSum⁡(5776t4+76t2+5,(t↦tlog⁡(304t3+2t+1)))- \operatorname{RootSum} {\left(5776 t^{4} + 76 t^{2} + 5, \left( t \mapsto t \log{\left(304 t^{3} + 2 t \right)} \right)\right)} + \operatorname{RootSum} {\left(5776 t^{4} + 76 t^{2} + 5, \left( t \mapsto t \log{\left(304 t^{3} + 2 t + 1 \right)} \right)\right)} 
-RootSum(5776*_t^4 + 76*_t^2 + 5, Lambda(_t, _t*log(2*_t + 304*_t^3))) + RootSum(5776*_t^4 + 76*_t^2 + 5, Lambda(_t, _t*log(1 + 2*_t + 304*_t^3)))
Respuesta numérica [src] 
0.0690488971170965
0.0690488971170965

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

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