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Resolución de integrales/ x^2+2/ 4*x^2/ (x+3)/ 5-4*x/ 3*x^5/ (x+3)/(3*x^5-4*x^2+2)

Integral de (x+3)/(3*x^5-4*x^2+2) dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
 oo                   
  /                   
 |                    
 |       x + 3        
 |  --------------- dx
 |     5      2       
 |  3*x  - 4*x  + 2   
 |                    
/                     
1
∫1∞x+3(3x5−4x2)+2 dx\int\limits_{1}^{\infty} \frac{x + 3}{\left(3 x^{5} - 4 x^{2}\right) + 2}\, dx 
Integral((x + 3)/(3*x^5 - 4*x^2 + 2), (x, 1, oo))
Solución detallada

  1. Vuelva a escribir el integrando:

    x+3(3x5−4x2)+2=x(3x5−4x2)+2+3(3x5−4x2)+2\frac{x + 3}{\left(3 x^{5} - 4 x^{2}\right) + 2} = \frac{x}{\left(3 x^{5} - 4 x^{2}\right) + 2} + \frac{3}{\left(3 x^{5} - 4 x^{2}\right) + 2}

  2. Integramos término a término:

    1. No puedo encontrar los pasos en la búsqueda de esta integral.

      Pero la integral

      RootSum⁡(114408t5+2880t3−80t2−20t+1,(t↦tlog⁡(−305088t425−19068t325−1536t25−32t3+x+15275)))\operatorname{RootSum} {\left(114408 t^{5} + 2880 t^{3} - 80 t^{2} - 20 t + 1, \left( t \mapsto t \log{\left(- \frac{305088 t^{4}}{25} - \frac{19068 t^{3}}{25} - \frac{1536 t^{2}}{5} - \frac{32 t}{3} + x + \frac{152}{75} \right)} \right)\right)}

    1. La integral del producto de una función por una constante es la constante por la integral de esta función:

      ∫3(3x5−4x2)+2 dx=3∫1(3x5−4x2)+2 dx\int \frac{3}{\left(3 x^{5} - 4 x^{2}\right) + 2}\, dx = 3 \int \frac{1}{\left(3 x^{5} - 4 x^{2}\right) + 2}\, dx

      1. No puedo encontrar los pasos en la búsqueda de esta integral.

        Pero la integral

        RootSum⁡(76272t5+2304t3−400t2−1,(t↦tlog⁡(−132442361856t435403001−1565482800t335403001−3047376192t235403001+751861690t35403001+x+1644600035403001)))\operatorname{RootSum} {\left(76272 t^{5} + 2304 t^{3} - 400 t^{2} - 1, \left( t \mapsto t \log{\left(- \frac{132442361856 t^{4}}{35403001} - \frac{1565482800 t^{3}}{35403001} - \frac{3047376192 t^{2}}{35403001} + \frac{751861690 t}{35403001} + x + \frac{16446000}{35403001} \right)} \right)\right)}

      Por lo tanto, el resultado es: 3RootSum⁡(76272t5+2304t3−400t2−1,(t↦tlog⁡(−132442361856t435403001−1565482800t335403001−3047376192t235403001+751861690t35403001+x+1644600035403001)))3 \operatorname{RootSum} {\left(76272 t^{5} + 2304 t^{3} - 400 t^{2} - 1, \left( t \mapsto t \log{\left(- \frac{132442361856 t^{4}}{35403001} - \frac{1565482800 t^{3}}{35403001} - \frac{3047376192 t^{2}}{35403001} + \frac{751861690 t}{35403001} + x + \frac{16446000}{35403001} \right)} \right)\right)}

    El resultado es: 3RootSum⁡(76272t5+2304t3−400t2−1,(t↦tlog⁡(−132442361856t435403001−1565482800t335403001−3047376192t235403001+751861690t35403001+x+1644600035403001)))+RootSum⁡(114408t5+2880t3−80t2−20t+1,(t↦tlog⁡(−305088t425−19068t325−1536t25−32t3+x+15275)))3 \operatorname{RootSum} {\left(76272 t^{5} + 2304 t^{3} - 400 t^{2} - 1, \left( t \mapsto t \log{\left(- \frac{132442361856 t^{4}}{35403001} - \frac{1565482800 t^{3}}{35403001} - \frac{3047376192 t^{2}}{35403001} + \frac{751861690 t}{35403001} + x + \frac{16446000}{35403001} \right)} \right)\right)} + \operatorname{RootSum} {\left(114408 t^{5} + 2880 t^{3} - 80 t^{2} - 20 t + 1, \left( t \mapsto t \log{\left(- \frac{305088 t^{4}}{25} - \frac{19068 t^{3}}{25} - \frac{1536 t^{2}}{5} - \frac{32 t}{3} + x + \frac{152}{75} \right)} \right)\right)}

  3. Añadimos la constante de integración:

    3RootSum⁡(76272t5+2304t3−400t2−1,(t↦tlog⁡(−132442361856t435403001−1565482800t335403001−3047376192t235403001+751861690t35403001+x+1644600035403001)))+RootSum⁡(114408t5+2880t3−80t2−20t+1,(t↦tlog⁡(−305088t425−19068t325−1536t25−32t3+x+15275)))+constant3 \operatorname{RootSum} {\left(76272 t^{5} + 2304 t^{3} - 400 t^{2} - 1, \left( t \mapsto t \log{\left(- \frac{132442361856 t^{4}}{35403001} - \frac{1565482800 t^{3}}{35403001} - \frac{3047376192 t^{2}}{35403001} + \frac{751861690 t}{35403001} + x + \frac{16446000}{35403001} \right)} \right)\right)} + \operatorname{RootSum} {\left(114408 t^{5} + 2880 t^{3} - 80 t^{2} - 20 t + 1, \left( t \mapsto t \log{\left(- \frac{305088 t^{4}}{25} - \frac{19068 t^{3}}{25} - \frac{1536 t^{2}}{5} - \frac{32 t}{3} + x + \frac{152}{75} \right)} \right)\right)}+ \mathrm{constant}

Respuesta:

3RootSum⁡(76272t5+2304t3−400t2−1,(t↦tlog⁡(−132442361856t435403001−1565482800t335403001−3047376192t235403001+751861690t35403001+x+1644600035403001)))+RootSum⁡(114408t5+2880t3−80t2−20t+1,(t↦tlog⁡(−305088t425−19068t325−1536t25−32t3+x+15275)))+constant3 \operatorname{RootSum} {\left(76272 t^{5} + 2304 t^{3} - 400 t^{2} - 1, \left( t \mapsto t \log{\left(- \frac{132442361856 t^{4}}{35403001} - \frac{1565482800 t^{3}}{35403001} - \frac{3047376192 t^{2}}{35403001} + \frac{751861690 t}{35403001} + x + \frac{16446000}{35403001} \right)} \right)\right)} + \operatorname{RootSum} {\left(114408 t^{5} + 2880 t^{3} - 80 t^{2} - 20 t + 1, \left( t \mapsto t \log{\left(- \frac{305088 t^{4}}{25} - \frac{19068 t^{3}}{25} - \frac{1536 t^{2}}{5} - \frac{32 t}{3} + x + \frac{152}{75} \right)} \right)\right)}+ \mathrm{constant}

Respuesta (Indefinida) [src] 
  /                                                                                                                                                                                                                                                                            
 |                                   /                                           /                             4               2               3              \\          /                                                  /                  4          3         2       \\
 |      x + 3                        |       5         3        2                |16446000       132442361856*t    3047376192*t    1565482800*t    751861690*t||          |        5         3       2                       |152       305088*t    19068*t    1536*t    32*t||
 | --------------- dx = C + 3*RootSum|76272*t  + 2304*t  - 400*t  - 1, t -> t*log|-------- + x - --------------- - ------------- - ------------- + -----------|| + RootSum|114408*t  + 2880*t  - 80*t  - 20*t + 1, t -> t*log|--- + x - --------- - -------- - ------- - ----||
 |    5      2                       \                                           \35403001           35403001         35403001        35403001       35403001 //          \                                                  \ 75           25         25         5       3  //
 | 3*x  - 4*x  + 2                                                                                                                                                                                                                                                             
 |                                                                                                                                                                                                                                                                             
/
∫x+3(3x5−4x2)+2 dx=C+3RootSum⁡(76272t5+2304t3−400t2−1,(t↦tlog⁡(−132442361856t435403001−1565482800t335403001−3047376192t235403001+751861690t35403001+x+1644600035403001)))+RootSum⁡(114408t5+2880t3−80t2−20t+1,(t↦tlog⁡(−305088t425−19068t325−1536t25−32t3+x+15275)))\int \frac{x + 3}{\left(3 x^{5} - 4 x^{2}\right) + 2}\, dx = C + 3 \operatorname{RootSum} {\left(76272 t^{5} + 2304 t^{3} - 400 t^{2} - 1, \left( t \mapsto t \log{\left(- \frac{132442361856 t^{4}}{35403001} - \frac{1565482800 t^{3}}{35403001} - \frac{3047376192 t^{2}}{35403001} + \frac{751861690 t}{35403001} + x + \frac{16446000}{35403001} \right)} \right)\right)} + \operatorname{RootSum} {\left(114408 t^{5} + 2880 t^{3} - 80 t^{2} - 20 t + 1, \left( t \mapsto t \log{\left(- \frac{305088 t^{4}}{25} - \frac{19068 t^{3}}{25} - \frac{1536 t^{2}}{5} - \frac{32 t}{3} + x + \frac{152}{75} \right)} \right)\right)}
Simplificar
Gráfica
1.00001.01001.00101.00201.00301.00401.00501.00601.00701.00801.00905-5
Trazar el gráfico f(x)
Respuesta [src] 
 oo                   
  /                   
 |                    
 |       3 + x        
 |  --------------- dx
 |         2      5   
 |  2 - 4*x  + 3*x    
 |                    
/                     
1
∫1∞x+33x5−4x2+2 dx\int\limits_{1}^{\infty} \frac{x + 3}{3 x^{5} - 4 x^{2} + 2}\, dx 
=
= 
 oo                   
  /                   
 |                    
 |       3 + x        
 |  --------------- dx
 |         2      5   
 |  2 - 4*x  + 3*x    
 |                    
/                     
1
∫1∞x+33x5−4x2+2 dx\int\limits_{1}^{\infty} \frac{x + 3}{3 x^{5} - 4 x^{2} + 2}\, dx 
Integral((3 + x)/(2 - 4*x^2 + 3*x^5), (x, 1, oo))

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

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