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Resolución de integrales/ x^2+3/ (9x^5-x+1)/(4x^5+x^2+3)

Integral de (9x^5-x+1)/(4x^5+x^2+3) dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
 oo                 
  /                 
 |                  
 |      5           
 |   9*x  - x + 1   
 |  ------------- dx
 |     5    2       
 |  4*x  + x  + 3   
 |                  
/                   
2
∫2∞(9x5−x)+1(4x5+x2)+3 dx\int\limits_{2}^{\infty} \frac{\left(9 x^{5} - x\right) + 1}{\left(4 x^{5} + x^{2}\right) + 3}\, dx 
Integral((9*x^5 - x + 1)/(4*x^5 + x^2 + 3), (x, 2, oo))
Respuesta (Indefinida) [src] 
  /                                 /                                       /                              2            3\\             /                                       /                       2                           3\\                                  /                                                      /                         2                           3\\             /                                     /                      3                       2\\
 |                                  |       4       2                       |  942       34791*t   129177*t    3287763*t ||             |       4       2                       |764283       52087500*t    3096620*t   1318838832*t ||                                  |        4          3         2                        |  196852       76595016*t    16312105*t   398320752*t ||             |       4        2                    | 9368       43920180*t    416941*t   1333440*t ||
 |     5                  55*RootSum|12501*t  - 42*t  - 12*t + 1, t -> t*log|- --- + x + ------- + --------- + ----------||   28*RootSum|66672*t  - 44*t  + 57*t + 3, t -> t*log|------ + x - ----------- + --------- + -------------||                        14*RootSum|266688*t  - 66672*t  + 6436*t  - 321*t + 9, t -> t*log|- ------ + x - ----------- + ---------- + ------------||   29*RootSum|16668*t  + 280*t  - t + 1, t -> t*log|----- + x - ----------- - -------- + ----------||
 |  9*x  - x + 1                    \                                       \  967         3868       1934        3868   //             \                                       \394169          394169       394169        394169   //   7*log(1 + x)   9*x             \                                                      \  65753           65753        197259        65753    //             \                                     \15233          15233       15233       15233   //
 | ------------- dx = C - ------------------------------------------------------------------------------------------------- - --------------------------------------------------------------------------------------------------------- - ------------ + --- + -------------------------------------------------------------------------------------------------------------------------- + --------------------------------------------------------------------------------------------------
 |    5    2                                                              12                                                                                                      9                                                            18         4                                                                9                                                                                                                12                                                
 | 4*x  + x  + 3                                                                                                                                                                                                                                                                                                                                                                                                                                                                              
 |                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            
/
∫(9x5−x)+1(4x5+x2)+3 dx=C+9x4−7log⁡(x+1)18−28RootSum⁡(66672t4−44t2+57t+3,(t↦tlog⁡(1318838832t3394169−52087500t2394169+3096620t394169+x+764283394169)))9+29RootSum⁡(16668t4+280t2−t+1,(t↦tlog⁡(−43920180t315233+1333440t215233−416941t15233+x+936815233)))12−55RootSum⁡(12501t4−42t2−12t+1,(t↦tlog⁡(3287763t33868+129177t21934+34791t3868+x−942967)))12+14RootSum⁡(266688t4−66672t3+6436t2−321t+9,(t↦tlog⁡(398320752t365753−76595016t265753+16312105t197259+x−19685265753)))9\int \frac{\left(9 x^{5} - x\right) + 1}{\left(4 x^{5} + x^{2}\right) + 3}\, dx = C + \frac{9 x}{4} - \frac{7 \log{\left(x + 1 \right)}}{18} - \frac{28 \operatorname{RootSum} {\left(66672 t^{4} - 44 t^{2} + 57 t + 3, \left( t \mapsto t \log{\left(\frac{1318838832 t^{3}}{394169} - \frac{52087500 t^{2}}{394169} + \frac{3096620 t}{394169} + x + \frac{764283}{394169} \right)} \right)\right)}}{9} + \frac{29 \operatorname{RootSum} {\left(16668 t^{4} + 280 t^{2} - t + 1, \left( t \mapsto t \log{\left(- \frac{43920180 t^{3}}{15233} + \frac{1333440 t^{2}}{15233} - \frac{416941 t}{15233} + x + \frac{9368}{15233} \right)} \right)\right)}}{12} - \frac{55 \operatorname{RootSum} {\left(12501 t^{4} - 42 t^{2} - 12 t + 1, \left( t \mapsto t \log{\left(\frac{3287763 t^{3}}{3868} + \frac{129177 t^{2}}{1934} + \frac{34791 t}{3868} + x - \frac{942}{967} \right)} \right)\right)}}{12} + \frac{14 \operatorname{RootSum} {\left(266688 t^{4} - 66672 t^{3} + 6436 t^{2} - 321 t + 9, \left( t \mapsto t \log{\left(\frac{398320752 t^{3}}{65753} - \frac{76595016 t^{2}}{65753} + \frac{16312105 t}{197259} + x - \frac{196852}{65753} \right)} \right)\right)}}{9}
Simplificar
Gráfica
2.00002.01002.00102.00202.00302.00402.00502.00602.00702.00802.00900.05.0
Trazar el gráfico f(x)
Respuesta [src] 
 oo                 
  /                 
 |                  
 |              5   
 |   1 - x + 9*x    
 |  ------------- dx
 |       2      5   
 |  3 + x  + 4*x    
 |                  
/                   
2
∫2∞9x5−x+14x5+x2+3 dx\int\limits_{2}^{\infty} \frac{9 x^{5} - x + 1}{4 x^{5} + x^{2} + 3}\, dx 
=
= 
 oo                 
  /                 
 |                  
 |              5   
 |   1 - x + 9*x    
 |  ------------- dx
 |       2      5   
 |  3 + x  + 4*x    
 |                  
/                   
2
∫2∞9x5−x+14x5+x2+3 dx\int\limits_{2}^{\infty} \frac{9 x^{5} - x + 1}{4 x^{5} + x^{2} + 3}\, dx 
Integral((1 - x + 9*x^5)/(3 + x^2 + 4*x^5), (x, 2, oo))

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

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