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

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

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  1             
  /             
 |              
 |          2   
 |  / 4    \    
 |  |x  + 5|    
 |  |------|  dx
 |  | 5    |    
 |  \x  + 3/    
 |              
/               
0
∫01(x4+5x5+3)2 dx\int\limits_{0}^{1} \left(\frac{x^{4} + 5}{x^{5} + 3}\right)^{2}\, dx 
Integral(((x^4 + 5)/(x^5 + 3))^2, (x, 0, 1))
Respuesta (Indefinida) [src] 
  /                                                                                                                                                                                                                           
 |                                                                                                                                                                                                                            
 |         2                                                                                                                                                                                                                  
 | / 4    \                                                                                                                                                  4                                                                
 | |x  + 5|                    /            5                /              4\\     2                /              5                   /    225*t\\      3*x          25*x             /      5                /          4\\
 | |------|  dx = C - 3*RootSum\7119140625*t  + 1, t -> t*log\x + 94921875*t // - ------ + 25*RootSum|192216796875*t  - 1024, t -> t*log|x + -----|| - ---------- + ---------- + RootSum\9375*t  + 1, t -> t*log\x + 1875*t //
 | | 5    |                                                                            5             \                                  \      4  //            5            5                                                
 | \x  + 3/                                                                       3 + x                                                                45 + 15*x    45 + 15*x                                                 
 |                                                                                                                                                                                                                            
/
∫(x4+5x5+3)2 dx=C−3x415x5+45+25x15x5+45+RootSum⁡(9375t5+1,(t↦tlog⁡(1875t4+x)))−3RootSum⁡(7119140625t5+1,(t↦tlog⁡(94921875t4+x)))+25RootSum⁡(192216796875t5−1024,(t↦tlog⁡(225t4+x)))−2x5+3\int \left(\frac{x^{4} + 5}{x^{5} + 3}\right)^{2}\, dx = C - \frac{3 x^{4}}{15 x^{5} + 45} + \frac{25 x}{15 x^{5} + 45} + \operatorname{RootSum} {\left(9375 t^{5} + 1, \left( t \mapsto t \log{\left(1875 t^{4} + x \right)} \right)\right)} - 3 \operatorname{RootSum} {\left(7119140625 t^{5} + 1, \left( t \mapsto t \log{\left(94921875 t^{4} + x \right)} \right)\right)} + 25 \operatorname{RootSum} {\left(192216796875 t^{5} - 1024, \left( t \mapsto t \log{\left(\frac{225 t}{4} + x \right)} \right)\right)} - \frac{2}{x^{5} + 3}
Simplificar
Gráfica
0.001.000.100.200.300.400.500.600.700.800.90-1010
Trazar el gráfico f(x)
Respuesta [src] 
            /                                                                        /                    2                            4\\          /                                                                        /                    2                            4\\
8           |              5                3                                        | 151875   34171875*t    87890625*t   7688671875*t ||          |              5                3                                        |5037968   34171875*t    87890625*t   7688671875*t ||
-- - RootSum|192216796875*t  + 68343750000*t  + 4860000000*t - 9993281536, t -> t*log|------- + ----------- + ---------- + -------------|| + RootSum|192216796875*t  + 68343750000*t  + 4860000000*t - 9993281536, t -> t*log|------- + ----------- + ---------- + -------------||
15          \                                                                        \4886093     39088744     39088744      2501679616 //          \                                                                        \4886093     39088744     39088744      2501679616 //
−RootSum⁡(192216796875t5+68343750000t3+4860000000t−9993281536,(t↦tlog⁡(7688671875t42501679616+34171875t239088744+87890625t39088744+1518754886093)))+RootSum⁡(192216796875t5+68343750000t3+4860000000t−9993281536,(t↦tlog⁡(7688671875t42501679616+34171875t239088744+87890625t39088744+50379684886093)))+815- \operatorname{RootSum} {\left(192216796875 t^{5} + 68343750000 t^{3} + 4860000000 t - 9993281536, \left( t \mapsto t \log{\left(\frac{7688671875 t^{4}}{2501679616} + \frac{34171875 t^{2}}{39088744} + \frac{87890625 t}{39088744} + \frac{151875}{4886093} \right)} \right)\right)} + \operatorname{RootSum} {\left(192216796875 t^{5} + 68343750000 t^{3} + 4860000000 t - 9993281536, \left( t \mapsto t \log{\left(\frac{7688671875 t^{4}}{2501679616} + \frac{34171875 t^{2}}{39088744} + \frac{87890625 t}{39088744} + \frac{5037968}{4886093} \right)} \right)\right)} + \frac{8}{15} 
=
= 
            /                                                                        /                    2                            4\\          /                                                                        /                    2                            4\\
8           |              5                3                                        | 151875   34171875*t    87890625*t   7688671875*t ||          |              5                3                                        |5037968   34171875*t    87890625*t   7688671875*t ||
-- - RootSum|192216796875*t  + 68343750000*t  + 4860000000*t - 9993281536, t -> t*log|------- + ----------- + ---------- + -------------|| + RootSum|192216796875*t  + 68343750000*t  + 4860000000*t - 9993281536, t -> t*log|------- + ----------- + ---------- + -------------||
15          \                                                                        \4886093     39088744     39088744      2501679616 //          \                                                                        \4886093     39088744     39088744      2501679616 //
−RootSum⁡(192216796875t5+68343750000t3+4860000000t−9993281536,(t↦tlog⁡(7688671875t42501679616+34171875t239088744+87890625t39088744+1518754886093)))+RootSum⁡(192216796875t5+68343750000t3+4860000000t−9993281536,(t↦tlog⁡(7688671875t42501679616+34171875t239088744+87890625t39088744+50379684886093)))+815- \operatorname{RootSum} {\left(192216796875 t^{5} + 68343750000 t^{3} + 4860000000 t - 9993281536, \left( t \mapsto t \log{\left(\frac{7688671875 t^{4}}{2501679616} + \frac{34171875 t^{2}}{39088744} + \frac{87890625 t}{39088744} + \frac{151875}{4886093} \right)} \right)\right)} + \operatorname{RootSum} {\left(192216796875 t^{5} + 68343750000 t^{3} + 4860000000 t - 9993281536, \left( t \mapsto t \log{\left(\frac{7688671875 t^{4}}{2501679616} + \frac{34171875 t^{2}}{39088744} + \frac{87890625 t}{39088744} + \frac{5037968}{4886093} \right)} \right)\right)} + \frac{8}{15} 
8/15 - RootSum(192216796875*_t^5 + 68343750000*_t^3 + 4860000000*_t - 9993281536, Lambda(_t, _t*log(151875/4886093 + 34171875*_t^2/39088744 + 87890625*_t/39088744 + 7688671875*_t^4/2501679616))) + RootSum(192216796875*_t^5 + 68343750000*_t^3 + 4860000000*_t - 9993281536, Lambda(_t, _t*log(5037968/4886093 + 34171875*_t^2/39088744 + 87890625*_t/39088744 + 7688671875*_t^4/2501679616)))
Respuesta numérica [src] 
2.70892697873092
2.70892697873092

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