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Resolución de integrales/ x^3+2/ -x^-2/ (x-8)/(x^3+2*x-x^-2+4)

Integral de (x-8)/(x^3+2*x-x^-2+4) dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  1                     
  /                     
 |                      
 |        x - 8         
 |  ----------------- dx
 |   3         1        
 |  x  + 2*x - -- + 4   
 |              2       
 |             x        
 |                      
/                       
0
∫01x−8((x3+2x)−1x2)+4 dx\int\limits_{0}^{1} \frac{x - 8}{\left(\left(x^{3} + 2 x\right) - \frac{1}{x^{2}}\right) + 4}\, dx 
Integral((x - 8)/(x^3 + 2*x - 1/x^2 + 4), (x, 0, 1))
Respuesta [src] 
         /                                                      /                            2                3                4                 \\                     /                                                      /                            2                3                4                 \\
         |      4         3         2                           |21895746448   117779837164*t    39834536324*t    46625933211*t    196049590526*t||                     |      4         3         2                           |75533431269   117779837164*t    39834536324*t    46625933211*t    196049590526*t||
- RootSum|3267*t  - 9801*t  + 7623*t  - 841*t - 1261, t -> t*log|----------- - --------------- + -------------- + -------------- + --------------|| - 3*log(2) + RootSum|3267*t  - 9801*t  + 7623*t  - 841*t - 1261, t -> t*log|----------- - --------------- + -------------- + -------------- + --------------||
         \                                                      \53637684821     22987579209      53637684821      53637684821      160913054463 //                     \                                                      \53637684821     22987579209      53637684821      53637684821      160913054463 //
−RootSum⁡(3267t4−9801t3+7623t2−841t−1261,(t↦tlog⁡(46625933211t453637684821+39834536324t353637684821−117779837164t222987579209+196049590526t160913054463+2189574644853637684821)))+RootSum⁡(3267t4−9801t3+7623t2−841t−1261,(t↦tlog⁡(46625933211t453637684821+39834536324t353637684821−117779837164t222987579209+196049590526t160913054463+7553343126953637684821)))−3log⁡(2)- \operatorname{RootSum} {\left(3267 t^{4} - 9801 t^{3} + 7623 t^{2} - 841 t - 1261, \left( t \mapsto t \log{\left(\frac{46625933211 t^{4}}{53637684821} + \frac{39834536324 t^{3}}{53637684821} - \frac{117779837164 t^{2}}{22987579209} + \frac{196049590526 t}{160913054463} + \frac{21895746448}{53637684821} \right)} \right)\right)} + \operatorname{RootSum} {\left(3267 t^{4} - 9801 t^{3} + 7623 t^{2} - 841 t - 1261, \left( t \mapsto t \log{\left(\frac{46625933211 t^{4}}{53637684821} + \frac{39834536324 t^{3}}{53637684821} - \frac{117779837164 t^{2}}{22987579209} + \frac{196049590526 t}{160913054463} + \frac{75533431269}{53637684821} \right)} \right)\right)} - 3 \log{\left(2 \right)} 
=
= 
         /                                                      /                            2                3                4                 \\                     /                                                      /                            2                3                4                 \\
         |      4         3         2                           |21895746448   117779837164*t    39834536324*t    46625933211*t    196049590526*t||                     |      4         3         2                           |75533431269   117779837164*t    39834536324*t    46625933211*t    196049590526*t||
- RootSum|3267*t  - 9801*t  + 7623*t  - 841*t - 1261, t -> t*log|----------- - --------------- + -------------- + -------------- + --------------|| - 3*log(2) + RootSum|3267*t  - 9801*t  + 7623*t  - 841*t - 1261, t -> t*log|----------- - --------------- + -------------- + -------------- + --------------||
         \                                                      \53637684821     22987579209      53637684821      53637684821      160913054463 //                     \                                                      \53637684821     22987579209      53637684821      53637684821      160913054463 //
−RootSum⁡(3267t4−9801t3+7623t2−841t−1261,(t↦tlog⁡(46625933211t453637684821+39834536324t353637684821−117779837164t222987579209+196049590526t160913054463+2189574644853637684821)))+RootSum⁡(3267t4−9801t3+7623t2−841t−1261,(t↦tlog⁡(46625933211t453637684821+39834536324t353637684821−117779837164t222987579209+196049590526t160913054463+7553343126953637684821)))−3log⁡(2)- \operatorname{RootSum} {\left(3267 t^{4} - 9801 t^{3} + 7623 t^{2} - 841 t - 1261, \left( t \mapsto t \log{\left(\frac{46625933211 t^{4}}{53637684821} + \frac{39834536324 t^{3}}{53637684821} - \frac{117779837164 t^{2}}{22987579209} + \frac{196049590526 t}{160913054463} + \frac{21895746448}{53637684821} \right)} \right)\right)} + \operatorname{RootSum} {\left(3267 t^{4} - 9801 t^{3} + 7623 t^{2} - 841 t - 1261, \left( t \mapsto t \log{\left(\frac{46625933211 t^{4}}{53637684821} + \frac{39834536324 t^{3}}{53637684821} - \frac{117779837164 t^{2}}{22987579209} + \frac{196049590526 t}{160913054463} + \frac{75533431269}{53637684821} \right)} \right)\right)} - 3 \log{\left(2 \right)} 
-RootSum(3267*_t^4 - 9801*_t^3 + 7623*_t^2 - 841*_t - 1261, Lambda(_t, _t*log(21895746448/53637684821 - 117779837164*_t^2/22987579209 + 39834536324*_t^3/53637684821 + 46625933211*_t^4/53637684821 + 196049590526*_t/160913054463))) - 3*log(2) + RootSum(3267*_t^4 - 9801*_t^3 + 7623*_t^2 - 841*_t - 1261, Lambda(_t, _t*log(75533431269/53637684821 - 117779837164*_t^2/22987579209 + 39834536324*_t^3/53637684821 + 46625933211*_t^4/53637684821 + 196049590526*_t/160913054463)))
Respuesta numérica [src] 
-1.73760097173703
-1.73760097173703

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

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