Sr Examen
Integral de (9x^5-x+1)/(4x^5+x^2+3) dx
Solución
Ha introducido
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oo / | | 5 | 9*x - x + 1 | ------------- dx | 5 2 | 4*x + x + 3 | / 2
$$\int\limits_{2}^{\infty} \frac{\left(9 x^{5} - x\right) + 1}{\left(4 x^{5} + x^{2}\right) + 3}\, dx$$
Integral((9*x^5 - x + 1)/(4*x^5 + x^2 + 3), (x, 2, oo))
Respuesta (Indefinida)
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/ / / 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 | /
$$\int \frac{\left(9 x^{5} - x\right) + 1}{\left(4 x^{5} + x^{2}\right) + 3}\, dx = C + \frac{9 x}{4} - \frac{7 \log{\left(x + 1 \right)}}{18} - \frac{28 \operatorname{RootSum} {\left(66672 t^{4} - 44 t^{2} + 57 t + 3, \left( t \mapsto t \log{\left(\frac{1318838832 t^{3}}{394169} - \frac{52087500 t^{2}}{394169} + \frac{3096620 t}{394169} + x + \frac{764283}{394169} \right)} \right)\right)}}{9} + \frac{29 \operatorname{RootSum} {\left(16668 t^{4} + 280 t^{2} - t + 1, \left( t \mapsto t \log{\left(- \frac{43920180 t^{3}}{15233} + \frac{1333440 t^{2}}{15233} - \frac{416941 t}{15233} + x + \frac{9368}{15233} \right)} \right)\right)}}{12} - \frac{55 \operatorname{RootSum} {\left(12501 t^{4} - 42 t^{2} - 12 t + 1, \left( t \mapsto t \log{\left(\frac{3287763 t^{3}}{3868} + \frac{129177 t^{2}}{1934} + \frac{34791 t}{3868} + x - \frac{942}{967} \right)} \right)\right)}}{12} + \frac{14 \operatorname{RootSum} {\left(266688 t^{4} - 66672 t^{3} + 6436 t^{2} - 321 t + 9, \left( t \mapsto t \log{\left(\frac{398320752 t^{3}}{65753} - \frac{76595016 t^{2}}{65753} + \frac{16312105 t}{197259} + x - \frac{196852}{65753} \right)} \right)\right)}}{9}$$
Gráfica
Respuesta
[src]
oo / | | 5 | 1 - x + 9*x | ------------- dx | 2 5 | 3 + x + 4*x | / 2
$$\int\limits_{2}^{\infty} \frac{9 x^{5} - x + 1}{4 x^{5} + x^{2} + 3}\, dx$$
=
=
oo / | | 5 | 1 - x + 9*x | ------------- dx | 2 5 | 3 + x + 4*x | / 2
$$\int\limits_{2}^{\infty} \frac{9 x^{5} - x + 1}{4 x^{5} + x^{2} + 3}\, dx$$
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.