Sr Examen
Integral de (((x^4)+5)/((x^5)+3))^2 dx
Solución
Ha introducido
[src]
1 / | | 2 | / 4 \ | |x + 5| | |------| dx | | 5 | | \x + 3/ | / 0
$$\int\limits_{0}^{1} \left(\frac{x^{4} + 5}{x^{5} + 3}\right)^{2}\, dx$$
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 | /
$$\int \left(\frac{x^{4} + 5}{x^{5} + 3}\right)^{2}\, dx = C - \frac{3 x^{4}}{15 x^{5} + 45} + \frac{25 x}{15 x^{5} + 45} + \operatorname{RootSum} {\left(9375 t^{5} + 1, \left( t \mapsto t \log{\left(1875 t^{4} + x \right)} \right)\right)} - 3 \operatorname{RootSum} {\left(7119140625 t^{5} + 1, \left( t \mapsto t \log{\left(94921875 t^{4} + x \right)} \right)\right)} + 25 \operatorname{RootSum} {\left(192216796875 t^{5} - 1024, \left( t \mapsto t \log{\left(\frac{225 t}{4} + x \right)} \right)\right)} - \frac{2}{x^{5} + 3}$$
Gráfica
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 //
$$- \operatorname{RootSum} {\left(192216796875 t^{5} + 68343750000 t^{3} + 4860000000 t - 9993281536, \left( t \mapsto t \log{\left(\frac{7688671875 t^{4}}{2501679616} + \frac{34171875 t^{2}}{39088744} + \frac{87890625 t}{39088744} + \frac{151875}{4886093} \right)} \right)\right)} + \operatorname{RootSum} {\left(192216796875 t^{5} + 68343750000 t^{3} + 4860000000 t - 9993281536, \left( t \mapsto t \log{\left(\frac{7688671875 t^{4}}{2501679616} + \frac{34171875 t^{2}}{39088744} + \frac{87890625 t}{39088744} + \frac{5037968}{4886093} \right)} \right)\right)} + \frac{8}{15}$$
=
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/ / 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 //
$$- \operatorname{RootSum} {\left(192216796875 t^{5} + 68343750000 t^{3} + 4860000000 t - 9993281536, \left( t \mapsto t \log{\left(\frac{7688671875 t^{4}}{2501679616} + \frac{34171875 t^{2}}{39088744} + \frac{87890625 t}{39088744} + \frac{151875}{4886093} \right)} \right)\right)} + \operatorname{RootSum} {\left(192216796875 t^{5} + 68343750000 t^{3} + 4860000000 t - 9993281536, \left( t \mapsto t \log{\left(\frac{7688671875 t^{4}}{2501679616} + \frac{34171875 t^{2}}{39088744} + \frac{87890625 t}{39088744} + \frac{5037968}{4886093} \right)} \right)\right)} + \frac{8}{15}$$
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)))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.