Sr Examen
Integral de (1-x^6)/(1+x+x^3) dx
Solución
Ha introducido
[src]
3 / | | 6 | 1 - x | ---------- dx | 3 | 1 + x + x | / 2
$$\int\limits_{2}^{3} \frac{1 - x^{6}}{x^{3} + \left(x + 1\right)}\, dx$$
Integral((1 - x^6)/(1 + x + x^3), (x, 2, 3))
Gráfica
Respuesta
[src]
/ / 2\\ / / 2\\ 51 | 3 2 |806 279*t 620*t || | 3 2 |535 279*t 620*t || - -- - RootSum|31*t - 31*t + 8*t + 9, t -> t*log|--- - ----- + ------|| + RootSum|31*t - 31*t + 8*t + 9, t -> t*log|--- - ----- + ------|| 4 \ \271 271 271 // \ \271 271 271 //
$$\operatorname{RootSum} {\left(31 t^{3} - 31 t^{2} + 8 t + 9, \left( t \mapsto t \log{\left(\frac{620 t^{2}}{271} - \frac{279 t}{271} + \frac{535}{271} \right)} \right)\right)} - \operatorname{RootSum} {\left(31 t^{3} - 31 t^{2} + 8 t + 9, \left( t \mapsto t \log{\left(\frac{620 t^{2}}{271} - \frac{279 t}{271} + \frac{806}{271} \right)} \right)\right)} - \frac{51}{4}$$
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/ / 2\\ / / 2\\ 51 | 3 2 |806 279*t 620*t || | 3 2 |535 279*t 620*t || - -- - RootSum|31*t - 31*t + 8*t + 9, t -> t*log|--- - ----- + ------|| + RootSum|31*t - 31*t + 8*t + 9, t -> t*log|--- - ----- + ------|| 4 \ \271 271 271 // \ \271 271 271 //
$$\operatorname{RootSum} {\left(31 t^{3} - 31 t^{2} + 8 t + 9, \left( t \mapsto t \log{\left(\frac{620 t^{2}}{271} - \frac{279 t}{271} + \frac{535}{271} \right)} \right)\right)} - \operatorname{RootSum} {\left(31 t^{3} - 31 t^{2} + 8 t + 9, \left( t \mapsto t \log{\left(\frac{620 t^{2}}{271} - \frac{279 t}{271} + \frac{806}{271} \right)} \right)\right)} - \frac{51}{4}$$
-51/4 - RootSum(31*_t^3 - 31*_t^2 + 8*_t + 9, Lambda(_t, _t*log(806/271 - 279*_t/271 + 620*_t^2/271))) + RootSum(31*_t^3 - 31*_t^2 + 8*_t + 9, Lambda(_t, _t*log(535/271 - 279*_t/271 + 620*_t^2/271)))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.