Sr Examen
Integral de (2x^2+4)/(x^3-x^2+x+1) dx
Solución
Ha introducido
[src]
___ \/ 3 ----- 3 / | | 2 | 2*x + 4 | --------------- dx | 3 2 | x - x + x + 1 | / 0
$$\int\limits_{0}^{\frac{\sqrt{3}}{3}} \frac{2 x^{2} + 4}{\left(x + \left(x^{3} - x^{2}\right)\right) + 1}\, dx$$
Integral((2*x^2 + 4)/(x^3 - x^2 + x + 1), (x, 0, sqrt(3)/3))
Respuesta (Indefinida)
[src]
/ | | 2 / / 2\\ / / 2 \\ | 2*x + 4 | 3 2 |13 110*t 176*t || | 3 | 3 88*t 66*t|| | --------------- dx = C + 2*RootSum|44*t - 44*t + 14*t - 1, t -> t*log|-- + x - ----- + ------|| + 4*RootSum|44*t - 2*t - 1, t -> t*log|- -- + x - ----- + ----|| | 3 2 \ \7 7 7 // \ \ 17 17 17 // | x - x + x + 1 | /
$$\int \frac{2 x^{2} + 4}{\left(x + \left(x^{3} - x^{2}\right)\right) + 1}\, dx = C + 4 \operatorname{RootSum} {\left(44 t^{3} - 2 t - 1, \left( t \mapsto t \log{\left(- \frac{88 t^{2}}{17} + \frac{66 t}{17} + x - \frac{3}{17} \right)} \right)\right)} + 2 \operatorname{RootSum} {\left(44 t^{3} - 44 t^{2} + 14 t - 1, \left( t \mapsto t \log{\left(\frac{176 t^{2}}{7} - \frac{110 t}{7} + x + \frac{13}{7} \right)} \right)\right)}$$
Gráfica
Respuesta
[src]
/ / ___ \\
/ 3 2 \ | 3 2 | \/ 3 ||
- RootSum\t - 2*t + 2*t - 2, t -> t*log(-1 + t)/ + RootSum|t - 2*t + 2*t - 2, t -> t*log|-1 + ----- + t||
\ \ 3 //
$$- \operatorname{RootSum} {\left(t^{3} - 2 t^{2} + 2 t - 2, \left( t \mapsto t \log{\left(t - 1 \right)} \right)\right)} + \operatorname{RootSum} {\left(t^{3} - 2 t^{2} + 2 t - 2, \left( t \mapsto t \log{\left(t - 1 + \frac{\sqrt{3}}{3} \right)} \right)\right)}$$
=
=
/ / ___ \\
/ 3 2 \ | 3 2 | \/ 3 ||
- RootSum\t - 2*t + 2*t - 2, t -> t*log(-1 + t)/ + RootSum|t - 2*t + 2*t - 2, t -> t*log|-1 + ----- + t||
\ \ 3 //
$$- \operatorname{RootSum} {\left(t^{3} - 2 t^{2} + 2 t - 2, \left( t \mapsto t \log{\left(t - 1 \right)} \right)\right)} + \operatorname{RootSum} {\left(t^{3} - 2 t^{2} + 2 t - 2, \left( t \mapsto t \log{\left(t - 1 + \frac{\sqrt{3}}{3} \right)} \right)\right)}$$
-RootSum(_t^3 - 2*_t^2 + 2*_t - 2, Lambda(_t, _t*log(-1 + _t))) + RootSum(_t^3 - 2*_t^2 + 2*_t - 2, Lambda(_t, _t*log(-1 + sqrt(3)/3 + _t)))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.