Sr Examen
Integral de x(8-x^3)^1/3dx dx
Solución
Ha introducido
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8 / | | ________ | 3 / 3 | x*\/ 8 - x dx | / 0
$$\int\limits_{0}^{8} x \sqrt[3]{8 - x^{3}}\, dx$$
Integral(x*(8 - x^3)^(1/3), (x, 0, 8))
Respuesta (Indefinida)
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/ _ / | 3 2*pi*I\ | 2 |_ |-1/3, 2/3 | x *e | | ________ 2*x *Gamma(2/3)* | | | ----------| | 3 / 3 2 1 \ 5/3 | 8 / | x*\/ 8 - x dx = C + --------------------------------------------- | 3*Gamma(5/3) /
$$\int x \sqrt[3]{8 - x^{3}}\, dx = C + \frac{2 x^{2} \Gamma\left(\frac{2}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{3}, \frac{2}{3} \\ \frac{5}{3} \end{matrix}\middle| {\frac{x^{3} e^{2 i \pi}}{8}} \right)}}{3 \Gamma\left(\frac{5}{3}\right)}$$
Respuesta
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_
|_ /-1/3, 2/3 | 2*pi*I\
128*Gamma(2/3)* | | | 64*e |
2 1 \ 5/3 | /
--------------------------------------------
3*Gamma(5/3)
$$\frac{128 \Gamma\left(\frac{2}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{3}, \frac{2}{3} \\ \frac{5}{3} \end{matrix}\middle| {64 e^{2 i \pi}} \right)}}{3 \Gamma\left(\frac{5}{3}\right)}$$
=
=
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|_ /-1/3, 2/3 | 2*pi*I\
128*Gamma(2/3)* | | | 64*e |
2 1 \ 5/3 | /
--------------------------------------------
3*Gamma(5/3)
$$\frac{128 \Gamma\left(\frac{2}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{3}, \frac{2}{3} \\ \frac{5}{3} \end{matrix}\middle| {64 e^{2 i \pi}} \right)}}{3 \Gamma\left(\frac{5}{3}\right)}$$
128*gamma(2/3)*hyper((-1/3, 2/3), (5/3,), 64*exp_polar(2*pi*i))/(3*gamma(5/3))
Respuesta numérica
[src]
(85.1223230820409 + 141.836330390552j)
(85.1223230820409 + 141.836330390552j)
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.