Sr Examen
Integral de (1+x^(3))^(1/3) dx
Solución
Ha introducido
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1/2 / | | ________ | 3 / 3 | \/ 1 + x dx | / 0
$$\int\limits_{0}^{\frac{1}{2}} \sqrt[3]{x^{3} + 1}\, dx$$
Integral((1 + x^3)^(1/3), (x, 0, 1/2))
Respuesta (Indefinida)
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/ _ | |_ /-1/3, 1/3 | 3 pi*I\ | ________ x*Gamma(1/3)* | | | x *e | | 3 / 3 2 1 \ 4/3 | / | \/ 1 + x dx = C + ---------------------------------------- | 3*Gamma(4/3) /
$$\int \sqrt[3]{x^{3} + 1}\, dx = C + \frac{x \Gamma\left(\frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{3}, \frac{1}{3} \\ \frac{4}{3} \end{matrix}\middle| {x^{3} e^{i \pi}} \right)}}{3 \Gamma\left(\frac{4}{3}\right)}$$
Gráfica
Respuesta
[src]
_
|_ /-1/3, 1/3 | \
Gamma(1/3)* | | | -1/8|
2 1 \ 4/3 | /
----------------------------------
6*Gamma(4/3)
$$\frac{\Gamma\left(\frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{3}, \frac{1}{3} \\ \frac{4}{3} \end{matrix}\middle| {- \frac{1}{8}} \right)}}{6 \Gamma\left(\frac{4}{3}\right)}$$
=
=
_
|_ /-1/3, 1/3 | \
Gamma(1/3)* | | | -1/8|
2 1 \ 4/3 | /
----------------------------------
6*Gamma(4/3)
$$\frac{\Gamma\left(\frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{3}, \frac{1}{3} \\ \frac{4}{3} \end{matrix}\middle| {- \frac{1}{8}} \right)}}{6 \Gamma\left(\frac{4}{3}\right)}$$
gamma(1/3)*hyper((-1/3, 1/3), (4/3,), -1/8)/(6*gamma(4/3))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.