Sr Examen
Integral de (5-x^3)^(1/2) dx
Solución
Ha introducido
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1 / | | ________ | / 3 | \/ 5 - x dx | / 0
$$\int\limits_{0}^{1} \sqrt{5 - x^{3}}\, dx$$
Integral(sqrt(5 - x^3), (x, 0, 1))
Respuesta (Indefinida)
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/ _ / | 3 2*pi*I\ | ___ |_ |-1/2, 1/3 | x *e | | ________ x*\/ 5 *Gamma(1/3)* | | | ----------| | / 3 2 1 \ 4/3 | 5 / | \/ 5 - x dx = C + ------------------------------------------------ | 3*Gamma(4/3) /
$$\int \sqrt{5 - x^{3}}\, dx = C + \frac{\sqrt{5} x \Gamma\left(\frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{1}{3} \\ \frac{4}{3} \end{matrix}\middle| {\frac{x^{3} e^{2 i \pi}}{5}} \right)}}{3 \Gamma\left(\frac{4}{3}\right)}$$
Gráfica
Respuesta
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_
___ |_ /-1/2, 1/3 | \
\/ 5 *Gamma(1/3)* | | | 1/5|
2 1 \ 4/3 | /
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3*Gamma(4/3)
$$\frac{\sqrt{5} \Gamma\left(\frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{1}{3} \\ \frac{4}{3} \end{matrix}\middle| {\frac{1}{5}} \right)}}{3 \Gamma\left(\frac{4}{3}\right)}$$
=
=
_
___ |_ /-1/2, 1/3 | \
\/ 5 *Gamma(1/3)* | | | 1/5|
2 1 \ 4/3 | /
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3*Gamma(4/3)
$$\frac{\sqrt{5} \Gamma\left(\frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{1}{3} \\ \frac{4}{3} \end{matrix}\middle| {\frac{1}{5}} \right)}}{3 \Gamma\left(\frac{4}{3}\right)}$$
sqrt(5)*gamma(1/3)*hyper((-1/2, 1/3), (4/3,), 1/5)/(3*gamma(4/3))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.