Sr Examen
Integral de x*((1-2x^3)^(2/8)) dx
Solución
Ha introducido
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1 / | | __________ | 4 / 3 | x*\/ 1 - 2*x dx | / 0
$$\int\limits_{0}^{1} x \sqrt[4]{1 - 2 x^{3}}\, dx$$
Integral(x*(1 - 2*x^3)^(1/4), (x, 0, 1))
Respuesta (Indefinida)
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/ _ | 2 |_ /-1/4, 2/3 | 3 2*pi*I\ | __________ x *Gamma(2/3)* | | | 2*x *e | | 4 / 3 2 1 \ 5/3 | / | x*\/ 1 - 2*x dx = C + --------------------------------------------- | 3*Gamma(5/3) /
$$\int x \sqrt[4]{1 - 2 x^{3}}\, dx = C + \frac{x^{2} \Gamma\left(\frac{2}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{4}, \frac{2}{3} \\ \frac{5}{3} \end{matrix}\middle| {2 x^{3} e^{2 i \pi}} \right)}}{3 \Gamma\left(\frac{5}{3}\right)}$$
Respuesta
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_
|_ /-1/4, 2/3 | 2*pi*I\
Gamma(2/3)* | | | 2*e |
2 1 \ 5/3 | /
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3*Gamma(5/3)
$$\frac{\Gamma\left(\frac{2}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{4}, \frac{2}{3} \\ \frac{5}{3} \end{matrix}\middle| {2 e^{2 i \pi}} \right)}}{3 \Gamma\left(\frac{5}{3}\right)}$$
=
=
_
|_ /-1/4, 2/3 | 2*pi*I\
Gamma(2/3)* | | | 2*e |
2 1 \ 5/3 | /
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3*Gamma(5/3)
$$\frac{\Gamma\left(\frac{2}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{4}, \frac{2}{3} \\ \frac{5}{3} \end{matrix}\middle| {2 e^{2 i \pi}} \right)}}{3 \Gamma\left(\frac{5}{3}\right)}$$
gamma(2/3)*hyper((-1/4, 2/3), (5/3,), 2*exp_polar(2*pi*i))/(3*gamma(5/3))
Respuesta numérica
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(0.369760183122459 + 0.10356830604935j)
(0.369760183122459 + 0.10356830604935j)
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.