Sr Examen
Integral de √(3-2x^3)^(1/11) dx
Solución
Ha introducido
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1 / | | _______________ | / __________ | 11/ / 3 | \/ \/ 3 - 2*x dx | / 0
$$\int\limits_{0}^{1} \sqrt[11]{\sqrt{3 - 2 x^{3}}}\, dx$$
Integral((sqrt(3 - 2*x^3))^(1/11), (x, 0, 1))
Respuesta (Indefinida)
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/ | _ / | 3 2*pi*I\ | _______________ 22___ |_ |-1/22, 1/3 | 2*x *e | | / __________ x*\/ 3 *Gamma(1/3)* | | | ------------| | 11/ / 3 2 1 \ 4/3 | 3 / | \/ \/ 3 - 2*x dx = C + --------------------------------------------------- | 3*Gamma(4/3) /
$$\int \sqrt[11]{\sqrt{3 - 2 x^{3}}}\, dx = C + \frac{\sqrt[22]{3} x \Gamma\left(\frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{22}, \frac{1}{3} \\ \frac{4}{3} \end{matrix}\middle| {\frac{2 x^{3} e^{2 i \pi}}{3}} \right)}}{3 \Gamma\left(\frac{4}{3}\right)}$$
Gráfica
Respuesta
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_
22___ |_ /-1/22, 1/3 | \
\/ 3 *Gamma(1/3)* | | | 2/3|
2 1 \ 4/3 | /
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3*Gamma(4/3)
$$\frac{\sqrt[22]{3} \Gamma\left(\frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{22}, \frac{1}{3} \\ \frac{4}{3} \end{matrix}\middle| {\frac{2}{3}} \right)}}{3 \Gamma\left(\frac{4}{3}\right)}$$
=
=
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22___ |_ /-1/22, 1/3 | \
\/ 3 *Gamma(1/3)* | | | 2/3|
2 1 \ 4/3 | /
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3*Gamma(4/3)
$$\frac{\sqrt[22]{3} \Gamma\left(\frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{22}, \frac{1}{3} \\ \frac{4}{3} \end{matrix}\middle| {\frac{2}{3}} \right)}}{3 \Gamma\left(\frac{4}{3}\right)}$$
3^(1/22)*gamma(1/3)*hyper((-1/22, 1/3), (4/3,), 2/3)/(3*gamma(4/3))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.