Sr Examen
Integral de (x^(2)dx)/(√(3-x^8)) dx
Solución
Ha introducido
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1 / | | 2 | x | ----------- dx | ________ | / 8 | \/ 3 - x | / 0
$$\int\limits_{0}^{1} \frac{x^{2}}{\sqrt{3 - x^{8}}}\, dx$$
Integral(x^2/sqrt(3 - x^8), (x, 0, 1))
Respuesta (Indefinida)
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/ _ / | 8 2*pi*I\ | ___ 3 |_ |3/8, 1/2 | x *e | | 2 \/ 3 *x *Gamma(3/8)* | | | ----------| | x 2 1 \ 11/8 | 3 / | ----------- dx = C + ------------------------------------------------ | ________ 24*Gamma(11/8) | / 8 | \/ 3 - x | /
$$\int \frac{x^{2}}{\sqrt{3 - x^{8}}}\, dx = C + \frac{\sqrt{3} x^{3} \Gamma\left(\frac{3}{8}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{3}{8}, \frac{1}{2} \\ \frac{11}{8} \end{matrix}\middle| {\frac{x^{8} e^{2 i \pi}}{3}} \right)}}{24 \Gamma\left(\frac{11}{8}\right)}$$
Gráfica
Respuesta
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_
___ |_ /3/8, 1/2 | \
\/ 3 *Gamma(3/8)* | | | 1/3|
2 1 \ 11/8 | /
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24*Gamma(11/8)
$$\frac{\sqrt{3} \Gamma\left(\frac{3}{8}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{3}{8}, \frac{1}{2} \\ \frac{11}{8} \end{matrix}\middle| {\frac{1}{3}} \right)}}{24 \Gamma\left(\frac{11}{8}\right)}$$
=
=
_
___ |_ /3/8, 1/2 | \
\/ 3 *Gamma(3/8)* | | | 1/3|
2 1 \ 11/8 | /
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24*Gamma(11/8)
$$\frac{\sqrt{3} \Gamma\left(\frac{3}{8}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{3}{8}, \frac{1}{2} \\ \frac{11}{8} \end{matrix}\middle| {\frac{1}{3}} \right)}}{24 \Gamma\left(\frac{11}{8}\right)}$$
sqrt(3)*gamma(3/8)*hyper((3/8, 1/2), (11/8,), 1/3)/(24*gamma(11/8))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.