Sr Examen
Integral de (√x)/(√(1-x^4)) dx
Solución
Ha introducido
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1 / | | ___ | \/ x | ----------- dx | ________ | / 4 | \/ 1 - x | / 0
$$\int\limits_{0}^{1} \frac{\sqrt{x}}{\sqrt{1 - x^{4}}}\, dx$$
Integral(sqrt(x)/sqrt(1 - x^4), (x, 0, 1))
Respuesta (Indefinida)
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/ _ | 3/2 |_ /3/8, 1/2 | 4 2*pi*I\ | ___ x *Gamma(3/8)* | | | x *e | | \/ x 2 1 \ 11/8 | / | ----------- dx = C + -------------------------------------------- | ________ 4*Gamma(11/8) | / 4 | \/ 1 - x | /
$$\int \frac{\sqrt{x}}{\sqrt{1 - x^{4}}}\, dx = C + \frac{x^{\frac{3}{2}} \Gamma\left(\frac{3}{8}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{3}{8}, \frac{1}{2} \\ \frac{11}{8} \end{matrix}\middle| {x^{4} e^{2 i \pi}} \right)}}{4 \Gamma\left(\frac{11}{8}\right)}$$
Gráfica
Respuesta
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_
|_ /3/8, 1/2 | \
Gamma(3/8)* | | | 1|
2 1 \ 11/8 | /
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4*Gamma(11/8)
$$\frac{\Gamma\left(\frac{3}{8}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{3}{8}, \frac{1}{2} \\ \frac{11}{8} \end{matrix}\middle| {1} \right)}}{4 \Gamma\left(\frac{11}{8}\right)}$$
=
=
_
|_ /3/8, 1/2 | \
Gamma(3/8)* | | | 1|
2 1 \ 11/8 | /
------------------------------
4*Gamma(11/8)
$$\frac{\Gamma\left(\frac{3}{8}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{3}{8}, \frac{1}{2} \\ \frac{11}{8} \end{matrix}\middle| {1} \right)}}{4 \Gamma\left(\frac{11}{8}\right)}$$
gamma(3/8)*hyper((3/8, 1/2), (11/8,), 1)/(4*gamma(11/8))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.