Sr Examen
Integral de 1/sqrt(81-x^4) dx
Solución
Ha introducido
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3 / | | 1 | ------------ dx | _________ | / 4 | \/ 81 - x | / 0
$$\int\limits_{0}^{3} \frac{1}{\sqrt{81 - x^{4}}}\, dx$$
Integral(1/(sqrt(81 - x^4)), (x, 0, 3))
Respuesta (Indefinida)
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_ / | 4 2*pi*I\
/ |_ |1/4, 1/2 | x *e |
| x*Gamma(1/4)* | | | ----------|
| 1 2 1 \ 5/4 | 81 /
| ------------ dx = C + -----------------------------------------
| _________ 36*Gamma(5/4)
| / 4
| \/ 81 - x
|
/
$$\int \frac{1}{\sqrt{81 - x^{4}}}\, dx = C + \frac{x \Gamma\left(\frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{4}, \frac{1}{2} \\ \frac{5}{4} \end{matrix}\middle| {\frac{x^{4} e^{2 i \pi}}{81}} \right)}}{36 \Gamma\left(\frac{5}{4}\right)}$$
Gráfica
Respuesta
[src]
_
|_ /1/4, 1/2 | \
Gamma(1/4)* | | | 1|
2 1 \ 5/4 | /
------------------------------
12*Gamma(5/4)
$$\frac{\Gamma\left(\frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{4}, \frac{1}{2} \\ \frac{5}{4} \end{matrix}\middle| {1} \right)}}{12 \Gamma\left(\frac{5}{4}\right)}$$
=
=
_
|_ /1/4, 1/2 | \
Gamma(1/4)* | | | 1|
2 1 \ 5/4 | /
------------------------------
12*Gamma(5/4)
$$\frac{\Gamma\left(\frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{4}, \frac{1}{2} \\ \frac{5}{4} \end{matrix}\middle| {1} \right)}}{12 \Gamma\left(\frac{5}{4}\right)}$$
gamma(1/4)*hyper((1/4, 1/2), (5/4,), 1)/(12*gamma(5/4))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.