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