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