Sr Examen
Integral de 1/((x^3-8)^(1/3)) dx
Solución
Ha introducido
[src]
2 / | | 1 | ----------- dx | ________ | 3 / 3 | \/ x - 8 | / 0
$$\int\limits_{0}^{2} \frac{1}{\sqrt[3]{x^{3} - 8}}\, dx$$
Integral(1/((x^3 - 8)^(1/3)), (x, 0, 2))
Respuesta (Indefinida)
[src]
-pi*I
------ _ / | 3\
/ 3 |_ |1/3, 1/3 | x |
| x*e *Gamma(1/3)* | | | --|
| 1 2 1 \ 4/3 | 8 /
| ----------- dx = C + -----------------------------------------
| ________ 6*Gamma(4/3)
| 3 / 3
| \/ x - 8
|
/
$$\int \frac{1}{\sqrt[3]{x^{3} - 8}}\, dx = C + \frac{x e^{- \frac{i \pi}{3}} \Gamma\left(\frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{3}, \frac{1}{3} \\ \frac{4}{3} \end{matrix}\middle| {\frac{x^{3}}{8}} \right)}}{6 \Gamma\left(\frac{4}{3}\right)}$$
Gráfica
Respuesta
[src]
-pi*I
------ _
3 |_ /1/3, 1/3 | \
e *Gamma(1/3)* | | | 1|
2 1 \ 4/3 | /
--------------------------------------
3*Gamma(4/3)
$$\frac{e^{- \frac{i \pi}{3}} \Gamma\left(\frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{3}, \frac{1}{3} \\ \frac{4}{3} \end{matrix}\middle| {1} \right)}}{3 \Gamma\left(\frac{4}{3}\right)}$$
=
=
-pi*I
------ _
3 |_ /1/3, 1/3 | \
e *Gamma(1/3)* | | | 1|
2 1 \ 4/3 | /
--------------------------------------
3*Gamma(4/3)
$$\frac{e^{- \frac{i \pi}{3}} \Gamma\left(\frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{3}, \frac{1}{3} \\ \frac{4}{3} \end{matrix}\middle| {1} \right)}}{3 \Gamma\left(\frac{4}{3}\right)}$$
exp(-pi*i/3)*gamma(1/3)*hyper((1/3, 1/3), (4/3,), 1)/(3*gamma(4/3))
Respuesta numérica
[src]
(0.604599788077965 - 1.04719755119641j)
(0.604599788077965 - 1.04719755119641j)
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.