Sr Examen
Integral de 1/(x^3-8)^(1/5) dx
Solución
Ha introducido
[src]
4 / | | 1 | ----------- dx | ________ | 5 / 3 | \/ x - 8 | / 3
$$\int\limits_{3}^{4} \frac{1}{\sqrt[5]{x^{3} - 8}}\, dx$$
Integral(1/((x^3 - 8)^(1/5)), (x, 3, 4))
Respuesta (Indefinida)
[src]
-pi*I
------ _ / | 3\
/ 2/5 5 |_ |1/5, 1/3 | x |
| x*2 *e *Gamma(1/3)* | | | --|
| 1 2 1 \ 4/3 | 8 /
| ----------- dx = C + ----------------------------------------------
| ________ 6*Gamma(4/3)
| 5 / 3
| \/ x - 8
|
/
$$\int \frac{1}{\sqrt[5]{x^{3} - 8}}\, dx = C + \frac{2^{\frac{2}{5}} x e^{- \frac{i \pi}{5}} \Gamma\left(\frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{5}, \frac{1}{3} \\ \frac{4}{3} \end{matrix}\middle| {\frac{x^{3}}{8}} \right)}}{6 \Gamma\left(\frac{4}{3}\right)}$$
Gráfica
Respuesta
[src]
-pi*I -pi*I
------ _ ------ _
2/5 5 |_ /1/5, 1/3 | \ 2/5 5 |_ /1/5, 1/3 | \
2 *e *Gamma(1/3)* | | | 27/8| 2*2 *e *Gamma(1/3)* | | | 8|
2 1 \ 4/3 | / 2 1 \ 4/3 | /
- ---------------------------------------------- + ---------------------------------------------
2*Gamma(4/3) 3*Gamma(4/3)
$$- \frac{2^{\frac{2}{5}} e^{- \frac{i \pi}{5}} \Gamma\left(\frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{5}, \frac{1}{3} \\ \frac{4}{3} \end{matrix}\middle| {\frac{27}{8}} \right)}}{2 \Gamma\left(\frac{4}{3}\right)} + \frac{2 \cdot 2^{\frac{2}{5}} e^{- \frac{i \pi}{5}} \Gamma\left(\frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{5}, \frac{1}{3} \\ \frac{4}{3} \end{matrix}\middle| {8} \right)}}{3 \Gamma\left(\frac{4}{3}\right)}$$
=
=
-pi*I -pi*I
------ _ ------ _
2/5 5 |_ /1/5, 1/3 | \ 2/5 5 |_ /1/5, 1/3 | \
2 *e *Gamma(1/3)* | | | 27/8| 2*2 *e *Gamma(1/3)* | | | 8|
2 1 \ 4/3 | / 2 1 \ 4/3 | /
- ---------------------------------------------- + ---------------------------------------------
2*Gamma(4/3) 3*Gamma(4/3)
$$- \frac{2^{\frac{2}{5}} e^{- \frac{i \pi}{5}} \Gamma\left(\frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{5}, \frac{1}{3} \\ \frac{4}{3} \end{matrix}\middle| {\frac{27}{8}} \right)}}{2 \Gamma\left(\frac{4}{3}\right)} + \frac{2 \cdot 2^{\frac{2}{5}} e^{- \frac{i \pi}{5}} \Gamma\left(\frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{5}, \frac{1}{3} \\ \frac{4}{3} \end{matrix}\middle| {8} \right)}}{3 \Gamma\left(\frac{4}{3}\right)}$$
-2^(2/5)*exp(-pi*i/5)*gamma(1/3)*hyper((1/5, 1/3), (4/3,), 27/8)/(2*gamma(4/3)) + 2*2^(2/5)*exp(-pi*i/5)*gamma(1/3)*hyper((1/5, 1/3), (4/3,), 8)/(3*gamma(4/3))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.