Sr Examen
Integral de 1/sqrt(3x^3-2) dx
Solución
Ha introducido
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1 / | | 1 | ------------- dx | __________ | / 3 | \/ 3*x - 2 | / 0
$$\int\limits_{0}^{1} \frac{1}{\sqrt{3 x^{3} - 2}}\, dx$$
Integral(1/(sqrt(3*x^3 - 2)), (x, 0, 1))
Respuesta (Indefinida)
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_ / | 3\
/ ___ |_ |1/3, 1/2 | 3*x |
| I*x*\/ 2 *Gamma(1/3)* | | | ----|
| 1 2 1 \ 4/3 | 2 /
| ------------- dx = C - -------------------------------------------
| __________ 6*Gamma(4/3)
| / 3
| \/ 3*x - 2
|
/
$$\int \frac{1}{\sqrt{3 x^{3} - 2}}\, dx = C - \frac{\sqrt{2} i x \Gamma\left(\frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{3}, \frac{1}{2} \\ \frac{4}{3} \end{matrix}\middle| {\frac{3 x^{3}}{2}} \right)}}{6 \Gamma\left(\frac{4}{3}\right)}$$
Gráfica
Respuesta
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_
___ |_ /1/3, 1/2 | \
-I*\/ 2 *Gamma(1/3)* | | | 3/2|
2 1 \ 4/3 | /
------------------------------------------
6*Gamma(4/3)
$$- \frac{\sqrt{2} i \Gamma\left(\frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{3}, \frac{1}{2} \\ \frac{4}{3} \end{matrix}\middle| {\frac{3}{2}} \right)}}{6 \Gamma\left(\frac{4}{3}\right)}$$
=
=
_
___ |_ /1/3, 1/2 | \
-I*\/ 2 *Gamma(1/3)* | | | 3/2|
2 1 \ 4/3 | /
------------------------------------------
6*Gamma(4/3)
$$- \frac{\sqrt{2} i \Gamma\left(\frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{3}, \frac{1}{2} \\ \frac{4}{3} \end{matrix}\middle| {\frac{3}{2}} \right)}}{6 \Gamma\left(\frac{4}{3}\right)}$$
-i*sqrt(2)*gamma(1/3)*hyper((1/3, 1/2), (4/3,), 3/2)/(6*gamma(4/3))
Respuesta numérica
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(0.231281876885952 - 0.874943472530304j)
(0.231281876885952 - 0.874943472530304j)
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.