Sr Examen
Integral de x/(a+cx^3)^0.5 dx
Solución
Ha introducido
[src]
1 / | | x | ------------- dx | __________ | / 3 | \/ a + c*x | / 0
$$\int\limits_{0}^{1} \frac{x}{\sqrt{a + c x^{3}}}\, dx$$
Integral(x/sqrt(a + c*x^3), (x, 0, 1))
Respuesta (Indefinida)
[src]
_ / | 3 pi*I\
/ 2 |_ |1/2, 2/3 | c*x *e |
| x *Gamma(2/3)* | | | ----------|
| x 2 1 \ 5/3 | a /
| ------------- dx = C + ------------------------------------------
| __________ ___
| / 3 3*\/ a *Gamma(5/3)
| \/ a + c*x
|
/
$$\int \frac{x}{\sqrt{a + c x^{3}}}\, dx = C + \frac{x^{2} \Gamma\left(\frac{2}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{2}{3} \\ \frac{5}{3} \end{matrix}\middle| {\frac{c x^{3} e^{i \pi}}{a}} \right)}}{3 \sqrt{a} \Gamma\left(\frac{5}{3}\right)}$$
Respuesta
[src]
_ / | pi*I\
|_ |1/2, 2/3 | c*e |
Gamma(2/3)* | | | -------|
2 1 \ 5/3 | a /
------------------------------------
___
3*\/ a *Gamma(5/3)
$$\frac{\Gamma\left(\frac{2}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{2}{3} \\ \frac{5}{3} \end{matrix}\middle| {\frac{c e^{i \pi}}{a}} \right)}}{3 \sqrt{a} \Gamma\left(\frac{5}{3}\right)}$$
=
=
_ / | pi*I\
|_ |1/2, 2/3 | c*e |
Gamma(2/3)* | | | -------|
2 1 \ 5/3 | a /
------------------------------------
___
3*\/ a *Gamma(5/3)
$$\frac{\Gamma\left(\frac{2}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{2}{3} \\ \frac{5}{3} \end{matrix}\middle| {\frac{c e^{i \pi}}{a}} \right)}}{3 \sqrt{a} \Gamma\left(\frac{5}{3}\right)}$$
gamma(2/3)*hyper((1/2, 2/3), (5/3,), c*exp_polar(pi*i)/a)/(3*sqrt(a)*gamma(5/3))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.