Sr Examen
Integral de x/(3qrt(1+x^3)) dx
Solución
Ha introducido
[src]
1 / | | x | ------------- dx | ________ | / 3 | 3*\/ 1 + x | / 0
$$\int\limits_{0}^{1} \frac{x}{3 \sqrt{x^{3} + 1}}\, dx$$
Integral(x/((3*sqrt(1 + x^3))), (x, 0, 1))
Respuesta (Indefinida)
[src]
_ / 2 |_ /1/2, 2/3 | 3 pi*I\ | x *Gamma(2/3)* | | | x *e | | x 2 1 \ 5/3 | / | ------------- dx = C + ---------------------------------------- | ________ 9*Gamma(5/3) | / 3 | 3*\/ 1 + x | /
$$\int \frac{x}{3 \sqrt{x^{3} + 1}}\, dx = C + \frac{x^{2} \Gamma\left(\frac{2}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{2}{3} \\ \frac{5}{3} \end{matrix}\middle| {x^{3} e^{i \pi}} \right)}}{9 \Gamma\left(\frac{5}{3}\right)}$$
Gráfica
Respuesta
[src]
_
|_ /1/2, 2/3 | \
Gamma(2/3)* | | | -1|
2 1 \ 5/3 | /
-------------------------------
9*Gamma(5/3)
$$\frac{\Gamma\left(\frac{2}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{2}{3} \\ \frac{5}{3} \end{matrix}\middle| {-1} \right)}}{9 \Gamma\left(\frac{5}{3}\right)}$$
=
=
_
|_ /1/2, 2/3 | \
Gamma(2/3)* | | | -1|
2 1 \ 5/3 | /
-------------------------------
9*Gamma(5/3)
$$\frac{\Gamma\left(\frac{2}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{2}{3} \\ \frac{5}{3} \end{matrix}\middle| {-1} \right)}}{9 \Gamma\left(\frac{5}{3}\right)}$$
gamma(2/3)*hyper((1/2, 2/3), (5/3,), -1)/(9*gamma(5/3))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.