Sr Examen
Integral de sqrt(x**5-1) dx
Solución
Ha introducido
[src]
1 / | | ________ | / 5 | \/ x - 1 dx | / 0
$$\int\limits_{0}^{1} \sqrt{x^{5} - 1}\, dx$$
Integral(sqrt(x^5 - 1), (x, 0, 1))
Respuesta (Indefinida)
[src]
/ _ | |_ /-1/2, 1/5 | 5\ | ________ I*x*Gamma(1/5)* | | | x | | / 5 2 1 \ 6/5 | / | \/ x - 1 dx = C + ------------------------------------ | 5*Gamma(6/5) /
$$\int \sqrt{x^{5} - 1}\, dx = C + \frac{i x \Gamma\left(\frac{1}{5}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{1}{5} \\ \frac{6}{5} \end{matrix}\middle| {x^{5}} \right)}}{5 \Gamma\left(\frac{6}{5}\right)}$$
Gráfica
Respuesta
[src]
_
|_ /-1/2, 1/5 | \
I*Gamma(1/5)* | | | 1|
2 1 \ 6/5 | /
---------------------------------
5*Gamma(6/5)
$$\frac{i \Gamma\left(\frac{1}{5}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{1}{5} \\ \frac{6}{5} \end{matrix}\middle| {1} \right)}}{5 \Gamma\left(\frac{6}{5}\right)}$$
=
=
_
|_ /-1/2, 1/5 | \
I*Gamma(1/5)* | | | 1|
2 1 \ 6/5 | /
---------------------------------
5*Gamma(6/5)
$$\frac{i \Gamma\left(\frac{1}{5}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{1}{5} \\ \frac{6}{5} \end{matrix}\middle| {1} \right)}}{5 \Gamma\left(\frac{6}{5}\right)}$$
i*gamma(1/5)*hyper((-1/2, 1/5), (6/5,), 1)/(5*gamma(6/5))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.