Sr Examen
Integral de 1/sqrt(x*x*x+1) dx
Solución
Ha introducido
[src]
25 / | | 1 | ------------- dx | ___________ | \/ x*x*x + 1 | / 0
$$\int\limits_{0}^{25} \frac{1}{\sqrt{x x x + 1}}\, dx$$
Integral(1/(sqrt((x*x)*x + 1)), (x, 0, 25))
Respuesta (Indefinida)
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_ / |_ /1/3, 1/2 | 3 pi*I\ | x*Gamma(1/3)* | | | x *e | | 1 2 1 \ 4/3 | / | ------------- dx = C + --------------------------------------- | ___________ 3*Gamma(4/3) | \/ x*x*x + 1 | /
$$\int \frac{1}{\sqrt{x x x + 1}}\, dx = C + \frac{x \Gamma\left(\frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{3}, \frac{1}{2} \\ \frac{4}{3} \end{matrix}\middle| {x^{3} e^{i \pi}} \right)}}{3 \Gamma\left(\frac{4}{3}\right)}$$
Gráfica
Respuesta
[src]
_
|_ /1/3, 1/2 | pi*I\
25*Gamma(1/3)* | | | 15625*e |
2 1 \ 4/3 | /
-------------------------------------------
3*Gamma(4/3)
$$\frac{25 \Gamma\left(\frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{3}, \frac{1}{2} \\ \frac{4}{3} \end{matrix}\middle| {15625 e^{i \pi}} \right)}}{3 \Gamma\left(\frac{4}{3}\right)}$$
=
=
_
|_ /1/3, 1/2 | pi*I\
25*Gamma(1/3)* | | | 15625*e |
2 1 \ 4/3 | /
-------------------------------------------
3*Gamma(4/3)
$$\frac{25 \Gamma\left(\frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{3}, \frac{1}{2} \\ \frac{4}{3} \end{matrix}\middle| {15625 e^{i \pi}} \right)}}{3 \Gamma\left(\frac{4}{3}\right)}$$
25*gamma(1/3)*hyper((1/3, 1/2), (4/3,), 15625*exp_polar(pi*i))/(3*gamma(4/3))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.