Sr Examen
Integral de 1/(sqrt(5*x^3+3)) dx
Solución
Ha introducido
[src]
1 / | | 1 | ------------- dx | __________ | / 3 | \/ 5*x + 3 | / 0
$$\int\limits_{0}^{1} \frac{1}{\sqrt{5 x^{3} + 3}}\, dx$$
Integral(1/(sqrt(5*x^3 + 3)), (x, 0, 1))
Respuesta (Indefinida)
[src]
_ / | 3 pi*I\
/ ___ |_ |1/3, 1/2 | 5*x *e |
| x*\/ 3 *Gamma(1/3)* | | | ----------|
| 1 2 1 \ 4/3 | 3 /
| ------------- dx = C + -----------------------------------------------
| __________ 9*Gamma(4/3)
| / 3
| \/ 5*x + 3
|
/
$$\int \frac{1}{\sqrt{5 x^{3} + 3}}\, dx = C + \frac{\sqrt{3} x \Gamma\left(\frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{3}, \frac{1}{2} \\ \frac{4}{3} \end{matrix}\middle| {\frac{5 x^{3} e^{i \pi}}{3}} \right)}}{9 \Gamma\left(\frac{4}{3}\right)}$$
Gráfica
Respuesta
[src]
_ / | pi*I\
___ |_ |1/3, 1/2 | 5*e |
\/ 3 *Gamma(1/3)* | | | -------|
2 1 \ 4/3 | 3 /
------------------------------------------
9*Gamma(4/3)
$$\frac{\sqrt{3} \Gamma\left(\frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{3}, \frac{1}{2} \\ \frac{4}{3} \end{matrix}\middle| {\frac{5 e^{i \pi}}{3}} \right)}}{9 \Gamma\left(\frac{4}{3}\right)}$$
=
=
_ / | pi*I\
___ |_ |1/3, 1/2 | 5*e |
\/ 3 *Gamma(1/3)* | | | -------|
2 1 \ 4/3 | 3 /
------------------------------------------
9*Gamma(4/3)
$$\frac{\sqrt{3} \Gamma\left(\frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{3}, \frac{1}{2} \\ \frac{4}{3} \end{matrix}\middle| {\frac{5 e^{i \pi}}{3}} \right)}}{9 \Gamma\left(\frac{4}{3}\right)}$$
sqrt(3)*gamma(1/3)*hyper((1/3, 1/2), (4/3,), 5*exp_polar(pi*i)/3)/(9*gamma(4/3))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.