Sr Examen
Integral de sqrt(x^3+8) dx
Solución
Ha introducido
[src]
11 / | | ________ | / 3 | \/ x + 8 dx | / 1
$$\int\limits_{1}^{11} \sqrt{x^{3} + 8}\, dx$$
Integral(sqrt(x^3 + 8), (x, 1, 11))
Respuesta (Indefinida)
[src]
/ _ / | 3 pi*I\ | ___ |_ |-1/2, 1/3 | x *e | | ________ 2*x*\/ 2 *Gamma(1/3)* | | | --------| | / 3 2 1 \ 4/3 | 8 / | \/ x + 8 dx = C + ------------------------------------------------ | 3*Gamma(4/3) /
$$\int \sqrt{x^{3} + 8}\, dx = C + \frac{2 \sqrt{2} x \Gamma\left(\frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{1}{3} \\ \frac{4}{3} \end{matrix}\middle| {\frac{x^{3} e^{i \pi}}{8}} \right)}}{3 \Gamma\left(\frac{4}{3}\right)}$$
Gráfica
Respuesta
[src]
_ _ / | pi*I\
___ |_ /-1/2, 1/3 | \ ___ |_ |-1/2, 1/3 | 1331*e |
2*\/ 2 *Gamma(1/3)* | | | -1/8| 22*\/ 2 *Gamma(1/3)* | | | ----------|
2 1 \ 4/3 | / 2 1 \ 4/3 | 8 /
- ------------------------------------------ + -------------------------------------------------
3*Gamma(4/3) 3*Gamma(4/3)
$$- \frac{2 \sqrt{2} \Gamma\left(\frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{1}{3} \\ \frac{4}{3} \end{matrix}\middle| {- \frac{1}{8}} \right)}}{3 \Gamma\left(\frac{4}{3}\right)} + \frac{22 \sqrt{2} \Gamma\left(\frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{1}{3} \\ \frac{4}{3} \end{matrix}\middle| {\frac{1331 e^{i \pi}}{8}} \right)}}{3 \Gamma\left(\frac{4}{3}\right)}$$
=
=
_ _ / | pi*I\
___ |_ /-1/2, 1/3 | \ ___ |_ |-1/2, 1/3 | 1331*e |
2*\/ 2 *Gamma(1/3)* | | | -1/8| 22*\/ 2 *Gamma(1/3)* | | | ----------|
2 1 \ 4/3 | / 2 1 \ 4/3 | 8 /
- ------------------------------------------ + -------------------------------------------------
3*Gamma(4/3) 3*Gamma(4/3)
$$- \frac{2 \sqrt{2} \Gamma\left(\frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{1}{3} \\ \frac{4}{3} \end{matrix}\middle| {- \frac{1}{8}} \right)}}{3 \Gamma\left(\frac{4}{3}\right)} + \frac{22 \sqrt{2} \Gamma\left(\frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{1}{3} \\ \frac{4}{3} \end{matrix}\middle| {\frac{1331 e^{i \pi}}{8}} \right)}}{3 \Gamma\left(\frac{4}{3}\right)}$$
-2*sqrt(2)*gamma(1/3)*hyper((-1/2, 1/3), (4/3,), -1/8)/(3*gamma(4/3)) + 22*sqrt(2)*gamma(1/3)*hyper((-1/2, 1/3), (4/3,), 1331*exp_polar(pi*i)/8)/(3*gamma(4/3))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.