Sr Examen
Integral de x*sin(x*x*x/2) dx
Solución
Ha introducido
[src]
1 / | | /x*x*x\ | x*sin|-----| dx | \ 2 / | / 0
$$\int\limits_{0}^{1} x \sin{\left(\frac{x x x}{2} \right)}\, dx$$
Integral(x*sin(((x*x)*x)/2), (x, 0, 1))
Respuesta (Indefinida)
[src]
_ / | 6 \
/ 5 |_ | 5/6 | -x |
| x *Gamma(5/6)* | | | ----|
| /x*x*x\ 1 2 \3/2, 11/6 | 16 /
| x*sin|-----| dx = C + -------------------------------------
| \ 2 / 12*Gamma(11/6)
|
/
$$\int x \sin{\left(\frac{x x x}{2} \right)}\, dx = C + \frac{x^{5} \Gamma\left(\frac{5}{6}\right) {{}_{1}F_{2}\left(\begin{matrix} \frac{5}{6} \\ \frac{3}{2}, \frac{11}{6} \end{matrix}\middle| {- \frac{x^{6}}{16}} \right)}}{12 \Gamma\left(\frac{11}{6}\right)}$$
Gráfica
Respuesta
[src]
_
|_ / 5/6 | \
Gamma(5/6)* | | | -1/16|
1 2 \3/2, 11/6 | /
-----------------------------------
12*Gamma(11/6)
$$\frac{\Gamma\left(\frac{5}{6}\right) {{}_{1}F_{2}\left(\begin{matrix} \frac{5}{6} \\ \frac{3}{2}, \frac{11}{6} \end{matrix}\middle| {- \frac{1}{16}} \right)}}{12 \Gamma\left(\frac{11}{6}\right)}$$
=
=
_
|_ / 5/6 | \
Gamma(5/6)* | | | -1/16|
1 2 \3/2, 11/6 | /
-----------------------------------
12*Gamma(11/6)
$$\frac{\Gamma\left(\frac{5}{6}\right) {{}_{1}F_{2}\left(\begin{matrix} \frac{5}{6} \\ \frac{3}{2}, \frac{11}{6} \end{matrix}\middle| {- \frac{1}{16}} \right)}}{12 \Gamma\left(\frac{11}{6}\right)}$$
gamma(5/6)*hyper((5/6,), (3/2, 11/6), -1/16)/(12*gamma(11/6))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.