Sr Examen
Integral de sin(x^5) dx
Solución
Ha introducido
[src]
1 / | | / 5\ | sin\x / dx | / 0
$$\int\limits_{0}^{1} \sin{\left(x^{5} \right)}\, dx$$
Integral(sin(x^5), (x, 0, 1))
Respuesta (Indefinida)
[src]
_ / | 10 \
/ 6 |_ | 3/5 | -x |
| x *Gamma(3/5)* | | | -----|
| / 5\ 1 2 \3/2, 8/5 | 4 /
| sin\x / dx = C + -------------------------------------
| 10*Gamma(8/5)
/
$$\int \sin{\left(x^{5} \right)}\, dx = C + \frac{x^{6} \Gamma\left(\frac{3}{5}\right) {{}_{1}F_{2}\left(\begin{matrix} \frac{3}{5} \\ \frac{3}{2}, \frac{8}{5} \end{matrix}\middle| {- \frac{x^{10}}{4}} \right)}}{10 \Gamma\left(\frac{8}{5}\right)}$$
Gráfica
Respuesta
[src]
_
|_ / 3/5 | \
Gamma(3/5)* | | | -1/4|
1 2 \3/2, 8/5 | /
---------------------------------
10*Gamma(8/5)
$$\frac{\Gamma\left(\frac{3}{5}\right) {{}_{1}F_{2}\left(\begin{matrix} \frac{3}{5} \\ \frac{3}{2}, \frac{8}{5} \end{matrix}\middle| {- \frac{1}{4}} \right)}}{10 \Gamma\left(\frac{8}{5}\right)}$$
=
=
_
|_ / 3/5 | \
Gamma(3/5)* | | | -1/4|
1 2 \3/2, 8/5 | /
---------------------------------
10*Gamma(8/5)
$$\frac{\Gamma\left(\frac{3}{5}\right) {{}_{1}F_{2}\left(\begin{matrix} \frac{3}{5} \\ \frac{3}{2}, \frac{8}{5} \end{matrix}\middle| {- \frac{1}{4}} \right)}}{10 \Gamma\left(\frac{8}{5}\right)}$$
gamma(3/5)*hyper((3/5,), (3/2, 8/5), -1/4)/(10*gamma(8/5))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.