Sr Examen
Integral de sin(x^3dx) dx
Solución
Ha introducido
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1/2 / | | / 3\ | sin\x / dx | / 0
$$\int\limits_{0}^{\frac{1}{2}} \sin{\left(x^{3} \right)}\, dx$$
Integral(sin(x^3), (x, 0, 1/2))
Respuesta (Indefinida)
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_ / | 6 \
/ 4 |_ | 2/3 | -x |
| x *Gamma(2/3)* | | | ----|
| / 3\ 1 2 \3/2, 5/3 | 4 /
| sin\x / dx = C + ------------------------------------
| 6*Gamma(5/3)
/
$$\int \sin{\left(x^{3} \right)}\, dx = C + \frac{x^{4} \Gamma\left(\frac{2}{3}\right) {{}_{1}F_{2}\left(\begin{matrix} \frac{2}{3} \\ \frac{3}{2}, \frac{5}{3} \end{matrix}\middle| {- \frac{x^{6}}{4}} \right)}}{6 \Gamma\left(\frac{5}{3}\right)}$$
Gráfica
Respuesta
[src]
_
|_ / 2/3 | \
Gamma(2/3)* | | | -1/256|
1 2 \3/2, 5/3 | /
-----------------------------------
96*Gamma(5/3)
$$\frac{\Gamma\left(\frac{2}{3}\right) {{}_{1}F_{2}\left(\begin{matrix} \frac{2}{3} \\ \frac{3}{2}, \frac{5}{3} \end{matrix}\middle| {- \frac{1}{256}} \right)}}{96 \Gamma\left(\frac{5}{3}\right)}$$
=
=
_
|_ / 2/3 | \
Gamma(2/3)* | | | -1/256|
1 2 \3/2, 5/3 | /
-----------------------------------
96*Gamma(5/3)
$$\frac{\Gamma\left(\frac{2}{3}\right) {{}_{1}F_{2}\left(\begin{matrix} \frac{2}{3} \\ \frac{3}{2}, \frac{5}{3} \end{matrix}\middle| {- \frac{1}{256}} \right)}}{96 \Gamma\left(\frac{5}{3}\right)}$$
gamma(2/3)*hyper((2/3,), (3/2, 5/3), -1/256)/(96*gamma(5/3))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.