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