Sr Examen
Integral de cos(x^6) dx
Solución
Ha introducido
[src]
1 / | | / 6\ | cos\x / dx | / 0
$$\int\limits_{0}^{1} \cos{\left(x^{6} \right)}\, dx$$
Integral(cos(x^6), (x, 0, 1))
Respuesta (Indefinida)
[src]
_ / 1/12 | 12 \
|_ | | -x |
/ x*Gamma(1/12)* | | 13 | -----|
| 1 2 |1/2, -- | 4 |
| / 6\ \ 12 | /
| cos\x / dx = C + ------------------------------------
| /13\
/ 12*Gamma|--|
\12/
$$\int \cos{\left(x^{6} \right)}\, dx = C + \frac{x \Gamma\left(\frac{1}{12}\right) {{}_{1}F_{2}\left(\begin{matrix} \frac{1}{12} \\ \frac{1}{2}, \frac{13}{12} \end{matrix}\middle| {- \frac{x^{12}}{4}} \right)}}{12 \Gamma\left(\frac{13}{12}\right)}$$
Gráfica
Respuesta
[src]
_ / 1/12 | \
|_ | | |
Gamma(1/12)* | | 13 | -1/4|
1 2 |1/2, -- | |
\ 12 | /
---------------------------------
/13\
12*Gamma|--|
\12/
$$\frac{\Gamma\left(\frac{1}{12}\right) {{}_{1}F_{2}\left(\begin{matrix} \frac{1}{12} \\ \frac{1}{2}, \frac{13}{12} \end{matrix}\middle| {- \frac{1}{4}} \right)}}{12 \Gamma\left(\frac{13}{12}\right)}$$
=
=
_ / 1/12 | \
|_ | | |
Gamma(1/12)* | | 13 | -1/4|
1 2 |1/2, -- | |
\ 12 | /
---------------------------------
/13\
12*Gamma|--|
\12/
$$\frac{\Gamma\left(\frac{1}{12}\right) {{}_{1}F_{2}\left(\begin{matrix} \frac{1}{12} \\ \frac{1}{2}, \frac{13}{12} \end{matrix}\middle| {- \frac{1}{4}} \right)}}{12 \Gamma\left(\frac{13}{12}\right)}$$
gamma(1/12)*hyper((1/12,), (1/2, 13/12), -1/4)/(12*gamma(13/12))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.