Sr Examen
Integral de cos(x^5) dx
Solución
Ha introducido
[src]
3/10 / | | / 5\ | cos\x / dx | / 1/10
$$\int\limits_{\frac{1}{10}}^{\frac{3}{10}} \cos{\left(x^{5} \right)}\, dx$$
Integral(cos(x^5), (x, 1/10, 3/10))
Respuesta (Indefinida)
[src]
_ / 1/10 | 10 \
|_ | | -x |
/ x*Gamma(1/10)* | | 11 | -----|
| 1 2 |1/2, -- | 4 |
| / 5\ \ 10 | /
| cos\x / dx = C + ------------------------------------
| /11\
/ 10*Gamma|--|
\10/
$$\int \cos{\left(x^{5} \right)}\, dx = C + \frac{x \Gamma\left(\frac{1}{10}\right) {{}_{1}F_{2}\left(\begin{matrix} \frac{1}{10} \\ \frac{1}{2}, \frac{11}{10} \end{matrix}\middle| {- \frac{x^{10}}{4}} \right)}}{10 \Gamma\left(\frac{11}{10}\right)}$$
Gráfica
Respuesta
[src]
_ / 1/10 | \ _ / 1/10 | \
|_ | | | |_ | | -59049 |
Gamma(1/10)* | | 11 | -1/40000000000| 3*Gamma(1/10)* | | 11 | -----------|
1 2 |1/2, -- | | 1 2 |1/2, -- | 40000000000|
\ 10 | / \ 10 | /
- ------------------------------------------- + ------------------------------------------
/11\ /11\
100*Gamma|--| 100*Gamma|--|
\10/ \10/
$$\frac{3 \Gamma\left(\frac{1}{10}\right) {{}_{1}F_{2}\left(\begin{matrix} \frac{1}{10} \\ \frac{1}{2}, \frac{11}{10} \end{matrix}\middle| {- \frac{59049}{40000000000}} \right)}}{100 \Gamma\left(\frac{11}{10}\right)} - \frac{\Gamma\left(\frac{1}{10}\right) {{}_{1}F_{2}\left(\begin{matrix} \frac{1}{10} \\ \frac{1}{2}, \frac{11}{10} \end{matrix}\middle| {- \frac{1}{40000000000}} \right)}}{100 \Gamma\left(\frac{11}{10}\right)}$$
=
=
_ / 1/10 | \ _ / 1/10 | \
|_ | | | |_ | | -59049 |
Gamma(1/10)* | | 11 | -1/40000000000| 3*Gamma(1/10)* | | 11 | -----------|
1 2 |1/2, -- | | 1 2 |1/2, -- | 40000000000|
\ 10 | / \ 10 | /
- ------------------------------------------- + ------------------------------------------
/11\ /11\
100*Gamma|--| 100*Gamma|--|
\10/ \10/
$$\frac{3 \Gamma\left(\frac{1}{10}\right) {{}_{1}F_{2}\left(\begin{matrix} \frac{1}{10} \\ \frac{1}{2}, \frac{11}{10} \end{matrix}\middle| {- \frac{59049}{40000000000}} \right)}}{100 \Gamma\left(\frac{11}{10}\right)} - \frac{\Gamma\left(\frac{1}{10}\right) {{}_{1}F_{2}\left(\begin{matrix} \frac{1}{10} \\ \frac{1}{2}, \frac{11}{10} \end{matrix}\middle| {- \frac{1}{40000000000}} \right)}}{100 \Gamma\left(\frac{11}{10}\right)}$$
-gamma(1/10)*hyper((1/10,), (1/2, 11/10), -1/40000000000)/(100*gamma(11/10)) + 3*gamma(1/10)*hyper((1/10,), (1/2, 11/10), -59049/40000000000)/(100*gamma(11/10))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.