Sr Examen
Integral de sinx*x^(-1/5) dx
Solución
Ha introducido
[src]
1 / | | sin(x) | ------ dx | 5 ___ | \/ x | / 0
$$\int\limits_{0}^{1} \frac{\sin{\left(x \right)}}{\sqrt[5]{x}}\, dx$$
Integral(sin(x)/x^(1/5), (x, 0, 1))
Respuesta (Indefinida)
[src]
_ / 9/10 | 2 \
9/5 |_ | | -x |
/ x *Gamma(9/10)* | | 19 | ----|
| 1 2 |3/2, -- | 4 |
| sin(x) \ 10 | /
| ------ dx = C + --------------------------------------
| 5 ___ /19\
| \/ x 2*Gamma|--|
| \10/
/
$$\int \frac{\sin{\left(x \right)}}{\sqrt[5]{x}}\, dx = C + \frac{x^{\frac{9}{5}} \Gamma\left(\frac{9}{10}\right) {{}_{1}F_{2}\left(\begin{matrix} \frac{9}{10} \\ \frac{3}{2}, \frac{19}{10} \end{matrix}\middle| {- \frac{x^{2}}{4}} \right)}}{2 \Gamma\left(\frac{19}{10}\right)}$$
Gráfica
Respuesta
[src]
_ / 9/10 | \
|_ | | |
Gamma(9/10)* | | 19 | -1/4|
1 2 |3/2, -- | |
\ 10 | /
---------------------------------
/19\
2*Gamma|--|
\10/
$$\frac{\Gamma\left(\frac{9}{10}\right) {{}_{1}F_{2}\left(\begin{matrix} \frac{9}{10} \\ \frac{3}{2}, \frac{19}{10} \end{matrix}\middle| {- \frac{1}{4}} \right)}}{2 \Gamma\left(\frac{19}{10}\right)}$$
=
=
_ / 9/10 | \
|_ | | |
Gamma(9/10)* | | 19 | -1/4|
1 2 |3/2, -- | |
\ 10 | /
---------------------------------
/19\
2*Gamma|--|
\10/
$$\frac{\Gamma\left(\frac{9}{10}\right) {{}_{1}F_{2}\left(\begin{matrix} \frac{9}{10} \\ \frac{3}{2}, \frac{19}{10} \end{matrix}\middle| {- \frac{1}{4}} \right)}}{2 \Gamma\left(\frac{19}{10}\right)}$$
gamma(9/10)*hyper((9/10,), (3/2, 19/10), -1/4)/(2*gamma(19/10))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.