Sr Examen
Integral de sin(5x^3) dx
Solución
Ha introducido
[src]
3*pi ---- 4 / | | / 3\ | sin\5*x / dx | / pi -- 3
$$\int\limits_{\frac{\pi}{3}}^{\frac{3 \pi}{4}} \sin{\left(5 x^{3} \right)}\, dx$$
Integral(sin(5*x^3), (x, pi/3, 3*pi/4))
Respuesta (Indefinida)
[src]
_ / | 6\
/ 4 |_ | 2/3 | -25*x |
| 5*x *Gamma(2/3)* | | | ------|
| / 3\ 1 2 \3/2, 5/3 | 4 /
| sin\5*x / dx = C + ----------------------------------------
| 6*Gamma(5/3)
/
$$\int \sin{\left(5 x^{3} \right)}\, dx = C + \frac{5 x^{4} \Gamma\left(\frac{2}{3}\right) {{}_{1}F_{2}\left(\begin{matrix} \frac{2}{3} \\ \frac{3}{2}, \frac{5}{3} \end{matrix}\middle| {- \frac{25 x^{6}}{4}} \right)}}{6 \Gamma\left(\frac{5}{3}\right)}$$
Gráfica
Respuesta
[src]
_ / | 6\ _ / | 6\
4 |_ | 2/3 | -25*pi | 4 |_ | 2/3 | -18225*pi |
5*pi *Gamma(2/3)* | | | -------| 135*pi *Gamma(2/3)* | | | ----------|
1 2 \3/2, 5/3 | 2916 / 1 2 \3/2, 5/3 | 16384 /
- ------------------------------------------ + -----------------------------------------------
486*Gamma(5/3) 512*Gamma(5/3)
$$\frac{135 \pi^{4} \Gamma\left(\frac{2}{3}\right) {{}_{1}F_{2}\left(\begin{matrix} \frac{2}{3} \\ \frac{3}{2}, \frac{5}{3} \end{matrix}\middle| {- \frac{18225 \pi^{6}}{16384}} \right)}}{512 \Gamma\left(\frac{5}{3}\right)} - \frac{5 \pi^{4} \Gamma\left(\frac{2}{3}\right) {{}_{1}F_{2}\left(\begin{matrix} \frac{2}{3} \\ \frac{3}{2}, \frac{5}{3} \end{matrix}\middle| {- \frac{25 \pi^{6}}{2916}} \right)}}{486 \Gamma\left(\frac{5}{3}\right)}$$
=
=
_ / | 6\ _ / | 6\
4 |_ | 2/3 | -25*pi | 4 |_ | 2/3 | -18225*pi |
5*pi *Gamma(2/3)* | | | -------| 135*pi *Gamma(2/3)* | | | ----------|
1 2 \3/2, 5/3 | 2916 / 1 2 \3/2, 5/3 | 16384 /
- ------------------------------------------ + -----------------------------------------------
486*Gamma(5/3) 512*Gamma(5/3)
$$\frac{135 \pi^{4} \Gamma\left(\frac{2}{3}\right) {{}_{1}F_{2}\left(\begin{matrix} \frac{2}{3} \\ \frac{3}{2}, \frac{5}{3} \end{matrix}\middle| {- \frac{18225 \pi^{6}}{16384}} \right)}}{512 \Gamma\left(\frac{5}{3}\right)} - \frac{5 \pi^{4} \Gamma\left(\frac{2}{3}\right) {{}_{1}F_{2}\left(\begin{matrix} \frac{2}{3} \\ \frac{3}{2}, \frac{5}{3} \end{matrix}\middle| {- \frac{25 \pi^{6}}{2916}} \right)}}{486 \Gamma\left(\frac{5}{3}\right)}$$
-5*pi^4*gamma(2/3)*hyper((2/3,), (3/2, 5/3), -25*pi^6/2916)/(486*gamma(5/3)) + 135*pi^4*gamma(2/3)*hyper((2/3,), (3/2, 5/3), -18225*pi^6/16384)/(512*gamma(5/3))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.