Integral de sin(5x^3) dx

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)              
/

$$\int \sin{\left(5 x^{3} \right)}\, dx = C + \frac{5 x^{4} \Gamma\left(\frac{2}{3}\right) {{}_{1}F_{2}\left(\begin{matrix} \frac{2}{3} \\ \frac{3}{2}, \frac{5}{3} \end{matrix}\middle| {- \frac{25 x^{6}}{4}} \right)}}{6 \Gamma\left(\frac{5}{3}\right)}$$

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Gráfica

Trazar el gráfico f(x)

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))

Respuesta numérica [src]

0.0574325074769088

0.0574325074769088

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Integral de sin(5x^3) dx

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