Sr Examen
Integral de (sqrt(x)-8*x)sin(3*x) dx
Solución
Ha introducido
[src]
1 / | | / ___ \ | \\/ x - 8*x/*sin(3*x) dx | / 0
$$\int\limits_{0}^{1} \left(\sqrt{x} - 8 x\right) \sin{\left(3 x \right)}\, dx$$
Integral((sqrt(x) - 8*x)*sin(3*x), (x, 0, 1))
Respuesta (Indefinida)
[src]
/ ___ ___\
___ ____ |\/ 6 *\/ x | _ / | 2\
/ x*\/ 6 *\/ pi *S|-----------| 5/2 |_ | 3/4, 5/4 | -9*x |
| | ____ | 3*x *Gamma(3/4)*Gamma(5/4)* | | | -----|
| / ___ \ 8*sin(3*x) 8*x*cos(3*x) \ \/ pi / 2 3 \3/2, 7/4, 9/4 | 4 /
| \\/ x - 8*x/*sin(3*x) dx = C - ---------- + ------------ + ----------------------------- - ---------------------------------------------------------
| 9 3 3 4*Gamma(7/4)*Gamma(9/4)
/
$$\int \left(\sqrt{x} - 8 x\right) \sin{\left(3 x \right)}\, dx = C - \frac{3 x^{\frac{5}{2}} \Gamma\left(\frac{3}{4}\right) \Gamma\left(\frac{5}{4}\right) {{}_{2}F_{3}\left(\begin{matrix} \frac{3}{4}, \frac{5}{4} \\ \frac{3}{2}, \frac{7}{4}, \frac{9}{4} \end{matrix}\middle| {- \frac{9 x^{2}}{4}} \right)}}{4 \Gamma\left(\frac{7}{4}\right) \Gamma\left(\frac{9}{4}\right)} + \frac{8 x \cos{\left(3 x \right)}}{3} + \frac{\sqrt{6} \sqrt{\pi} x S\left(\frac{\sqrt{6} \sqrt{x}}{\sqrt{\pi}}\right)}{3} - \frac{8 \sin{\left(3 x \right)}}{9}$$
Gráfica
Respuesta
[src]
/ ___ \
___ ____ |\/ 6 | _
\/ 6 *\/ pi *S|------| |_ / 3/4, 5/4 | \
| ____| 3*Gamma(3/4)*Gamma(5/4)* | | | -9/4|
8*sin(3) 8*cos(3) \\/ pi / 2 3 \3/2, 7/4, 9/4 | /
- -------- + -------- + ---------------------- - ---------------------------------------------------
9 3 3 4*Gamma(7/4)*Gamma(9/4)
$$- \frac{3 \Gamma\left(\frac{3}{4}\right) \Gamma\left(\frac{5}{4}\right) {{}_{2}F_{3}\left(\begin{matrix} \frac{3}{4}, \frac{5}{4} \\ \frac{3}{2}, \frac{7}{4}, \frac{9}{4} \end{matrix}\middle| {- \frac{9}{4}} \right)}}{4 \Gamma\left(\frac{7}{4}\right) \Gamma\left(\frac{9}{4}\right)} + \frac{8 \cos{\left(3 \right)}}{3} - \frac{8 \sin{\left(3 \right)}}{9} + \frac{\sqrt{6} \sqrt{\pi} S\left(\frac{\sqrt{6}}{\sqrt{\pi}}\right)}{3}$$
=
=
/ ___ \
___ ____ |\/ 6 | _
\/ 6 *\/ pi *S|------| |_ / 3/4, 5/4 | \
| ____| 3*Gamma(3/4)*Gamma(5/4)* | | | -9/4|
8*sin(3) 8*cos(3) \\/ pi / 2 3 \3/2, 7/4, 9/4 | /
- -------- + -------- + ---------------------- - ---------------------------------------------------
9 3 3 4*Gamma(7/4)*Gamma(9/4)
$$- \frac{3 \Gamma\left(\frac{3}{4}\right) \Gamma\left(\frac{5}{4}\right) {{}_{2}F_{3}\left(\begin{matrix} \frac{3}{4}, \frac{5}{4} \\ \frac{3}{2}, \frac{7}{4}, \frac{9}{4} \end{matrix}\middle| {- \frac{9}{4}} \right)}}{4 \Gamma\left(\frac{7}{4}\right) \Gamma\left(\frac{9}{4}\right)} + \frac{8 \cos{\left(3 \right)}}{3} - \frac{8 \sin{\left(3 \right)}}{9} + \frac{\sqrt{6} \sqrt{\pi} S\left(\frac{\sqrt{6}}{\sqrt{\pi}}\right)}{3}$$
-8*sin(3)/9 + 8*cos(3)/3 + sqrt(6)*sqrt(pi)*fresnels(sqrt(6)/sqrt(pi))/3 - 3*gamma(3/4)*gamma(5/4)*hyper((3/4, 5/4), (3/2, 7/4, 9/4), -9/4)/(4*gamma(7/4)*gamma(9/4))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.