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