Sr Examen
Integral de cosx/x^(3/2) dx
Solución
Ha introducido
[src]
oo / | | cos(x) | ------ dx | 3/2 | x | / 2
$$\int\limits_{2}^{\infty} \frac{\cos{\left(x \right)}}{x^{\frac{3}{2}}}\, dx$$
Integral(cos(x)/x^(3/2), (x, 2, oo))
Respuesta (Indefinida)
[src]
/ / | | | cos(x) | cos(x) | ------ dx = C + | ------ dx | 3/2 | 3/2 | x | x | | / /
$$\int \frac{\cos{\left(x \right)}}{x^{\frac{3}{2}}}\, dx = C + \int \frac{\cos{\left(x \right)}}{x^{\frac{3}{2}}}\, dx$$
Respuesta
[src]
/ / ____ / 2 \ \ \
| |2*\/ pi *S|------| + cos(2)|*Gamma(1/4)|
| | | ____| | |
___ ____ |Gamma(-1/4) \ \\/ pi / / |
\/ 2 *\/ pi *|----------- + ----------------------------------------|
| Gamma(3/4) ____ |
\ \/ pi *Gamma(5/4) /
---------------------------------------------------------------------
4
$$\frac{\sqrt{2} \sqrt{\pi} \left(\frac{\Gamma\left(- \frac{1}{4}\right)}{\Gamma\left(\frac{3}{4}\right)} + \frac{\left(\cos{\left(2 \right)} + 2 \sqrt{\pi} S\left(\frac{2}{\sqrt{\pi}}\right)\right) \Gamma\left(\frac{1}{4}\right)}{\sqrt{\pi} \Gamma\left(\frac{5}{4}\right)}\right)}{4}$$
=
=
/ / ____ / 2 \ \ \
| |2*\/ pi *S|------| + cos(2)|*Gamma(1/4)|
| | | ____| | |
___ ____ |Gamma(-1/4) \ \\/ pi / / |
\/ 2 *\/ pi *|----------- + ----------------------------------------|
| Gamma(3/4) ____ |
\ \/ pi *Gamma(5/4) /
---------------------------------------------------------------------
4
$$\frac{\sqrt{2} \sqrt{\pi} \left(\frac{\Gamma\left(- \frac{1}{4}\right)}{\Gamma\left(\frac{3}{4}\right)} + \frac{\left(\cos{\left(2 \right)} + 2 \sqrt{\pi} S\left(\frac{2}{\sqrt{\pi}}\right)\right) \Gamma\left(\frac{1}{4}\right)}{\sqrt{\pi} \Gamma\left(\frac{5}{4}\right)}\right)}{4}$$
sqrt(2)*sqrt(pi)*(gamma(-1/4)/gamma(3/4) + (2*sqrt(pi)*fresnels(2/sqrt(pi)) + cos(2))*gamma(1/4)/(sqrt(pi)*gamma(5/4)))/4
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.