Sr Examen
Integral de (x(cosx)^2)/(sqrt(x^6-1)) dx
Solución
Ha introducido
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oo / | | 2 | x*cos (x) | ----------- dx | ________ | / 6 | \/ x - 1 | / 1
$$\int\limits_{1}^{\infty} \frac{x \cos^{2}{\left(x \right)}}{\sqrt{x^{6} - 1}}\, dx$$
Integral((x*cos(x)^2)/sqrt(x^6 - 1), (x, 1, oo))
Respuesta (Indefinida)
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/ / | | | 2 | 2 | x*cos (x) | x*cos (x) | ----------- dx = C + | ----------------------------------------------- dx | ________ | ____________________________________________ | / 6 | / / 2\ / 2 \ | \/ x - 1 | \/ (1 + x)*(-1 + x)*\1 + x + x /*\1 + x - x/ | | / /
$$\int \frac{x \cos^{2}{\left(x \right)}}{\sqrt{x^{6} - 1}}\, dx = C + \int \frac{x \cos^{2}{\left(x \right)}}{\sqrt{\left(x - 1\right) \left(x + 1\right) \left(x^{2} - x + 1\right) \left(x^{2} + x + 1\right)}}\, dx$$
Respuesta
[src]
___ __0, 4 /2/3, 1/3, 0, 1/2 1/2, 1/6, -1/6 | \ ____ 3*pi*\/ 3 */__ | | 729| \/ pi *Gamma(1/6) \_|7, 1 \ 0 | / ----------------- + ----------------------------------------------------------- 12*Gamma(2/3) 4
$$\frac{3 \sqrt{3} \pi {G_{7, 1}^{0, 4}\left(\begin{matrix} \frac{2}{3}, \frac{1}{3}, 0, \frac{1}{2} & \frac{1}{2}, \frac{1}{6}, - \frac{1}{6} \\ & 0 \end{matrix} \middle| {729} \right)}}{4} + \frac{\sqrt{\pi} \Gamma\left(\frac{1}{6}\right)}{12 \Gamma\left(\frac{2}{3}\right)}$$
=
=
___ __0, 4 /2/3, 1/3, 0, 1/2 1/2, 1/6, -1/6 | \ ____ 3*pi*\/ 3 */__ | | 729| \/ pi *Gamma(1/6) \_|7, 1 \ 0 | / ----------------- + ----------------------------------------------------------- 12*Gamma(2/3) 4
$$\frac{3 \sqrt{3} \pi {G_{7, 1}^{0, 4}\left(\begin{matrix} \frac{2}{3}, \frac{1}{3}, 0, \frac{1}{2} & \frac{1}{2}, \frac{1}{6}, - \frac{1}{6} \\ & 0 \end{matrix} \middle| {729} \right)}}{4} + \frac{\sqrt{\pi} \Gamma\left(\frac{1}{6}\right)}{12 \Gamma\left(\frac{2}{3}\right)}$$
sqrt(pi)*gamma(1/6)/(12*gamma(2/3)) + 3*pi*sqrt(3)*meijerg(((2/3, 1/3, 0, 1/2), (1/2, 1/6, -1/6)), ((), (0,)), 729)/4
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.