Sr Examen
Integral de log(x)*dx/sqrt(x^3+3) dx
Solución
Ha introducido
[src]
oo / | | log(x) | ----------- dx | ________ | / 3 | \/ x + 3 | / 1
$$\int\limits_{1}^{\infty} \frac{\log{\left(x \right)}}{\sqrt{x^{3} + 3}}\, dx$$
Integral(log(x)/sqrt(x^3 + 3), (x, 1, oo))
Respuesta (Indefinida)
[src]
/ / | | | log(x) | log(x) | ----------- dx = C + | ----------- dx | ________ | ________ | / 3 | / 3 | \/ x + 3 | \/ 3 + x | | / /
$$\int \frac{\log{\left(x \right)}}{\sqrt{x^{3} + 3}}\, dx = C + \int \frac{\log{\left(x \right)}}{\sqrt{x^{3} + 3}}\, dx$$
Respuesta
[src]
_
2 |_ /1/6, 1/6, 1/2 | pi*I\
Gamma (1/6)* | | | 3*e |
3 2 \ 7/6, 7/6 | /
------------------------------------------
2
9*Gamma (7/6)
$$\frac{\Gamma^{2}\left(\frac{1}{6}\right) {{}_{3}F_{2}\left(\begin{matrix} \frac{1}{6}, \frac{1}{6}, \frac{1}{2} \\ \frac{7}{6}, \frac{7}{6} \end{matrix}\middle| {3 e^{i \pi}} \right)}}{9 \Gamma^{2}\left(\frac{7}{6}\right)}$$
=
=
_
2 |_ /1/6, 1/6, 1/2 | pi*I\
Gamma (1/6)* | | | 3*e |
3 2 \ 7/6, 7/6 | /
------------------------------------------
2
9*Gamma (7/6)
$$\frac{\Gamma^{2}\left(\frac{1}{6}\right) {{}_{3}F_{2}\left(\begin{matrix} \frac{1}{6}, \frac{1}{6}, \frac{1}{2} \\ \frac{7}{6}, \frac{7}{6} \end{matrix}\middle| {3 e^{i \pi}} \right)}}{9 \Gamma^{2}\left(\frac{7}{6}\right)}$$
gamma(1/6)^2*hyper((1/6, 1/6, 1/2), (7/6, 7/6), 3*exp_polar(pi*i))/(9*gamma(7/6)^2)
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.