Sr Examen
Integral de ln(x)^2/(x^2+2) dx
Solución
Ha introducido
[src]
oo / | | 2 | log (x) | ------- dx | 2 | x + 2 | / 0
$$\int\limits_{0}^{\infty} \frac{\log{\left(x \right)}^{2}}{x^{2} + 2}\, dx$$
Integral(log(x)^2/(x^2 + 2), (x, 0, oo))
Respuesta (Indefinida)
[src]
/ / | | | 2 | 2 | log (x) | log (x) | ------- dx = C + | ------- dx | 2 | 2 | x + 2 | 2 + x | | / /
$$\int \frac{\log{\left(x \right)}^{2}}{x^{2} + 2}\, dx = C + \int \frac{\log{\left(x \right)}^{2}}{x^{2} + 2}\, dx$$
Respuesta
[src]
/ 3*pi*I\ / ___ \ / pi*I\ / ___\
| ------| ___ | -I*\/ 2 | | ----| ___ | I*\/ 2 |
___ | ___ 2 | I*\/ 2 *polylog|3, ---------| ___ | ___ 2 | I*\/ 2 *polylog|3, -------|
I*\/ 2 *polylog\3, \/ 2 *e / \ 2 / I*\/ 2 *polylog\3, \/ 2 *e / \ 2 /
--------------------------------- + ----------------------------- - ------------------------------- - ---------------------------
2 2 2 2
$$\frac{\sqrt{2} i \operatorname{Li}_{3}\left(\sqrt{2} e^{\frac{3 i \pi}{2}}\right)}{2} + \frac{\sqrt{2} i \operatorname{Li}_{3}\left(- \frac{\sqrt{2} i}{2}\right)}{2} - \frac{\sqrt{2} i \operatorname{Li}_{3}\left(\frac{\sqrt{2} i}{2}\right)}{2} - \frac{\sqrt{2} i \operatorname{Li}_{3}\left(\sqrt{2} e^{\frac{i \pi}{2}}\right)}{2}$$
=
=
/ 3*pi*I\ / ___ \ / pi*I\ / ___\
| ------| ___ | -I*\/ 2 | | ----| ___ | I*\/ 2 |
___ | ___ 2 | I*\/ 2 *polylog|3, ---------| ___ | ___ 2 | I*\/ 2 *polylog|3, -------|
I*\/ 2 *polylog\3, \/ 2 *e / \ 2 / I*\/ 2 *polylog\3, \/ 2 *e / \ 2 /
--------------------------------- + ----------------------------- - ------------------------------- - ---------------------------
2 2 2 2
$$\frac{\sqrt{2} i \operatorname{Li}_{3}\left(\sqrt{2} e^{\frac{3 i \pi}{2}}\right)}{2} + \frac{\sqrt{2} i \operatorname{Li}_{3}\left(- \frac{\sqrt{2} i}{2}\right)}{2} - \frac{\sqrt{2} i \operatorname{Li}_{3}\left(\frac{\sqrt{2} i}{2}\right)}{2} - \frac{\sqrt{2} i \operatorname{Li}_{3}\left(\sqrt{2} e^{\frac{i \pi}{2}}\right)}{2}$$
i*sqrt(2)*polylog(3, sqrt(2)*exp_polar(3*pi*i/2))/2 + i*sqrt(2)*polylog(3, -i*sqrt(2)/2)/2 - i*sqrt(2)*polylog(3, sqrt(2)*exp_polar(pi*i/2))/2 - i*sqrt(2)*polylog(3, i*sqrt(2)/2)/2
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.