Sr Examen
Integral de 1/(x*((ln(x)^2-9))) dx
Solución
Ha introducido
[src]
x e / | | 1 | --------------- dx | / 2 \ | x*\log (x) - 9/ | / 1
$$\int\limits_{1}^{e^{x}} \frac{1}{x \left(\log{\left(x \right)}^{2} - 9\right)}\, dx$$
Integral(1/(x*(log(x)^2 - 9)), (x, 1, exp(x)))
Respuesta (Indefinida)
[src]
/ | | 1 log(3 + log(x)) log(-3 + log(x)) | --------------- dx = C - --------------- + ---------------- | / 2 \ 6 6 | x*\log (x) - 9/ | /
$$\int \frac{1}{x \left(\log{\left(x \right)}^{2} - 9\right)}\, dx = C + \frac{\log{\left(\log{\left(x \right)} - 3 \right)}}{6} - \frac{\log{\left(\log{\left(x \right)} + 3 \right)}}{6}$$
Respuesta
[src]
/ / x\\ / / x\\
log\3 + log\e // log\-3 + log\e // pi*I
- ---------------- + ----------------- - ----
6 6 6
$$\frac{\log{\left(\log{\left(e^{x} \right)} - 3 \right)}}{6} - \frac{\log{\left(\log{\left(e^{x} \right)} + 3 \right)}}{6} - \frac{i \pi}{6}$$
=
=
/ / x\\ / / x\\
log\3 + log\e // log\-3 + log\e // pi*I
- ---------------- + ----------------- - ----
6 6 6
$$\frac{\log{\left(\log{\left(e^{x} \right)} - 3 \right)}}{6} - \frac{\log{\left(\log{\left(e^{x} \right)} + 3 \right)}}{6} - \frac{i \pi}{6}$$
-log(3 + log(exp(x)))/6 + log(-3 + log(exp(x)))/6 - pi*i/6
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.