Sr Examen
Integral de lnx/[x*(lnx-1)*((lnx^2)-2)] dx
Solución
Ha introducido
[src]
1 / | | log(x) | ---------------------------- dx | / 2 \ | x*(log(x) - 1)*\log (x) - 2/ | / 0
$$\int\limits_{0}^{1} \frac{\log{\left(x \right)}}{x \left(\log{\left(x \right)} - 1\right) \left(\log{\left(x \right)}^{2} - 2\right)}\, dx$$
Integral(log(x)/(((x*(log(x) - 1))*(log(x)^2 - 2))), (x, 0, 1))
Respuesta (Indefinida)
[src]
// / ___ \ \
|| ___ |\/ 2 *log(x)| |
||-\/ 2 *acoth|------------| |
/ || \ 2 / 2 |
| / 2 \ ||--------------------------- for log (x) > 2|
| log(x) log\-2 + log (x)/ || 2 |
| ---------------------------- dx = C + ----------------- - log(-1 + log(x)) + 2*|< |
| / 2 \ 2 || / ___ \ |
| x*(log(x) - 1)*\log (x) - 2/ || ___ |\/ 2 *log(x)| |
| ||-\/ 2 *atanh|------------| |
/ || \ 2 / 2 |
||--------------------------- for log (x) < 2|
\\ 2 /
$$\int \frac{\log{\left(x \right)}}{x \left(\log{\left(x \right)} - 1\right) \left(\log{\left(x \right)}^{2} - 2\right)}\, dx = C + 2 \left(\begin{cases} - \frac{\sqrt{2} \operatorname{acoth}{\left(\frac{\sqrt{2} \log{\left(x \right)}}{2} \right)}}{2} & \text{for}\: \log{\left(x \right)}^{2} > 2 \\- \frac{\sqrt{2} \operatorname{atanh}{\left(\frac{\sqrt{2} \log{\left(x \right)}}{2} \right)}}{2} & \text{for}\: \log{\left(x \right)}^{2} < 2 \end{cases}\right) - \log{\left(\log{\left(x \right)} - 1 \right)} + \frac{\log{\left(\log{\left(x \right)}^{2} - 2 \right)}}{2}$$
Gráfica
Respuesta
[src]
1 / | | log(x) | ------------------------------ dx | / 2 \ | x*(-1 + log(x))*\-2 + log (x)/ | / 0
$$\int\limits_{0}^{1} \frac{\log{\left(x \right)}}{x \left(\log{\left(x \right)} - 1\right) \left(\log{\left(x \right)}^{2} - 2\right)}\, dx$$
=
=
1 / | | log(x) | ------------------------------ dx | / 2 \ | x*(-1 + log(x))*\-2 + log (x)/ | / 0
$$\int\limits_{0}^{1} \frac{\log{\left(x \right)}}{x \left(\log{\left(x \right)} - 1\right) \left(\log{\left(x \right)}^{2} - 2\right)}\, dx$$
Integral(log(x)/(x*(-1 + log(x))*(-2 + log(x)^2)), (x, 0, 1))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.