Sr Examen
Integral de (ln(x)+2)/(x*(1-ln(x)-(ln(x))^2)) dx
Solución
Ha introducido
[src]
1 / | | log(x) + 2 | ------------------------ dx | / 2 \ | x*\1 - log(x) - log (x)/ | / 0
$$\int\limits_{0}^{1} \frac{\log{\left(x \right)} + 2}{x \left(\left(1 - \log{\left(x \right)}\right) - \log{\left(x \right)}^{2}\right)}\, dx$$
Integral((log(x) + 2)/((x*(1 - log(x) - log(x)^2))), (x, 0, 1))
Respuesta (Indefinida)
[src]
// / ___ \ \
|| ___ |2*\/ 5 *(1/2 + log(x))| |
||-\/ 5 *acoth|----------------------| |
/ || \ 5 / 2 |
| ||------------------------------------- for (1/2 + log(x)) > 5/4| / 2 \
| log(x) + 2 || 10 | log\-1 + log (x) + log(x)/
| ------------------------ dx = C - 6*|< | - --------------------------
| / 2 \ || / ___ \ | 2
| x*\1 - log(x) - log (x)/ || ___ |2*\/ 5 *(1/2 + log(x))| |
| ||-\/ 5 *atanh|----------------------| |
/ || \ 5 / 2 |
||------------------------------------- for (1/2 + log(x)) < 5/4|
\\ 10 /
$$\int \frac{\log{\left(x \right)} + 2}{x \left(\left(1 - \log{\left(x \right)}\right) - \log{\left(x \right)}^{2}\right)}\, dx = C - 6 \left(\begin{cases} - \frac{\sqrt{5} \operatorname{acoth}{\left(\frac{2 \sqrt{5} \left(\log{\left(x \right)} + \frac{1}{2}\right)}{5} \right)}}{10} & \text{for}\: \left(\log{\left(x \right)} + \frac{1}{2}\right)^{2} > \frac{5}{4} \\- \frac{\sqrt{5} \operatorname{atanh}{\left(\frac{2 \sqrt{5} \left(\log{\left(x \right)} + \frac{1}{2}\right)}{5} \right)}}{10} & \text{for}\: \left(\log{\left(x \right)} + \frac{1}{2}\right)^{2} < \frac{5}{4} \end{cases}\right) - \frac{\log{\left(\log{\left(x \right)}^{2} + \log{\left(x \right)} - 1 \right)}}{2}$$
Gráfica
Respuesta
[src]
1 / | | 2 + log(x) - | ------------------------- dx | / 2 \ | x*\-1 + log (x) + log(x)/ | / 0
$$- \int\limits_{0}^{1} \frac{\log{\left(x \right)} + 2}{x \left(\log{\left(x \right)}^{2} + \log{\left(x \right)} - 1\right)}\, dx$$
=
=
1 / | | 2 + log(x) - | ------------------------- dx | / 2 \ | x*\-1 + log (x) + log(x)/ | / 0
$$- \int\limits_{0}^{1} \frac{\log{\left(x \right)} + 2}{x \left(\log{\left(x \right)}^{2} + \log{\left(x \right)} - 1\right)}\, dx$$
-Integral((2 + log(x))/(x*(-1 + log(x)^2 + log(x))), (x, 0, 1))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.