Sr Examen
Integral de logx/(x(1-log^3x)) dx
Solución
Ha introducido
[src]
1 / | | log(x) | --------------- dx | / 3 \ | x*\1 - log (x)/ | / 0
$$\int\limits_{0}^{1} \frac{\log{\left(x \right)}}{x \left(1 - \log{\left(x \right)}^{3}\right)}\, dx$$
Integral(log(x)/((x*(1 - log(x)^3))), (x, 0, 1))
Respuesta (Indefinida)
[src]
/ ___ \ / ___ |2*\/ 3 *(1/2 + log(x))| | / 2 \ \/ 3 *atan|----------------------| | log(x) log(-1 + log(x)) log\1 + log (x) + log(x)/ \ 3 / | --------------- dx = C - ---------------- + ------------------------- - ---------------------------------- | / 3 \ 3 6 3 | x*\1 - log (x)/ | /
$$\int \frac{\log{\left(x \right)}}{x \left(1 - \log{\left(x \right)}^{3}\right)}\, dx = C - \frac{\log{\left(\log{\left(x \right)} - 1 \right)}}{3} + \frac{\log{\left(\log{\left(x \right)}^{2} + \log{\left(x \right)} + 1 \right)}}{6} - \frac{\sqrt{3} \operatorname{atan}{\left(\frac{2 \sqrt{3} \left(\log{\left(x \right)} + \frac{1}{2}\right)}{3} \right)}}{3}$$
Gráfica
Respuesta
[src]
1 / | | log(x) - | -------------------------------------- dx | / 2 \ | x*(-1 + log(x))*\1 + log (x) + log(x)/ | / 0
$$- \int\limits_{0}^{1} \frac{\log{\left(x \right)}}{x \left(\log{\left(x \right)} - 1\right) \left(\log{\left(x \right)}^{2} + \log{\left(x \right)} + 1\right)}\, dx$$
=
=
1 / | | log(x) - | -------------------------------------- dx | / 2 \ | x*(-1 + log(x))*\1 + log (x) + log(x)/ | / 0
$$- \int\limits_{0}^{1} \frac{\log{\left(x \right)}}{x \left(\log{\left(x \right)} - 1\right) \left(\log{\left(x \right)}^{2} + \log{\left(x \right)} + 1\right)}\, dx$$
-Integral(log(x)/(x*(-1 + log(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.