Sr Examen
Integral de (((lnx)^2)-1)/(x^3+x^2+x) dx
Solución
Ha introducido
[src]
-1 e / | | 2 | log (x) - 1 | ----------- dx | 3 2 | x + x + x | / 0
$$\int\limits_{0}^{e^{-1}} \frac{\log{\left(x \right)}^{2} - 1}{x + \left(x^{3} + x^{2}\right)}\, dx$$
Integral((log(x)^2 - 1)/(x^3 + x^2 + x), (x, 0, exp(-1)))
Respuesta (Indefinida)
[src]
/ / ___ \ / | ___ |2*\/ 3 *(1/2 + x)| | | 2 / 2\ \/ 3 *atan|-----------------| | 2 | log (x) - 1 log\1 + x + x / \ 3 / | log (x) | ----------- dx = C + --------------- - log(x) + ----------------------------- + | -------------- dx | 3 2 2 3 | / 2\ | x + x + x | x*\1 + x + x / | | / /
$$\int \frac{\log{\left(x \right)}^{2} - 1}{x + \left(x^{3} + x^{2}\right)}\, dx = C - \log{\left(x \right)} + \frac{\log{\left(x^{2} + x + 1 \right)}}{2} + \frac{\sqrt{3} \operatorname{atan}{\left(\frac{2 \sqrt{3} \left(x + \frac{1}{2}\right)}{3} \right)}}{3} + \int \frac{\log{\left(x \right)}^{2}}{x \left(x^{2} + x + 1\right)}\, dx$$
Respuesta
[src]
-1 e / | | (1 + log(x))*(-1 + log(x)) | -------------------------- dx | / 2\ | x*\1 + x + x / | / 0
$$\int\limits_{0}^{e^{-1}} \frac{\left(\log{\left(x \right)} - 1\right) \left(\log{\left(x \right)} + 1\right)}{x \left(x^{2} + x + 1\right)}\, dx$$
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-1 e / | | (1 + log(x))*(-1 + log(x)) | -------------------------- dx | / 2\ | x*\1 + x + x / | / 0
$$\int\limits_{0}^{e^{-1}} \frac{\left(\log{\left(x \right)} - 1\right) \left(\log{\left(x \right)} + 1\right)}{x \left(x^{2} + x + 1\right)}\, dx$$
Integral((1 + log(x))*(-1 + log(x))/(x*(1 + x + x^2)), (x, 0, exp(-1)))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.