Sr Examen
Integral de (ln(x)+2)/(x(ln^2(x)+2ln(x)+5)) dx
Solución
Ha introducido
[src]
1 / | | log(x) + 2 | -------------------------- dx | / 2 \ | x*\log (x) + 2*log(x) + 5/ | / 0
$$\int\limits_{0}^{1} \frac{\log{\left(x \right)} + 2}{x \left(\left(\log{\left(x \right)}^{2} + 2 \log{\left(x \right)}\right) + 5\right)}\, dx$$
Integral((log(x) + 2)/((x*(log(x)^2 + 2*log(x) + 5))), (x, 0, 1))
Respuesta (Indefinida)
[src]
/ /1 log(x)\ | atan|- + ------| / 2 \ | log(x) + 2 \2 2 / log\5 + log (x) + 2*log(x)/ | -------------------------- dx = C + ---------------- + --------------------------- | / 2 \ 2 2 | x*\log (x) + 2*log(x) + 5/ | /
$$\int \frac{\log{\left(x \right)} + 2}{x \left(\left(\log{\left(x \right)}^{2} + 2 \log{\left(x \right)}\right) + 5\right)}\, dx = C + \frac{\log{\left(\log{\left(x \right)}^{2} + 2 \log{\left(x \right)} + 5 \right)}}{2} + \frac{\operatorname{atan}{\left(\frac{\log{\left(x \right)}}{2} + \frac{1}{2} \right)}}{2}$$
Gráfica
Respuesta
[src]
1 / | | 2 + log(x) | -------------------------- dx | / 2 \ | x*\5 + log (x) + 2*log(x)/ | / 0
$$\int\limits_{0}^{1} \frac{\log{\left(x \right)} + 2}{x \left(\log{\left(x \right)}^{2} + 2 \log{\left(x \right)} + 5\right)}\, dx$$
=
=
1 / | | 2 + log(x) | -------------------------- dx | / 2 \ | x*\5 + log (x) + 2*log(x)/ | / 0
$$\int\limits_{0}^{1} \frac{\log{\left(x \right)} + 2}{x \left(\log{\left(x \right)}^{2} + 2 \log{\left(x \right)} + 5\right)}\, dx$$
Integral((2 + log(x))/(x*(5 + log(x)^2 + 2*log(x))), (x, 0, 1))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.