Sr Examen
Integral de (x)/(x(1+lnx)^5) dx
Solución
Ha introducido
[src]
1 / | | x | --------------- dx | 5 | x*(1 + log(x)) | / 0
$$\int\limits_{0}^{1} \frac{x}{x \left(\log{\left(x \right)} + 1\right)^{5}}\, dx$$
Integral(x/((x*(1 + log(x))^5)), (x, 0, 1))
Respuesta (Indefinida)
[src]
/
|
| 1
| ---------- dx
/ | 1 + log(x)
| | 3 2
| x / -10*x - x*log (x) - 7*x*log(x) - 4*x*log (x)
| --------------- dx = C + ---------------- + ------------------------------------------------------
| 5 24 4 3 2
| x*(1 + log(x)) 24 + 24*log (x) + 96*log (x) + 96*log(x) + 144*log (x)
|
/
$$\int \frac{x}{x \left(\log{\left(x \right)} + 1\right)^{5}}\, dx = C + \frac{- x \log{\left(x \right)}^{3} - 4 x \log{\left(x \right)}^{2} - 7 x \log{\left(x \right)} - 10 x}{24 \log{\left(x \right)}^{4} + 96 \log{\left(x \right)}^{3} + 144 \log{\left(x \right)}^{2} + 96 \log{\left(x \right)} + 24} + \frac{\int \frac{1}{\log{\left(x \right)} + 1}\, dx}{24}$$
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.