Sr Examen
Integral de dx/(x(ln^4)x) dx
Solución
Ha introducido
[src]
oo / | | 1 | ----------- dx | 4 | x*log (x)*x | / 2
$$\int\limits_{2}^{\infty} \frac{1}{x x \log{\left(x \right)}^{4}}\, dx$$
Integral(1/((x*log(x)^4)*x), (x, 2, oo))
Respuesta (Indefinida)
[src]
/ | 2 | 1 Ei(-log(x)) -2 - log (x) + log(x) | ----------- dx = C - ----------- + --------------------- | 4 6 3 | x*log (x)*x 6*x*log (x) | /
$$\int \frac{1}{x x \log{\left(x \right)}^{4}}\, dx = C - \frac{\operatorname{Ei}{\left(- \log{\left(x \right)} \right)}}{6} + \frac{- \log{\left(x \right)}^{2} + \log{\left(x \right)} - 2}{6 x \log{\left(x \right)}^{3}}$$
Gráfica
Respuesta
[src]
2
Ei(-log(2)) -2 - log (2) + log(2)
----------- - ---------------------
6 3
12*log (2)
$$\frac{\operatorname{Ei}{\left(- \log{\left(2 \right)} \right)}}{6} - \frac{-2 - \log{\left(2 \right)}^{2} + \log{\left(2 \right)}}{12 \log{\left(2 \right)}^{3}}$$
=
=
2
Ei(-log(2)) -2 - log (2) + log(2)
----------- - ---------------------
6 3
12*log (2)
$$\frac{\operatorname{Ei}{\left(- \log{\left(2 \right)} \right)}}{6} - \frac{-2 - \log{\left(2 \right)}^{2} + \log{\left(2 \right)}}{12 \log{\left(2 \right)}^{3}}$$
Ei(-log(2))/6 - (-2 - log(2)^2 + log(2))/(12*log(2)^3)
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.