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