Sr Examen
Integral de 1/((x^2+2x)(lnx)^3) dx
Solución
Ha introducido
[src]
oo / | | 1 | ------------------ dx | / 2 \ 3 | \x + 2*x/*log (x) | / 1
$$\int\limits_{1}^{\infty} \frac{1}{\left(x^{2} + 2 x\right) \log{\left(x \right)}^{3}}\, dx$$
Integral(1/((x^2 + 2*x)*log(x)^3), (x, 1, oo))
Respuesta (Indefinida)
[src]
/ /
| |
| -2 | x
| ------------------------------------------------ dx + | ------------------------------------------------ dx
| 3 2 | 3 2
/ | 8*log(x) + x *log(x) + 6*x *log(x) + 12*x*log(x) | 8*log(x) + x *log(x) + 6*x *log(x) + 12*x*log(x)
| | |
| 1 / / -2 - x + x*log(x)
| ------------------ dx = C + --------------------------------------------------------------------------------------------------------------- + ------------------------
| / 2 \ 3 2 / 2 \ 2
| \x + 2*x/*log (x) \8 + 2*x + 8*x/*log (x)
|
/
$$\int \frac{1}{\left(x^{2} + 2 x\right) \log{\left(x \right)}^{3}}\, dx = C + \frac{\int \frac{x}{x^{3} \log{\left(x \right)} + 6 x^{2} \log{\left(x \right)} + 12 x \log{\left(x \right)} + 8 \log{\left(x \right)}}\, dx + \int \left(- \frac{2}{x^{3} \log{\left(x \right)} + 6 x^{2} \log{\left(x \right)} + 12 x \log{\left(x \right)} + 8 \log{\left(x \right)}}\right)\, dx}{2} + \frac{x \log{\left(x \right)} - x - 2}{\left(2 x^{2} + 8 x + 8\right) \log{\left(x \right)}^{2}}$$
Respuesta
[src]
oo / | | 1 | ------------------ dx | / 2 \ 3 | \x + 2*x/*log (x) | / 1
$$\int\limits_{1}^{\infty} \frac{1}{\left(x^{2} + 2 x\right) \log{\left(x \right)}^{3}}\, dx$$
=
=
oo / | | 1 | ------------------ dx | / 2 \ 3 | \x + 2*x/*log (x) | / 1
$$\int\limits_{1}^{\infty} \frac{1}{\left(x^{2} + 2 x\right) \log{\left(x \right)}^{3}}\, dx$$
Integral(1/((x^2 + 2*x)*log(x)^3), (x, 1, oo))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.