Sr Examen
Integral de x/((x^2-3)*(ln(x))^2) dx
Solución
Ha introducido
[src]
oo / | | x | ---------------- dx | / 2 \ 2 | \x - 3/*log (x) | / 2
$$\int\limits_{2}^{\infty} \frac{x}{\left(x^{2} - 3\right) \log{\left(x \right)}^{2}}\, dx$$
Integral(x/(((x^2 - 3)*log(x)^2)), (x, 2, oo))
Respuesta (Indefinida)
[src]
/ / | | 2 | x | x x | ---------------- dx = C - 6* | ---------------------------------- dx - ---------------- | / 2 \ 2 | 4 2 / 2\ | \x - 3/*log (x) | 9*log(x) + x *log(x) - 6*x *log(x) \-3 + x /*log(x) | | / /
$$\int \frac{x}{\left(x^{2} - 3\right) \log{\left(x \right)}^{2}}\, dx = C - \frac{x^{2}}{\left(x^{2} - 3\right) \log{\left(x \right)}} - 6 \int \frac{x}{x^{4} \log{\left(x \right)} - 6 x^{2} \log{\left(x \right)} + 9 \log{\left(x \right)}}\, dx$$
Respuesta
[src]
oo
/
|
| x 4
- 6* | ---------------------------------- dx + ------
| 4 2 log(2)
| 9*log(x) + x *log(x) - 6*x *log(x)
|
/
2
$$- 6 \int\limits_{2}^{\infty} \frac{x}{x^{4} \log{\left(x \right)} - 6 x^{2} \log{\left(x \right)} + 9 \log{\left(x \right)}}\, dx + \frac{4}{\log{\left(2 \right)}}$$
=
=
oo
/
|
| x 4
- 6* | ---------------------------------- dx + ------
| 4 2 log(2)
| 9*log(x) + x *log(x) - 6*x *log(x)
|
/
2
$$- 6 \int\limits_{2}^{\infty} \frac{x}{x^{4} \log{\left(x \right)} - 6 x^{2} \log{\left(x \right)} + 9 \log{\left(x \right)}}\, dx + \frac{4}{\log{\left(2 \right)}}$$
-6*Integral(x/(9*log(x) + x^4*log(x) - 6*x^2*log(x)), (x, 2, oo)) + 4/log(2)
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.