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