Integral de lnx/[x*(lnx-1)*((lnx^2)-2)] dx
Solución
Respuesta (Indefinida)
[src]
// / ___ \ \
|| ___ |\/ 2 *log(x)| |
||-\/ 2 *acoth|------------| |
/ || \ 2 / 2 |
| / 2 \ ||--------------------------- for log (x) > 2|
| log(x) log\-2 + log (x)/ || 2 |
| ---------------------------- dx = C + ----------------- - log(-1 + log(x)) + 2*|< |
| / 2 \ 2 || / ___ \ |
| x*(log(x) - 1)*\log (x) - 2/ || ___ |\/ 2 *log(x)| |
| ||-\/ 2 *atanh|------------| |
/ || \ 2 / 2 |
||--------------------------- for log (x) < 2|
\\ 2 /
∫x(log(x)−1)(log(x)2−2)log(x)dx=C+2⎩⎨⎧−22acoth(22log(x))−22atanh(22log(x))forlog(x)2>2forlog(x)2<2−log(log(x)−1)+2log(log(x)2−2)
Gráfica
1
/
|
| log(x)
| ------------------------------ dx
| / 2 \
| x*(-1 + log(x))*\-2 + log (x)/
|
/
0
0∫1x(log(x)−1)(log(x)2−2)log(x)dx
=
1
/
|
| log(x)
| ------------------------------ dx
| / 2 \
| x*(-1 + log(x))*\-2 + log (x)/
|
/
0
0∫1x(log(x)−1)(log(x)2−2)log(x)dx
Integral(log(x)/(x*(-1 + log(x))*(-2 + log(x)^2)), (x, 0, 1))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.