Sr Examen
Integral de ln(abs(sin(x)))*ln(cos(x))/sin(x)/cos(x) dx
Solución
Ha introducido
[src]
pi / | | /log(|sin(x)|)*log(cos(x))\ | |-------------------------| | \ sin(x) / | --------------------------- dx | cos(x) | / 0
$$\int\limits_{0}^{\pi} \frac{\log{\left(\cos{\left(x \right)} \right)} \log{\left(\left|{\sin{\left(x \right)}}\right| \right)} \frac{1}{\sin{\left(x \right)}}}{\cos{\left(x \right)}}\, dx$$
Integral(((log(Abs(sin(x)))*log(cos(x)))/sin(x))/cos(x), (x, 0, pi))
Respuesta (Indefinida)
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/ | | /log(|sin(x)|)*log(cos(x))\ / | |-------------------------| | | \ sin(x) / | log(|sin(x)|)*log(cos(x)) | --------------------------- dx = C + | ------------------------- dx | cos(x) | cos(x)*sin(x) | | / /
$$\int \frac{\log{\left(\cos{\left(x \right)} \right)} \log{\left(\left|{\sin{\left(x \right)}}\right| \right)} \frac{1}{\sin{\left(x \right)}}}{\cos{\left(x \right)}}\, dx = C + \int \frac{\log{\left(\cos{\left(x \right)} \right)} \log{\left(\left|{\sin{\left(x \right)}}\right| \right)}}{\sin{\left(x \right)} \cos{\left(x \right)}}\, dx$$
Respuesta numérica
[src]
(-4.83163586248317e-18 + 2109.71529713965j)
(-4.83163586248317e-18 + 2109.71529713965j)
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.