Sr Examen
Integral de sin(2x)*ln(cos(x)) dx
Solución
Ha introducido
[src]
1 / | | sin(2*x)*log(cos(x)) dx | / 0
$$\int\limits_{0}^{1} \log{\left(\cos{\left(x \right)} \right)} \sin{\left(2 x \right)}\, dx$$
Integral(sin(2*x)*log(cos(x)), (x, 0, 1))
Respuesta (Indefinida)
[src]
/ 2 | cos (x) log(cos(x)) cos(2*x)*log(cos(x)) | sin(2*x)*log(cos(x)) dx = C + ------- - ----------- - -------------------- | 2 2 2 /
$$\int \log{\left(\cos{\left(x \right)} \right)} \sin{\left(2 x \right)}\, dx = C - \frac{\log{\left(\cos{\left(x \right)} \right)} \cos{\left(2 x \right)}}{2} - \frac{\log{\left(\cos{\left(x \right)} \right)}}{2} + \frac{\cos^{2}{\left(x \right)}}{2}$$
Gráfica
Respuesta
[src]
2 1 cos (1) log(cos(1)) cos(2)*log(cos(1)) - - + ------- - ----------- - ------------------ 2 2 2 2
$$- \frac{1}{2} - \frac{\log{\left(\cos{\left(1 \right)} \right)} \cos{\left(2 \right)}}{2} + \frac{\cos^{2}{\left(1 \right)}}{2} - \frac{\log{\left(\cos{\left(1 \right)} \right)}}{2}$$
=
=
2 1 cos (1) log(cos(1)) cos(2)*log(cos(1)) - - + ------- - ----------- - ------------------ 2 2 2 2
$$- \frac{1}{2} - \frac{\log{\left(\cos{\left(1 \right)} \right)} \cos{\left(2 \right)}}{2} + \frac{\cos^{2}{\left(1 \right)}}{2} - \frac{\log{\left(\cos{\left(1 \right)} \right)}}{2}$$
-1/2 + cos(1)^2/2 - log(cos(1))/2 - cos(2)*log(cos(1))/2
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.