Sr Examen
Integral de sinxcosx/((1+cos^2x)(1+cosx)) dx
Solución
Ha introducido
[src]
1 / | | sin(x)*cos(x) | -------------------------- dx | / 2 \ | \1 + cos (x)/*(1 + cos(x)) | / 0
$$\int\limits_{0}^{1} \frac{\sin{\left(x \right)} \cos{\left(x \right)}}{\left(\cos{\left(x \right)} + 1\right) \left(\cos^{2}{\left(x \right)} + 1\right)}\, dx$$
Integral((sin(x)*cos(x))/(((1 + cos(x)^2)*(1 + cos(x)))), (x, 0, 1))
Respuesta (Indefinida)
[src]
/ | / 2 \ | sin(x)*cos(x) log(1 + cos(x)) atan(cos(x)) log\1 + cos (x)/ | -------------------------- dx = C + --------------- - ------------ - ---------------- | / 2 \ 2 2 4 | \1 + cos (x)/*(1 + cos(x)) | /
$$\int \frac{\sin{\left(x \right)} \cos{\left(x \right)}}{\left(\cos{\left(x \right)} + 1\right) \left(\cos^{2}{\left(x \right)} + 1\right)}\, dx = C + \frac{\log{\left(\cos{\left(x \right)} + 1 \right)}}{2} - \frac{\log{\left(\cos^{2}{\left(x \right)} + 1 \right)}}{4} - \frac{\operatorname{atan}{\left(\cos{\left(x \right)} \right)}}{2}$$
Gráfica
Respuesta
[src]
/ 2 \
log(1 + cos(1)) atan(cos(1)) log(2) log\1 + cos (1)/ pi
--------------- - ------------ - ------ - ---------------- + --
2 2 4 4 8
$$- \frac{\operatorname{atan}{\left(\cos{\left(1 \right)} \right)}}{2} - \frac{\log{\left(2 \right)}}{4} - \frac{\log{\left(\cos^{2}{\left(1 \right)} + 1 \right)}}{4} + \frac{\log{\left(\cos{\left(1 \right)} + 1 \right)}}{2} + \frac{\pi}{8}$$
=
=
/ 2 \
log(1 + cos(1)) atan(cos(1)) log(2) log\1 + cos (1)/ pi
--------------- - ------------ - ------ - ---------------- + --
2 2 4 4 8
$$- \frac{\operatorname{atan}{\left(\cos{\left(1 \right)} \right)}}{2} - \frac{\log{\left(2 \right)}}{4} - \frac{\log{\left(\cos^{2}{\left(1 \right)} + 1 \right)}}{4} + \frac{\log{\left(\cos{\left(1 \right)} + 1 \right)}}{2} + \frac{\pi}{8}$$
log(1 + cos(1))/2 - atan(cos(1))/2 - log(2)/4 - log(1 + cos(1)^2)/4 + pi/8
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.