Sr Examen
Integral de (sin(x)-cos(x))/(cos(x)+sin(x))^3 dx
Solución
Ha introducido
[src]
p - 4 / | | sin(x) - cos(x) | ------------------ dx | 3 | (cos(x) + sin(x)) | / 0
$$\int\limits_{0}^{\frac{p}{4}} \frac{\sin{\left(x \right)} - \cos{\left(x \right)}}{\left(\sin{\left(x \right)} + \cos{\left(x \right)}\right)^{3}}\, dx$$
Integral((sin(x) - cos(x))/(cos(x) + sin(x))^3, (x, 0, p/4))
Respuesta
[src]
1 1
- - + ---------------------------------------
2 2/p\ 2/p\ /p\ /p\
2*cos |-| + 2*sin |-| + 4*cos|-|*sin|-|
\4/ \4/ \4/ \4/
$$- \frac{1}{2} + \frac{1}{2 \sin^{2}{\left(\frac{p}{4} \right)} + 4 \sin{\left(\frac{p}{4} \right)} \cos{\left(\frac{p}{4} \right)} + 2 \cos^{2}{\left(\frac{p}{4} \right)}}$$
=
=
1 1
- - + ---------------------------------------
2 2/p\ 2/p\ /p\ /p\
2*cos |-| + 2*sin |-| + 4*cos|-|*sin|-|
\4/ \4/ \4/ \4/
$$- \frac{1}{2} + \frac{1}{2 \sin^{2}{\left(\frac{p}{4} \right)} + 4 \sin{\left(\frac{p}{4} \right)} \cos{\left(\frac{p}{4} \right)} + 2 \cos^{2}{\left(\frac{p}{4} \right)}}$$
-1/2 + 1/(2*cos(p/4)^2 + 2*sin(p/4)^2 + 4*cos(p/4)*sin(p/4))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.