Sr Examen
Integral de (sin(x)-cos(x))/((sin(x)+cos(x))^5) dx
Solución
Ha introducido
[src]
p - 4 / | | sin(x) - cos(x) | ------------------ dx | 5 | (sin(x) + cos(x)) | / 0
$$\int\limits_{0}^{\frac{p}{4}} \frac{\sin{\left(x \right)} - \cos{\left(x \right)}}{\left(\sin{\left(x \right)} + \cos{\left(x \right)}\right)^{5}}\, dx$$
Integral((sin(x) - cos(x))/(sin(x) + cos(x))^5, (x, 0, p/4))
Respuesta
[src]
1 1
- - + ----------------------------------------------------------------------------------
4 4/p\ 4/p\ 3/p\ /p\ 3/p\ /p\ 2/p\ 2/p\
4*cos |-| + 4*sin |-| + 16*cos |-|*sin|-| + 16*sin |-|*cos|-| + 24*cos |-|*sin |-|
\4/ \4/ \4/ \4/ \4/ \4/ \4/ \4/
$$- \frac{1}{4} + \frac{1}{4 \sin^{4}{\left(\frac{p}{4} \right)} + 16 \sin^{3}{\left(\frac{p}{4} \right)} \cos{\left(\frac{p}{4} \right)} + 24 \sin^{2}{\left(\frac{p}{4} \right)} \cos^{2}{\left(\frac{p}{4} \right)} + 16 \sin{\left(\frac{p}{4} \right)} \cos^{3}{\left(\frac{p}{4} \right)} + 4 \cos^{4}{\left(\frac{p}{4} \right)}}$$
=
=
1 1
- - + ----------------------------------------------------------------------------------
4 4/p\ 4/p\ 3/p\ /p\ 3/p\ /p\ 2/p\ 2/p\
4*cos |-| + 4*sin |-| + 16*cos |-|*sin|-| + 16*sin |-|*cos|-| + 24*cos |-|*sin |-|
\4/ \4/ \4/ \4/ \4/ \4/ \4/ \4/
$$- \frac{1}{4} + \frac{1}{4 \sin^{4}{\left(\frac{p}{4} \right)} + 16 \sin^{3}{\left(\frac{p}{4} \right)} \cos{\left(\frac{p}{4} \right)} + 24 \sin^{2}{\left(\frac{p}{4} \right)} \cos^{2}{\left(\frac{p}{4} \right)} + 16 \sin{\left(\frac{p}{4} \right)} \cos^{3}{\left(\frac{p}{4} \right)} + 4 \cos^{4}{\left(\frac{p}{4} \right)}}$$
-1/4 + 1/(4*cos(p/4)^4 + 4*sin(p/4)^4 + 16*cos(p/4)^3*sin(p/4) + 16*sin(p/4)^3*cos(p/4) + 24*cos(p/4)^2*sin(p/4)^2)
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.