Sr Examen
Integral de (2cosx-3sinx)/(2sinx+3cosx)^3 dx
Solución
Ha introducido
[src]
p - 4 / | | 2*cos(x) - 3*sin(x) | ---------------------- dx | 3 | (2*sin(x) + 3*cos(x)) | / 0
$$\int\limits_{0}^{\frac{p}{4}} \frac{- 3 \sin{\left(x \right)} + 2 \cos{\left(x \right)}}{\left(2 \sin{\left(x \right)} + 3 \cos{\left(x \right)}\right)^{3}}\, dx$$
Integral((2*cos(x) - 3*sin(x))/(2*sin(x) + 3*cos(x))^3, (x, 0, p/4))
Respuesta (Indefinida)
[src]
/ 3/x\ 2/x\ 2/x\ /x\ | 12*tan |-| 6*tan |-| 8*tan |-| 12*tan|-| | 2*cos(x) - 3*sin(x) \2/ \2/ \2/ \2/ | ---------------------- dx = C - ------------------------------------------------------- - ---------------------------------------------------- + ------------------------------------------------------- + ------------------------------------------------------- | 3 3/x\ 2/x\ 4/x\ /x\ 3/x\ 2/x\ 4/x\ /x\ 3/x\ 2/x\ 4/x\ /x\ 3/x\ 2/x\ 4/x\ /x\ | (2*sin(x) + 3*cos(x)) 81 - 216*tan |-| - 18*tan |-| + 81*tan |-| + 216*tan|-| 27 - 72*tan |-| - 6*tan |-| + 27*tan |-| + 72*tan|-| 81 - 216*tan |-| - 18*tan |-| + 81*tan |-| + 216*tan|-| 81 - 216*tan |-| - 18*tan |-| + 81*tan |-| + 216*tan|-| | \2/ \2/ \2/ \2/ \2/ \2/ \2/ \2/ \2/ \2/ \2/ \2/ \2/ \2/ \2/ \2/ /
$$\int \frac{- 3 \sin{\left(x \right)} + 2 \cos{\left(x \right)}}{\left(2 \sin{\left(x \right)} + 3 \cos{\left(x \right)}\right)^{3}}\, dx = C - \frac{12 \tan^{3}{\left(\frac{x}{2} \right)}}{81 \tan^{4}{\left(\frac{x}{2} \right)} - 216 \tan^{3}{\left(\frac{x}{2} \right)} - 18 \tan^{2}{\left(\frac{x}{2} \right)} + 216 \tan{\left(\frac{x}{2} \right)} + 81} + \frac{8 \tan^{2}{\left(\frac{x}{2} \right)}}{81 \tan^{4}{\left(\frac{x}{2} \right)} - 216 \tan^{3}{\left(\frac{x}{2} \right)} - 18 \tan^{2}{\left(\frac{x}{2} \right)} + 216 \tan{\left(\frac{x}{2} \right)} + 81} + \frac{12 \tan{\left(\frac{x}{2} \right)}}{81 \tan^{4}{\left(\frac{x}{2} \right)} - 216 \tan^{3}{\left(\frac{x}{2} \right)} - 18 \tan^{2}{\left(\frac{x}{2} \right)} + 216 \tan{\left(\frac{x}{2} \right)} + 81} - \frac{6 \tan^{2}{\left(\frac{x}{2} \right)}}{27 \tan^{4}{\left(\frac{x}{2} \right)} - 72 \tan^{3}{\left(\frac{x}{2} \right)} - 6 \tan^{2}{\left(\frac{x}{2} \right)} + 72 \tan{\left(\frac{x}{2} \right)} + 27}$$
Respuesta
[src]
1 1
-- - -----------------------------------------
18 2/p\ 2/p\ /p\ /p\
8*sin |-| + 18*cos |-| + 24*cos|-|*sin|-|
\4/ \4/ \4/ \4/
$$\frac{1}{18} - \frac{1}{8 \sin^{2}{\left(\frac{p}{4} \right)} + 24 \sin{\left(\frac{p}{4} \right)} \cos{\left(\frac{p}{4} \right)} + 18 \cos^{2}{\left(\frac{p}{4} \right)}}$$
=
=
1 1
-- - -----------------------------------------
18 2/p\ 2/p\ /p\ /p\
8*sin |-| + 18*cos |-| + 24*cos|-|*sin|-|
\4/ \4/ \4/ \4/
$$\frac{1}{18} - \frac{1}{8 \sin^{2}{\left(\frac{p}{4} \right)} + 24 \sin{\left(\frac{p}{4} \right)} \cos{\left(\frac{p}{4} \right)} + 18 \cos^{2}{\left(\frac{p}{4} \right)}}$$
1/18 - 1/(8*sin(p/4)^2 + 18*cos(p/4)^2 + 24*cos(p/4)*sin(p/4))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.