Sr Examen
Simplificación de expresiones/
Descomposición en fracciones simples/
cos(x)/(x^2+3)-2*x*sin(x)/(x^2+3)^2
¿Cómo vas a descomponer esta cos(x)/(x^2+3)-2*x*sin(x)/(x^2+3)^2 expresión en fracciones?
Solución
Ha introducido
[src]
cos(x) 2*x*sin(x)
------ - ----------
2 2
x + 3 / 2 \
\x + 3/
$$- \frac{2 x \sin{\left(x \right)}}{\left(x^{2} + 3\right)^{2}} + \frac{\cos{\left(x \right)}}{x^{2} + 3}$$
cos(x)/(x^2 + 3) - (2*x)*sin(x)/(x^2 + 3)^2
Simplificación general
[src]
/ 2\
\3 + x /*cos(x) - 2*x*sin(x)
----------------------------
2
/ 2\
\3 + x /
$$\frac{- 2 x \sin{\left(x \right)} + \left(x^{2} + 3\right) \cos{\left(x \right)}}{\left(x^{2} + 3\right)^{2}}$$
((3 + x^2)*cos(x) - 2*x*sin(x))/(3 + x^2)^2
Respuesta numérica
[src]
cos(x)/(3.0 + x^2) - 0.222222222222222*x*sin(x)/(1 + 0.333333333333333*x^2)^2
cos(x)/(3.0 + x^2) - 0.222222222222222*x*sin(x)/(1 + 0.333333333333333*x^2)^2
Potencias
[src]
I*x -I*x
e e
---- + ----- / -I*x I*x\
2 2 I*x*\- e + e /
------------ + --------------------
2 2
3 + x / 2\
\3 + x /
$$\frac{i x \left(e^{i x} - e^{- i x}\right)}{\left(x^{2} + 3\right)^{2}} + \frac{\frac{e^{i x}}{2} + \frac{e^{- i x}}{2}}{x^{2} + 3}$$
(exp(i*x)/2 + exp(-i*x)/2)/(3 + x^2) + i*x*(-exp(-i*x) + exp(i*x))/(3 + x^2)^2
Denominador común
[src]
2
3*cos(x) + x *cos(x) - 2*x*sin(x)
---------------------------------
4 2
9 + x + 6*x
$$\frac{x^{2} \cos{\left(x \right)} - 2 x \sin{\left(x \right)} + 3 \cos{\left(x \right)}}{x^{4} + 6 x^{2} + 9}$$
(3*cos(x) + x^2*cos(x) - 2*x*sin(x))/(9 + x^4 + 6*x^2)
Unión de expresiones racionales
[src]
/ 2\
\3 + x /*cos(x) - 2*x*sin(x)
----------------------------
2
/ 2\
\3 + x /
$$\frac{- 2 x \sin{\left(x \right)} + \left(x^{2} + 3\right) \cos{\left(x \right)}}{\left(x^{2} + 3\right)^{2}}$$
((3 + x^2)*cos(x) - 2*x*sin(x))/(3 + x^2)^2
Parte trigonométrica
[src]
/ pi\
2*x*cos|x - --|
cos(x) \ 2 /
------ - ---------------
2 2
3 + x / 2\
\3 + x /
$$- \frac{2 x \cos{\left(x - \frac{\pi}{2} \right)}}{\left(x^{2} + 3\right)^{2}} + \frac{\cos{\left(x \right)}}{x^{2} + 3}$$
2/x\ /x\
1 - tan |-| 4*x*tan|-|
\2/ \2/
---------------------- - -----------------------
/ 2/x\\ / 2\ 2
|1 + tan |-||*\3 + x / / 2/x\\ / 2\
\ \2// |1 + tan |-||*\3 + x /
\ \2//
$$- \frac{4 x \tan{\left(\frac{x}{2} \right)}}{\left(x^{2} + 3\right)^{2} \left(\tan^{2}{\left(\frac{x}{2} \right)} + 1\right)} + \frac{1 - \tan^{2}{\left(\frac{x}{2} \right)}}{\left(x^{2} + 3\right) \left(\tan^{2}{\left(\frac{x}{2} \right)} + 1\right)}$$
1 2*x
--------------- - ----------------
/ 2\ 2
\3 + x /*sec(x) / 2\
\3 + x / *csc(x)
$$- \frac{2 x}{\left(x^{2} + 3\right)^{2} \csc{\left(x \right)}} + \frac{1}{\left(x^{2} + 3\right) \sec{\left(x \right)}}$$
1 2*x
-------------------- - ----------------
/ 2\ /pi \ 2
\3 + x /*csc|-- - x| / 2\
\2 / \3 + x / *csc(x)
$$- \frac{2 x}{\left(x^{2} + 3\right)^{2} \csc{\left(x \right)}} + \frac{1}{\left(x^{2} + 3\right) \csc{\left(- x + \frac{\pi}{2} \right)}}$$
/ pi\
sin|x + --|
\ 2 / 2*x*sin(x)
----------- - ----------
2 2
3 + x / 2\
\3 + x /
$$- \frac{2 x \sin{\left(x \right)}}{\left(x^{2} + 3\right)^{2}} + \frac{\sin{\left(x + \frac{\pi}{2} \right)}}{x^{2} + 3}$$
2/x\ /x\
-1 + cot |-| 4*x*cot|-|
\2/ \2/
---------------------- - -----------------------
/ 2/x\\ / 2\ 2
|1 + cot |-||*\3 + x / / 2/x\\ / 2\
\ \2// |1 + cot |-||*\3 + x /
\ \2//
$$- \frac{4 x \cot{\left(\frac{x}{2} \right)}}{\left(x^{2} + 3\right)^{2} \left(\cot^{2}{\left(\frac{x}{2} \right)} + 1\right)} + \frac{\cot^{2}{\left(\frac{x}{2} \right)} - 1}{\left(x^{2} + 3\right) \left(\cot^{2}{\left(\frac{x}{2} \right)} + 1\right)}$$
1 2*x
--------------- - ---------------------
/ 2\ 2
\3 + x /*sec(x) / 2\ / pi\
\3 + x / *sec|x - --|
\ 2 /
$$- \frac{2 x}{\left(x^{2} + 3\right)^{2} \sec{\left(x - \frac{\pi}{2} \right)}} + \frac{1}{\left(x^{2} + 3\right) \sec{\left(x \right)}}$$
1/((3 + x^2)*sec(x)) - 2*x/((3 + x^2)^2*sec(x - pi/2))
Combinatoria
[src]
2
3*cos(x) + x *cos(x) - 2*x*sin(x)
---------------------------------
2
/ 2\
\3 + x /
$$\frac{x^{2} \cos{\left(x \right)} - 2 x \sin{\left(x \right)} + 3 \cos{\left(x \right)}}{\left(x^{2} + 3\right)^{2}}$$
(3*cos(x) + x^2*cos(x) - 2*x*sin(x))/(3 + x^2)^2
Denominador racional
[src]
2
/ 2\ / 2\
\3 + x / *cos(x) - 2*x*\3 + x /*sin(x)
--------------------------------------
3
/ 2\
\3 + x /
$$\frac{- 2 x \left(x^{2} + 3\right) \sin{\left(x \right)} + \left(x^{2} + 3\right)^{2} \cos{\left(x \right)}}{\left(x^{2} + 3\right)^{3}}$$
((3 + x^2)^2*cos(x) - 2*x*(3 + x^2)*sin(x))/(3 + x^2)^3