Sr Examen
¿Cómo vas a descomponer esta -sin(x)/(1+x)-cos(x)/(1+x)^2 expresión en fracciones?
Solución
Ha introducido
[src]
-sin(x) cos(x)
-------- - --------
1 + x 2
(1 + x)
$$- \frac{\cos{\left(x \right)}}{\left(x + 1\right)^{2}} + \frac{\left(-1\right) \sin{\left(x \right)}}{x + 1}$$
(-sin(x))/(1 + x) - cos(x)/(1 + x)^2
Simplificación general
[src]
-((1 + x)*sin(x) + cos(x))
---------------------------
2
(1 + x)
$$- \frac{\left(x + 1\right) \sin{\left(x \right)} + \cos{\left(x \right)}}{\left(x + 1\right)^{2}}$$
-((1 + x)*sin(x) + cos(x))/(1 + x)^2
Respuesta numérica
[src]
-sin(x)/(1.0 + x) - cos(x)/(1.0 + x)^2
-sin(x)/(1.0 + x) - cos(x)/(1.0 + x)^2
Potencias
[src]
I*x -I*x
e e
---- + ----- / -I*x I*x\
2 2 I*\- e + e /
- ------------ + ------------------
2 2*(1 + x)
(1 + x)
$$\frac{i \left(e^{i x} - e^{- i x}\right)}{2 \left(x + 1\right)} - \frac{\frac{e^{i x}}{2} + \frac{e^{- i x}}{2}}{\left(x + 1\right)^{2}}$$
sin(x) cos(x)
- ------ - --------
1 + x 2
(1 + x)
$$- \frac{\sin{\left(x \right)}}{x + 1} - \frac{\cos{\left(x \right)}}{\left(x + 1\right)^{2}}$$
-sin(x)/(1 + x) - cos(x)/(1 + x)^2
Denominador racional
[src]
2
- (1 + x) *sin(x) - (1 + x)*cos(x)
----------------------------------
3
(1 + x)
$$\frac{- \left(x + 1\right)^{2} \sin{\left(x \right)} - \left(x + 1\right) \cos{\left(x \right)}}{\left(x + 1\right)^{3}}$$
(-(1 + x)^2*sin(x) - (1 + x)*cos(x))/(1 + x)^3
Combinatoria
[src]
-(x*sin(x) + cos(x) + sin(x))
------------------------------
2
(1 + x)
$$- \frac{x \sin{\left(x \right)} + \sin{\left(x \right)} + \cos{\left(x \right)}}{\left(x + 1\right)^{2}}$$
-(x*sin(x) + cos(x) + sin(x))/(1 + x)^2
Unión de expresiones racionales
[src]
-cos(x) - (1 + x)*sin(x)
------------------------
2
(1 + x)
$$\frac{- \left(x + 1\right) \sin{\left(x \right)} - \cos{\left(x \right)}}{\left(x + 1\right)^{2}}$$
(-cos(x) - (1 + x)*sin(x))/(1 + x)^2
Denominador común
[src]
-(x*sin(x) + cos(x) + sin(x))
------------------------------
2
1 + x + 2*x
$$- \frac{x \sin{\left(x \right)} + \sin{\left(x \right)} + \cos{\left(x \right)}}{x^{2} + 2 x + 1}$$
-(x*sin(x) + cos(x) + sin(x))/(1 + x^2 + 2*x)
Compilar la expresión
[src]
sin(x) cos(x)
- ------ - --------
1 + x 2
(1 + x)
$$- \frac{\sin{\left(x \right)}}{x + 1} - \frac{\cos{\left(x \right)}}{\left(x + 1\right)^{2}}$$
-sin(x)/(1 + x) - cos(x)/(1 + x)^2
Parte trigonométrica
[src]
1 1
- -------------- - --------------------
(1 + x)*csc(x) 2 /pi \
(1 + x) *csc|-- - x|
\2 /
$$- \frac{1}{\left(x + 1\right) \csc{\left(x \right)}} - \frac{1}{\left(x + 1\right)^{2} \csc{\left(- x + \frac{\pi}{2} \right)}}$$
1 1
- ------------------- - ---------------
/ pi\ 2
(1 + x)*sec|x - --| (1 + x) *sec(x)
\ 2 /
$$- \frac{1}{\left(x + 1\right) \sec{\left(x - \frac{\pi}{2} \right)}} - \frac{1}{\left(x + 1\right)^{2} \sec{\left(x \right)}}$$
/ pi\
sin|x + --|
sin(x) \ 2 /
- ------ - -----------
1 + x 2
(1 + x)
$$- \frac{\sin{\left(x \right)}}{x + 1} - \frac{\sin{\left(x + \frac{\pi}{2} \right)}}{\left(x + 1\right)^{2}}$$
sin(x) cos(x)
- ------ - --------
1 + x 2
(1 + x)
$$- \frac{\sin{\left(x \right)}}{x + 1} - \frac{\cos{\left(x \right)}}{\left(x + 1\right)^{2}}$$
1 1
- -------------- - ---------------
(1 + x)*csc(x) 2
(1 + x) *sec(x)
$$- \frac{1}{\left(x + 1\right) \csc{\left(x \right)}} - \frac{1}{\left(x + 1\right)^{2} \sec{\left(x \right)}}$$
2/x\ /x\
-1 + cot |-| 2*cot|-|
\2/ \2/
- ---------------------- - ---------------------
2 / 2/x\\ / 2/x\\
(1 + x) *|1 + cot |-|| (1 + x)*|1 + cot |-||
\ \2// \ \2//
$$- \frac{2 \cot{\left(\frac{x}{2} \right)}}{\left(x + 1\right) \left(\cot^{2}{\left(\frac{x}{2} \right)} + 1\right)} - \frac{\cot^{2}{\left(\frac{x}{2} \right)} - 1}{\left(x + 1\right)^{2} \left(\cot^{2}{\left(\frac{x}{2} \right)} + 1\right)}$$
2/x\ /x\
1 - tan |-| 2*tan|-|
\2/ \2/
- ---------------------- - ---------------------
2 / 2/x\\ / 2/x\\
(1 + x) *|1 + tan |-|| (1 + x)*|1 + tan |-||
\ \2// \ \2//
$$- \frac{1 - \tan^{2}{\left(\frac{x}{2} \right)}}{\left(x + 1\right)^{2} \left(\tan^{2}{\left(\frac{x}{2} \right)} + 1\right)} - \frac{2 \tan{\left(\frac{x}{2} \right)}}{\left(x + 1\right) \left(\tan^{2}{\left(\frac{x}{2} \right)} + 1\right)}$$
/ pi\
cos|x - --|
\ 2 / cos(x)
- ----------- - --------
1 + x 2
(1 + x)
$$- \frac{\cos{\left(x - \frac{\pi}{2} \right)}}{x + 1} - \frac{\cos{\left(x \right)}}{\left(x + 1\right)^{2}}$$
-cos(x - pi/2)/(1 + x) - cos(x)/(1 + x)^2