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