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