Sr Examen
Simplificación de expresiones/
Descomposición en fracciones simples/
atan(((2*sin(2*x))/(1+cos(2*x))+1)/sqrt(3))/sqrt(3)
¿Cómo vas a descomponer esta atan(((2*sin(2*x))/(1+cos(2*x))+1)/sqrt(3))/sqrt(3) expresión en fracciones?
Solución
Ha introducido
[src]
/ 2*sin(2*x) \
|------------ + 1|
|1 + cos(2*x) |
atan|----------------|
| ___ |
\ \/ 3 /
----------------------
___
\/ 3
$$\frac{\operatorname{atan}{\left(\frac{1 + \frac{2 \sin{\left(2 x \right)}}{\cos{\left(2 x \right)} + 1}}{\sqrt{3}} \right)}}{\sqrt{3}}$$
atan(((2*sin(2*x))/(1 + cos(2*x)) + 1)/sqrt(3))/sqrt(3)
Descomposición de una fracción
[src]
sqrt(3)*atan(sqrt(3)/3 + 2*(sqrt(3)/3)*sin(2*x)/(1 + cos(2*x)))/3
$$\frac{\sqrt{3} \operatorname{atan}{\left(\frac{\sqrt{3}}{3} + \frac{2 \frac{\sqrt{3}}{3} \sin{\left(2 x \right)}}{\cos{\left(2 x \right)} + 1} \right)}}{3}$$
/ ___ \
| \/ 3 |
| ___ 2*-----*sin(2*x)|
___ |\/ 3 3 |
\/ 3 *atan|----- + ----------------|
\ 3 1 + cos(2*x) /
------------------------------------
3
Simplificación general
[src]
/ ___ \
___ |\/ 3 *(1 + 2*tan(x))|
\/ 3 *atan|--------------------|
\ 3 /
--------------------------------
3
$$\frac{\sqrt{3} \operatorname{atan}{\left(\frac{\sqrt{3} \left(2 \tan{\left(x \right)} + 1\right)}{3} \right)}}{3}$$
sqrt(3)*atan(sqrt(3)*(1 + 2*tan(x))/3)/3
Denominador común
[src]
/ ___ ___ \
___ |\/ 3 2*\/ 3 *sin(2*x)|
\/ 3 *atan|----- + ----------------|
\ 3 3*(1 + cos(2*x))/
------------------------------------
3
$$\frac{\sqrt{3} \operatorname{atan}{\left(\frac{\sqrt{3}}{3} + \frac{2 \sqrt{3} \sin{\left(2 x \right)}}{3 \left(\cos{\left(2 x \right)} + 1\right)} \right)}}{3}$$
sqrt(3)*atan(sqrt(3)/3 + 2*sqrt(3)*sin(2*x)/(3*(1 + cos(2*x))))/3
Combinatoria
[src]
/ ___ ___ \
___ |\/ 3 2*\/ 3 *sin(2*x)|
\/ 3 *atan|----- + ----------------|
\ 3 3*(1 + cos(2*x))/
------------------------------------
3
$$\frac{\sqrt{3} \operatorname{atan}{\left(\frac{\sqrt{3}}{3} + \frac{2 \sqrt{3} \sin{\left(2 x \right)}}{3 \left(\cos{\left(2 x \right)} + 1\right)} \right)}}{3}$$
sqrt(3)*atan(sqrt(3)/3 + 2*sqrt(3)*sin(2*x)/(3*(1 + cos(2*x))))/3
Unión de expresiones racionales
[src]
/ ___ \
___ |\/ 3 *(1 + 2*sin(2*x) + cos(2*x))|
\/ 3 *atan|---------------------------------|
\ 3*(1 + cos(2*x)) /
---------------------------------------------
3
$$\frac{\sqrt{3} \operatorname{atan}{\left(\frac{\sqrt{3} \left(2 \sin{\left(2 x \right)} + \cos{\left(2 x \right)} + 1\right)}{3 \left(\cos{\left(2 x \right)} + 1\right)} \right)}}{3}$$
sqrt(3)*atan(sqrt(3)*(1 + 2*sin(2*x) + cos(2*x))/(3*(1 + cos(2*x))))/3
Compilar la expresión
[src]
/ 2*sin(2*x) \
|------------ + 1|
___ |1 + cos(2*x) |
\/ 3 *atan|----------------|
| ___ |
\ \/ 3 /
----------------------------
3
$$\frac{\sqrt{3} \operatorname{atan}{\left(\frac{1 + \frac{2 \sin{\left(2 x \right)}}{\cos{\left(2 x \right)} + 1}}{\sqrt{3}} \right)}}{3}$$
sqrt(3)*atan(((2*sin(2*x))/(1 + cos(2*x)) + 1)/sqrt(3))/3
Respuesta numérica
[src]
0.577350269189626*atan(((2*sin(2*x))/(1 + cos(2*x)) + 1)/sqrt(3))
0.577350269189626*atan(((2*sin(2*x))/(1 + cos(2*x)) + 1)/sqrt(3))
Denominador racional
[src]
/ ___ \
___ |\/ 3 *(1 + 2*sin(2*x) + cos(2*x))|
\/ 3 *atan|---------------------------------|
\ 3*(1 + cos(2*x)) /
---------------------------------------------
3
$$\frac{\sqrt{3} \operatorname{atan}{\left(\frac{\sqrt{3} \left(2 \sin{\left(2 x \right)} + \cos{\left(2 x \right)} + 1\right)}{3 \left(\cos{\left(2 x \right)} + 1\right)} \right)}}{3}$$
sqrt(3)*atan(sqrt(3)*(1 + 2*sin(2*x) + cos(2*x))/(3*(1 + cos(2*x))))/3
Parte trigonométrica
[src]
/ ___ \
___ |\/ 3 *(1 + 2*tan(x))|
\/ 3 *atan|--------------------|
\ 3 /
--------------------------------
3
$$\frac{\sqrt{3} \operatorname{atan}{\left(\frac{\sqrt{3} \left(2 \tan{\left(x \right)} + 1\right)}{3} \right)}}{3}$$
/ ___ / 2*sin(2*x) \\
|\/ 3 *|1 + ------------||
___ | \ 1 + cos(2*x)/|
\/ 3 *atan|------------------------|
\ 3 /
------------------------------------
3
$$\frac{\sqrt{3} \operatorname{atan}{\left(\frac{\sqrt{3} \left(1 + \frac{2 \sin{\left(2 x \right)}}{\cos{\left(2 x \right)} + 1}\right)}{3} \right)}}{3}$$
/ ___ / 4*cot(x) \\
|\/ 3 *|1 + --------------------------------||
| | / 2 \||
| | / 2 \ | -1 + cot (x)|||
| | \1 + cot (x)/*|1 + ------------|||
| | | 2 |||
___ | \ \ 1 + cot (x) //|
\/ 3 *atan|--------------------------------------------|
\ 3 /
--------------------------------------------------------
3
$$\frac{\sqrt{3} \operatorname{atan}{\left(\frac{\sqrt{3} \left(1 + \frac{4 \cot{\left(x \right)}}{\left(\frac{\cot^{2}{\left(x \right)} - 1}{\cot^{2}{\left(x \right)} + 1} + 1\right) \left(\cot^{2}{\left(x \right)} + 1\right)}\right)}{3} \right)}}{3}$$
/ / 2 \\
| ___ | 4*sin (x)||
|\/ 3 *|1 + ---------||
___ | \ sin(2*x)/|
\/ 3 *atan|---------------------|
\ 3 /
---------------------------------
3
$$\frac{\sqrt{3} \operatorname{atan}{\left(\frac{\sqrt{3} \left(\frac{4 \sin^{2}{\left(x \right)}}{\sin{\left(2 x \right)}} + 1\right)}{3} \right)}}{3}$$
/ ___ / 2 \\
|\/ 3 *|1 + -----------------------||
| | / 1 \ ||
| | |1 + --------|*csc(2*x)||
___ | \ \ sec(2*x)/ /|
\/ 3 *atan|-----------------------------------|
\ 3 /
-----------------------------------------------
3
$$\frac{\sqrt{3} \operatorname{atan}{\left(\frac{\sqrt{3} \left(1 + \frac{2}{\left(1 + \frac{1}{\sec{\left(2 x \right)}}\right) \csc{\left(2 x \right)}}\right)}{3} \right)}}{3}$$
/ / /pi \\\
| | 2*csc|-- - x|||
| ___ | \2 /||
|\/ 3 *|1 + -------------||
___ | \ csc(x) /|
\/ 3 *atan|-------------------------|
\ 3 /
-------------------------------------
3
$$\frac{\sqrt{3} \operatorname{atan}{\left(\frac{\sqrt{3} \left(1 + \frac{2 \csc{\left(- x + \frac{\pi}{2} \right)}}{\csc{\left(x \right)}}\right)}{3} \right)}}{3}$$
/ ___ / 4*tan(x) \\
|\/ 3 *|1 + -------------------------------||
| | / 2 \||
| | / 2 \ | 1 - tan (x)|||
| | \1 + tan (x)/*|1 + -----------|||
| | | 2 |||
___ | \ \ 1 + tan (x)//|
\/ 3 *atan|-------------------------------------------|
\ 3 /
-------------------------------------------------------
3
$$\frac{\sqrt{3} \operatorname{atan}{\left(\frac{\sqrt{3} \left(1 + \frac{4 \tan{\left(x \right)}}{\left(\frac{1 - \tan^{2}{\left(x \right)}}{\tan^{2}{\left(x \right)} + 1} + 1\right) \left(\tan^{2}{\left(x \right)} + 1\right)}\right)}{3} \right)}}{3}$$
/ / / pi\\\
| | 2*cos|x - --|||
| ___ | \ 2 /||
|\/ 3 *|1 + -------------||
___ | \ cos(x) /|
\/ 3 *atan|-------------------------|
\ 3 /
-------------------------------------
3
$$\frac{\sqrt{3} \operatorname{atan}{\left(\frac{\sqrt{3} \left(1 + \frac{2 \cos{\left(x - \frac{\pi}{2} \right)}}{\cos{\left(x \right)}}\right)}{3} \right)}}{3}$$
/ ___ / 2*sec(x) \\
|\/ 3 *|1 + -----------||
| | / pi\||
| | sec|x - --|||
___ | \ \ 2 //|
\/ 3 *atan|-----------------------|
\ 3 /
-----------------------------------
3
$$\frac{\sqrt{3} \operatorname{atan}{\left(\frac{\sqrt{3} \left(\frac{2 \sec{\left(x \right)}}{\sec{\left(x - \frac{\pi}{2} \right)}} + 1\right)}{3} \right)}}{3}$$
/ ___ / 2 \\
|\/ 3 *|1 + ----------------------------||
| | / 1 \ / pi\||
| | |1 + --------|*sec|2*x - --|||
___ | \ \ sec(2*x)/ \ 2 //|
\/ 3 *atan|----------------------------------------|
\ 3 /
----------------------------------------------------
3
$$\frac{\sqrt{3} \operatorname{atan}{\left(\frac{\sqrt{3} \left(1 + \frac{2}{\left(1 + \frac{1}{\sec{\left(2 x \right)}}\right) \sec{\left(2 x - \frac{\pi}{2} \right)}}\right)}{3} \right)}}{3}$$
/ ___ / 2 \\
|\/ 3 *|1 + ----------------------------||
| | / 1 \ ||
| | |1 + -------------|*csc(2*x)||
| | | /pi \| ||
| | | csc|-- - 2*x|| ||
___ | \ \ \2 // /|
\/ 3 *atan|----------------------------------------|
\ 3 /
----------------------------------------------------
3
$$\frac{\sqrt{3} \operatorname{atan}{\left(\frac{\sqrt{3} \left(1 + \frac{2}{\left(1 + \frac{1}{\csc{\left(- 2 x + \frac{\pi}{2} \right)}}\right) \csc{\left(2 x \right)}}\right)}{3} \right)}}{3}$$
/ / / pi\\\
| | 2*cos|2*x - --|||
| ___ | \ 2 /||
|\/ 3 *|1 + ---------------||
___ | \ 1 + cos(2*x) /|
\/ 3 *atan|---------------------------|
\ 3 /
---------------------------------------
3
$$\frac{\sqrt{3} \operatorname{atan}{\left(\frac{\sqrt{3} \left(1 + \frac{2 \cos{\left(2 x - \frac{\pi}{2} \right)}}{\cos{\left(2 x \right)} + 1}\right)}{3} \right)}}{3}$$
/ ___ / 2*sin(2*x) \\
|\/ 3 *|1 + -----------------||
| | /pi \||
| | 1 + sin|-- + 2*x|||
___ | \ \2 //|
\/ 3 *atan|-----------------------------|
\ 3 /
-----------------------------------------
3
$$\frac{\sqrt{3} \operatorname{atan}{\left(\frac{\sqrt{3} \left(1 + \frac{2 \sin{\left(2 x \right)}}{\sin{\left(2 x + \frac{\pi}{2} \right)} + 1}\right)}{3} \right)}}{3}$$
/ ___ / 2 \\
|\/ 3 *|1 + ------||
___ | \ cot(x)/|
\/ 3 *atan|------------------|
\ 3 /
------------------------------
3
$$\frac{\sqrt{3} \operatorname{atan}{\left(\frac{\sqrt{3} \left(1 + \frac{2}{\cot{\left(x \right)}}\right)}{3} \right)}}{3}$$
sqrt(3)*atan(sqrt(3)*(1 + 2/cot(x))/3)/3
Potencias
[src]
/ ___ / 2*sin(2*x) \\
|\/ 3 *|1 + ------------||
___ | \ 1 + cos(2*x)/|
\/ 3 *atan|------------------------|
\ 3 /
------------------------------------
3
$$\frac{\sqrt{3} \operatorname{atan}{\left(\frac{\sqrt{3} \left(1 + \frac{2 \sin{\left(2 x \right)}}{\cos{\left(2 x \right)} + 1}\right)}{3} \right)}}{3}$$
___ / ___ /1 2*sin(2*x) \\
\/ 3 *atan|\/ 3 *|- + ----------------||
\ \3 3*(1 + cos(2*x))//
----------------------------------------
3
$$\frac{\sqrt{3} \operatorname{atan}{\left(\sqrt{3} \left(\frac{1}{3} + \frac{2 \sin{\left(2 x \right)}}{3 \left(\cos{\left(2 x \right)} + 1\right)}\right) \right)}}{3}$$
/ / / -2*I*x 2*I*x\\\
| ___ | I*\- e + e /||
|\/ 3 *|1 - ----------------------||
| | -2*I*x 2*I*x ||
| | e e ||
| | 1 + ------- + ------ ||
___ | \ 2 2 /|
\/ 3 *atan|----------------------------------|
\ 3 /
----------------------------------------------
3
$$\frac{\sqrt{3} \operatorname{atan}{\left(\frac{\sqrt{3} \left(- \frac{i \left(e^{2 i x} - e^{- 2 i x}\right)}{\frac{e^{2 i x}}{2} + 1 + \frac{e^{- 2 i x}}{2}} + 1\right)}{3} \right)}}{3}$$
sqrt(3)*atan(sqrt(3)*(1 - i*(-exp(-2*i*x) + exp(2*i*x))/(1 + exp(-2*i*x)/2 + exp(2*i*x)/2))/3)/3