Sr Examen
Simplificación de expresiones/
Descomposición en fracciones simples/
atan((2*sin(2*x))/(sqrt(6)*(1+cos(2*x))))/(2*sqrt(6))
¿Cómo vas a descomponer esta atan((2*sin(2*x))/(sqrt(6)*(1+cos(2*x))))/(2*sqrt(6)) expresión en fracciones?
Solución
Ha introducido
[src]
/ 2*sin(2*x) \
atan|--------------------|
| ___ |
\\/ 6 *(1 + cos(2*x))/
--------------------------
___
2*\/ 6
$$\frac{\operatorname{atan}{\left(\frac{2 \sin{\left(2 x \right)}}{\sqrt{6} \left(\cos{\left(2 x \right)} + 1\right)} \right)}}{2 \sqrt{6}}$$
atan((2*sin(2*x))/((sqrt(6)*(1 + cos(2*x)))))/((2*sqrt(6)))
Descomposición de una fracción
[src]
sqrt(6)*atan(2*sin(2*x)/(sqrt(6) + sqrt(6)*cos(2*x)))/12
$$\frac{\sqrt{6} \operatorname{atan}{\left(\frac{2 \sin{\left(2 x \right)}}{\sqrt{6} \cos{\left(2 x \right)} + \sqrt{6}} \right)}}{12}$$
___ / 2*sin(2*x) \
\/ 6 *atan|----------------------|
| ___ ___ |
\\/ 6 + \/ 6 *cos(2*x)/
----------------------------------
12
Simplificación general
[src]
/ ___ \
___ |\/ 6 *tan(x)|
\/ 6 *atan|------------|
\ 3 /
------------------------
12
$$\frac{\sqrt{6} \operatorname{atan}{\left(\frac{\sqrt{6} \tan{\left(x \right)}}{3} \right)}}{12}$$
sqrt(6)*atan(sqrt(6)*tan(x)/3)/12
Respuesta numérica
[src]
0.204124145231932*atan((2*sin(2*x))/((sqrt(6)*(1 + cos(2*x)))))
0.204124145231932*atan((2*sin(2*x))/((sqrt(6)*(1 + cos(2*x)))))
Denominador racional
[src]
/ ___ \
___ | \/ 6 *sin(2*x) |
\/ 6 *atan|----------------|
\3*(1 + cos(2*x))/
----------------------------
12
$$\frac{\sqrt{6} \operatorname{atan}{\left(\frac{\sqrt{6} \sin{\left(2 x \right)}}{3 \left(\cos{\left(2 x \right)} + 1\right)} \right)}}{12}$$
sqrt(6)*atan(sqrt(6)*sin(2*x)/(3*(1 + cos(2*x))))/12
Unión de expresiones racionales
[src]
/ ___ \
___ | \/ 6 *sin(2*x) |
\/ 6 *atan|----------------|
\3*(1 + cos(2*x))/
----------------------------
12
$$\frac{\sqrt{6} \operatorname{atan}{\left(\frac{\sqrt{6} \sin{\left(2 x \right)}}{3 \left(\cos{\left(2 x \right)} + 1\right)} \right)}}{12}$$
sqrt(6)*atan(sqrt(6)*sin(2*x)/(3*(1 + cos(2*x))))/12
Potencias
[src]
/ ___ / -2*I*x 2*I*x\\
___ |I*\/ 6 *\- e + e /|
-\/ 6 *atan|----------------------------|
| / -2*I*x 2*I*x\ |
| | e e | |
| 6*|1 + ------- + ------| |
\ \ 2 2 / /
------------------------------------------
12
$$- \frac{\sqrt{6} \operatorname{atan}{\left(\frac{\sqrt{6} i \left(e^{2 i x} - e^{- 2 i x}\right)}{6 \left(\frac{e^{2 i x}}{2} + 1 + \frac{e^{- 2 i x}}{2}\right)} \right)}}{12}$$
/ ___ \
___ | \/ 6 *sin(2*x) |
\/ 6 *atan|----------------|
\3*(1 + cos(2*x))/
----------------------------
12
$$\frac{\sqrt{6} \operatorname{atan}{\left(\frac{\sqrt{6} \sin{\left(2 x \right)}}{3 \left(\cos{\left(2 x \right)} + 1\right)} \right)}}{12}$$
sqrt(6)*atan(sqrt(6)*sin(2*x)/(3*(1 + cos(2*x))))/12
Combinatoria
[src]
/ ___ \
___ | \/ 6 *sin(2*x) |
\/ 6 *atan|----------------|
\3*(1 + cos(2*x))/
----------------------------
12
$$\frac{\sqrt{6} \operatorname{atan}{\left(\frac{\sqrt{6} \sin{\left(2 x \right)}}{3 \left(\cos{\left(2 x \right)} + 1\right)} \right)}}{12}$$
sqrt(6)*atan(sqrt(6)*sin(2*x)/(3*(1 + cos(2*x))))/12
Denominador común
[src]
/ ___ \
___ | \/ 6 *sin(2*x) |
\/ 6 *atan|----------------|
\3*(1 + cos(2*x))/
----------------------------
12
$$\frac{\sqrt{6} \operatorname{atan}{\left(\frac{\sqrt{6} \sin{\left(2 x \right)}}{3 \left(\cos{\left(2 x \right)} + 1\right)} \right)}}{12}$$
sqrt(6)*atan(sqrt(6)*sin(2*x)/(3*(1 + cos(2*x))))/12
Compilar la expresión
[src]
___ / 2*sin(2*x) \
\/ 6 *atan|--------------------|
| ___ |
\\/ 6 *(1 + cos(2*x))/
--------------------------------
12
$$\frac{\sqrt{6} \operatorname{atan}{\left(\frac{2 \sin{\left(2 x \right)}}{\sqrt{6} \left(\cos{\left(2 x \right)} + 1\right)} \right)}}{12}$$
sqrt(6)*atan((2*sin(2*x))/((sqrt(6)*(1 + cos(2*x)))))/12
Parte trigonométrica
[src]
/ ___ / pi\\
|\/ 6 *cos|x - --||
___ | \ 2 /|
\/ 6 *atan|-----------------|
\ 3*cos(x) /
-----------------------------
12
$$\frac{\sqrt{6} \operatorname{atan}{\left(\frac{\sqrt{6} \cos{\left(x - \frac{\pi}{2} \right)}}{3 \cos{\left(x \right)}} \right)}}{12}$$
/ ___ \
___ |\/ 6 *tan(x)|
\/ 6 *atan|------------|
\ 3 /
------------------------
12
$$\frac{\sqrt{6} \operatorname{atan}{\left(\frac{\sqrt{6} \tan{\left(x \right)}}{3} \right)}}{12}$$
/ ___ \
___ | \/ 6 |
\/ 6 *atan|------------------------------|
| / 1 \ / pi\|
|3*|1 + --------|*sec|2*x - --||
\ \ sec(2*x)/ \ 2 //
------------------------------------------
12
$$\frac{\sqrt{6} \operatorname{atan}{\left(\frac{\sqrt{6}}{3 \left(1 + \frac{1}{\sec{\left(2 x \right)}}\right) \sec{\left(2 x - \frac{\pi}{2} \right)}} \right)}}{12}$$
/ ___ 2 \
___ |2*\/ 6 *sin (x)|
\/ 6 *atan|---------------|
\ 3*sin(2*x) /
---------------------------
12
$$\frac{\sqrt{6} \operatorname{atan}{\left(\frac{2 \sqrt{6} \sin^{2}{\left(x \right)}}{3 \sin{\left(2 x \right)}} \right)}}{12}$$
/ ___ \
___ | \/ 6 *sin(2*x) |
\/ 6 *atan|---------------------|
| / /pi \\|
|3*|1 + sin|-- + 2*x|||
\ \ \2 ///
---------------------------------
12
$$\frac{\sqrt{6} \operatorname{atan}{\left(\frac{\sqrt{6} \sin{\left(2 x \right)}}{3 \left(\sin{\left(2 x + \frac{\pi}{2} \right)} + 1\right)} \right)}}{12}$$
/ ___ \
___ | \/ 6 *sec(x)|
\/ 6 *atan|-------------|
| / pi\|
|3*sec|x - --||
\ \ 2 //
-------------------------
12
$$\frac{\sqrt{6} \operatorname{atan}{\left(\frac{\sqrt{6} \sec{\left(x \right)}}{3 \sec{\left(x - \frac{\pi}{2} \right)}} \right)}}{12}$$
/ ___ \
___ | \/ 6 |
\/ 6 *atan|--------|
\3*cot(x)/
--------------------
12
$$\frac{\sqrt{6} \operatorname{atan}{\left(\frac{\sqrt{6}}{3 \cot{\left(x \right)}} \right)}}{12}$$
/ ___ / pi\\
|\/ 6 *cos|2*x - --||
___ | \ 2 /|
\/ 6 *atan|-------------------|
\ 3*(1 + cos(2*x)) /
-------------------------------
12
$$\frac{\sqrt{6} \operatorname{atan}{\left(\frac{\sqrt{6} \cos{\left(2 x - \frac{\pi}{2} \right)}}{3 \left(\cos{\left(2 x \right)} + 1\right)} \right)}}{12}$$
/ ___ \
___ | \/ 6 |
\/ 6 *atan|-------------------------|
| / 1 \ |
|3*|1 + --------|*csc(2*x)|
\ \ sec(2*x)/ /
-------------------------------------
12
$$\frac{\sqrt{6} \operatorname{atan}{\left(\frac{\sqrt{6}}{3 \left(1 + \frac{1}{\sec{\left(2 x \right)}}\right) \csc{\left(2 x \right)}} \right)}}{12}$$
/ ___ \
___ | 2*\/ 6 *tan(x) |
\/ 6 *atan|---------------------------------|
| / 2 \|
| / 2 \ | 1 - tan (x)||
|3*\1 + tan (x)/*|1 + -----------||
| | 2 ||
\ \ 1 + tan (x)//
---------------------------------------------
12
$$\frac{\sqrt{6} \operatorname{atan}{\left(\frac{2 \sqrt{6} \tan{\left(x \right)}}{3 \left(\frac{1 - \tan^{2}{\left(x \right)}}{\tan^{2}{\left(x \right)} + 1} + 1\right) \left(\tan^{2}{\left(x \right)} + 1\right)} \right)}}{12}$$
/ ___ \
___ | 2*\/ 6 *cot(x) |
\/ 6 *atan|----------------------------------|
| / 2 \|
| / 2 \ | -1 + cot (x)||
|3*\1 + cot (x)/*|1 + ------------||
| | 2 ||
\ \ 1 + cot (x) //
----------------------------------------------
12
$$\frac{\sqrt{6} \operatorname{atan}{\left(\frac{2 \sqrt{6} \cot{\left(x \right)}}{3 \left(\frac{\cot^{2}{\left(x \right)} - 1}{\cot^{2}{\left(x \right)} + 1} + 1\right) \left(\cot^{2}{\left(x \right)} + 1\right)} \right)}}{12}$$
/ ___ /pi \\
|\/ 6 *csc|-- - x||
___ | \2 /|
\/ 6 *atan|-----------------|
\ 3*csc(x) /
-----------------------------
12
$$\frac{\sqrt{6} \operatorname{atan}{\left(\frac{\sqrt{6} \csc{\left(- x + \frac{\pi}{2} \right)}}{3 \csc{\left(x \right)}} \right)}}{12}$$
/ ___ \
___ | \/ 6 |
\/ 6 *atan|------------------------------|
| / 1 \ |
|3*|1 + -------------|*csc(2*x)|
| | /pi \| |
| | csc|-- - 2*x|| |
\ \ \2 // /
------------------------------------------
12
$$\frac{\sqrt{6} \operatorname{atan}{\left(\frac{\sqrt{6}}{3 \left(1 + \frac{1}{\csc{\left(- 2 x + \frac{\pi}{2} \right)}}\right) \csc{\left(2 x \right)}} \right)}}{12}$$
/ ___ \
___ | \/ 6 *sin(2*x) |
\/ 6 *atan|----------------|
\3*(1 + cos(2*x))/
----------------------------
12
$$\frac{\sqrt{6} \operatorname{atan}{\left(\frac{\sqrt{6} \sin{\left(2 x \right)}}{3 \left(\cos{\left(2 x \right)} + 1\right)} \right)}}{12}$$
sqrt(6)*atan(sqrt(6)*sin(2*x)/(3*(1 + cos(2*x))))/12