Sr Examen
Simplificación de expresiones/
Descomposición en fracciones simples/
atan(((6*sin(x))/(1+cos(x))-2)/2^(5/2))/sqrt(2)
¿Cómo vas a descomponer esta atan(((6*sin(x))/(1+cos(x))-2)/2^(5/2))/sqrt(2) expresión en fracciones?
Solución
Ha introducido
[src]
/ 6*sin(x) \
|---------- - 2|
|1 + cos(x) |
atan|--------------|
| 5/2 |
\ 2 /
--------------------
___
\/ 2
$$\frac{\operatorname{atan}{\left(\frac{-2 + \frac{6 \sin{\left(x \right)}}{\cos{\left(x \right)} + 1}}{2^{\frac{5}{2}}} \right)}}{\sqrt{2}}$$
atan(((6*sin(x))/(1 + cos(x)) - 2)/2^(5/2))/sqrt(2)
Simplificación general
[src]
/ ___ \
___ |\/ 2 *(1 - 3*sin(x) + cos(x))|
-\/ 2 *atan|-----------------------------|
\ 4*(1 + cos(x)) /
-------------------------------------------
2
$$- \frac{\sqrt{2} \operatorname{atan}{\left(\frac{\sqrt{2} \left(- 3 \sin{\left(x \right)} + \cos{\left(x \right)} + 1\right)}{4 \left(\cos{\left(x \right)} + 1\right)} \right)}}{2}$$
-sqrt(2)*atan(sqrt(2)*(1 - 3*sin(x) + cos(x))/(4*(1 + cos(x))))/2
Descomposición de una fracción
[src]
sqrt(2)*atan(-sqrt(2)/4 + 6*(sqrt(2)/8)*sin(x)/(1 + cos(x)))/2
$$\frac{\sqrt{2} \operatorname{atan}{\left(- \frac{\sqrt{2}}{4} + \frac{6 \frac{\sqrt{2}}{8} \sin{\left(x \right)}}{\cos{\left(x \right)} + 1} \right)}}{2}$$
/ ___ \
| \/ 2 |
| ___ 6*-----*sin(x)|
___ | 2*\/ 2 8 |
\/ 2 *atan|- ------- + --------------|
\ 8 1 + cos(x) /
--------------------------------------
2
Respuesta numérica
[src]
0.707106781186547*atan(((6*sin(x))/(1 + cos(x)) - 2)/2^(5/2))
0.707106781186547*atan(((6*sin(x))/(1 + cos(x)) - 2)/2^(5/2))
Denominador común
[src]
/ ___ ___ \
___ |\/ 2 3*\/ 2 *sin(x)|
-\/ 2 *atan|----- - --------------|
\ 4 4*(1 + cos(x))/
------------------------------------
2
$$- \frac{\sqrt{2} \operatorname{atan}{\left(\frac{\sqrt{2}}{4} - \frac{3 \sqrt{2} \sin{\left(x \right)}}{4 \left(\cos{\left(x \right)} + 1\right)} \right)}}{2}$$
-sqrt(2)*atan(sqrt(2)/4 - 3*sqrt(2)*sin(x)/(4*(1 + cos(x))))/2
Combinatoria
[src]
/ ___ ___ \
___ |\/ 2 3*\/ 2 *sin(x)|
-\/ 2 *atan|----- - --------------|
\ 4 4*(1 + cos(x))/
------------------------------------
2
$$- \frac{\sqrt{2} \operatorname{atan}{\left(\frac{\sqrt{2}}{4} - \frac{3 \sqrt{2} \sin{\left(x \right)}}{4 \left(\cos{\left(x \right)} + 1\right)} \right)}}{2}$$
-sqrt(2)*atan(sqrt(2)/4 - 3*sqrt(2)*sin(x)/(4*(1 + cos(x))))/2
Denominador racional
[src]
/ ___ \
___ |\/ 2 *(1 - 3*sin(x) + cos(x))|
-\/ 2 *atan|-----------------------------|
\ 4*(1 + cos(x)) /
-------------------------------------------
2
$$- \frac{\sqrt{2} \operatorname{atan}{\left(\frac{\sqrt{2} \left(- 3 \sin{\left(x \right)} + \cos{\left(x \right)} + 1\right)}{4 \left(\cos{\left(x \right)} + 1\right)} \right)}}{2}$$
-sqrt(2)*atan(sqrt(2)*(1 - 3*sin(x) + cos(x))/(4*(1 + cos(x))))/2
Compilar la expresión
[src]
/ 6*sin(x) \
|---------- - 2|
___ |1 + cos(x) |
\/ 2 *atan|--------------|
| 5/2 |
\ 2 /
--------------------------
2
$$\frac{\sqrt{2} \operatorname{atan}{\left(\frac{-2 + \frac{6 \sin{\left(x \right)}}{\cos{\left(x \right)} + 1}}{2^{\frac{5}{2}}} \right)}}{2}$$
sqrt(2)*atan(((6*sin(x))/(1 + cos(x)) - 2)/2^(5/2))/2
Potencias
[src]
/ / / -I*x I*x\\ \
| ___ | 3*I*\- e + e /| |
|-\/ 2 *|-2 - --------------------| |
| | I*x -I*x | |
| | e e | |
| | 1 + ---- + ----- | |
___ | \ 2 2 / |
-\/ 2 *atan|-----------------------------------|
\ 8 /
-------------------------------------------------
2
$$- \frac{\sqrt{2} \operatorname{atan}{\left(- \frac{\sqrt{2} \left(- \frac{3 i \left(e^{i x} - e^{- i x}\right)}{\frac{e^{i x}}{2} + 1 + \frac{e^{- i x}}{2}} - 2\right)}{8} \right)}}{2}$$
___ / ___ / 1 3*sin(x) \\
\/ 2 *atan|\/ 2 *|- - + --------------||
\ \ 4 4*(1 + cos(x))//
----------------------------------------
2
$$\frac{\sqrt{2} \operatorname{atan}{\left(\sqrt{2} \left(- \frac{1}{4} + \frac{3 \sin{\left(x \right)}}{4 \left(\cos{\left(x \right)} + 1\right)}\right) \right)}}{2}$$
/ ___ / 6*sin(x) \\
|\/ 2 *|-2 + ----------||
___ | \ 1 + cos(x)/|
\/ 2 *atan|-----------------------|
\ 8 /
-----------------------------------
2
$$\frac{\sqrt{2} \operatorname{atan}{\left(\frac{\sqrt{2} \left(-2 + \frac{6 \sin{\left(x \right)}}{\cos{\left(x \right)} + 1}\right)}{8} \right)}}{2}$$
sqrt(2)*atan(sqrt(2)*(-2 + 6*sin(x)/(1 + cos(x)))/8)/2
Parte trigonométrica
[src]
/ ___ / 6 \\
|\/ 2 *|-2 + ------------------------||
| | / 1 \ / pi\||
| | |1 + ------|*sec|x - --|||
___ | \ \ sec(x)/ \ 2 //|
\/ 2 *atan|-------------------------------------|
\ 8 /
-------------------------------------------------
2
$$\frac{\sqrt{2} \operatorname{atan}{\left(\frac{\sqrt{2} \left(-2 + \frac{6}{\left(1 + \frac{1}{\sec{\left(x \right)}}\right) \sec{\left(x - \frac{\pi}{2} \right)}}\right)}{8} \right)}}{2}$$
/ / /x\ \\
| | 12*cot|-| ||
| ___ | \2/ ||
|\/ 2 *|-2 + --------------------------------||
| | / 2/x\\||
| | | -1 + cot |-||||
| | / 2/x\\ | \2/|||
| | |1 + cot |-||*|1 + ------------|||
| | \ \2// | 2/x\ |||
| | | 1 + cot |-| |||
___ | \ \ \2/ //|
\/ 2 *atan|---------------------------------------------|
\ 8 /
---------------------------------------------------------
2
$$\frac{\sqrt{2} \operatorname{atan}{\left(\frac{\sqrt{2} \left(-2 + \frac{12 \cot{\left(\frac{x}{2} \right)}}{\left(\frac{\cot^{2}{\left(\frac{x}{2} \right)} - 1}{\cot^{2}{\left(\frac{x}{2} \right)} + 1} + 1\right) \left(\cot^{2}{\left(\frac{x}{2} \right)} + 1\right)}\right)}{8} \right)}}{2}$$
/ ___ / 6*sin(x) \\
|\/ 2 *|-2 + ----------||
___ | \ 1 + cos(x)/|
\/ 2 *atan|-----------------------|
\ 8 /
-----------------------------------
2
$$\frac{\sqrt{2} \operatorname{atan}{\left(\frac{\sqrt{2} \left(-2 + \frac{6 \sin{\left(x \right)}}{\cos{\left(x \right)} + 1}\right)}{8} \right)}}{2}$$
/ / /x\ \\
| | 12*tan|-| ||
| ___ | \2/ ||
|\/ 2 *|-2 + -------------------------------||
| | / 2/x\\||
| | | 1 - tan |-||||
| | / 2/x\\ | \2/|||
| | |1 + tan |-||*|1 + -----------|||
| | \ \2// | 2/x\|||
| | | 1 + tan |-||||
___ | \ \ \2///|
\/ 2 *atan|--------------------------------------------|
\ 8 /
--------------------------------------------------------
2
$$\frac{\sqrt{2} \operatorname{atan}{\left(\frac{\sqrt{2} \left(-2 + \frac{12 \tan{\left(\frac{x}{2} \right)}}{\left(\frac{1 - \tan^{2}{\left(\frac{x}{2} \right)}}{\tan^{2}{\left(\frac{x}{2} \right)} + 1} + 1\right) \left(\tan^{2}{\left(\frac{x}{2} \right)} + 1\right)}\right)}{8} \right)}}{2}$$
/ / / pi\\\
| | 6*cos|x - --|||
| ___ | \ 2 /||
|\/ 2 *|-2 + -------------||
___ | \ 1 + cos(x) /|
\/ 2 *atan|--------------------------|
\ 8 /
--------------------------------------
2
$$\frac{\sqrt{2} \operatorname{atan}{\left(\frac{\sqrt{2} \left(-2 + \frac{6 \cos{\left(x - \frac{\pi}{2} \right)}}{\cos{\left(x \right)} + 1}\right)}{8} \right)}}{2}$$
/ ___ / 6*sin(x) \\
|\/ 2 *|-2 + ---------------||
| | / pi\||
| | 1 + sin|x + --|||
___ | \ \ 2 //|
\/ 2 *atan|----------------------------|
\ 8 /
----------------------------------------
2
$$\frac{\sqrt{2} \operatorname{atan}{\left(\frac{\sqrt{2} \left(-2 + \frac{6 \sin{\left(x \right)}}{\sin{\left(x + \frac{\pi}{2} \right)} + 1}\right)}{8} \right)}}{2}$$
/ ___ / 6 \\
|\/ 2 *|-2 + ------------------------||
| | / 1 \ ||
| | |1 + -----------|*csc(x)||
| | | /pi \| ||
| | | csc|-- - x|| ||
___ | \ \ \2 // /|
\/ 2 *atan|-------------------------------------|
\ 8 /
-------------------------------------------------
2
$$\frac{\sqrt{2} \operatorname{atan}{\left(\frac{\sqrt{2} \left(-2 + \frac{6}{\left(1 + \frac{1}{\csc{\left(- x + \frac{\pi}{2} \right)}}\right) \csc{\left(x \right)}}\right)}{8} \right)}}{2}$$
/ ___ / 6 \\
|\/ 2 *|-2 + -------------------||
| | / 1 \ ||
| | |1 + ------|*csc(x)||
___ | \ \ sec(x)/ /|
\/ 2 *atan|--------------------------------|
\ 8 /
--------------------------------------------
2
$$\frac{\sqrt{2} \operatorname{atan}{\left(\frac{\sqrt{2} \left(-2 + \frac{6}{\left(1 + \frac{1}{\sec{\left(x \right)}}\right) \csc{\left(x \right)}}\right)}{8} \right)}}{2}$$
sqrt(2)*atan(sqrt(2)*(-2 + 6/((1 + 1/sec(x))*csc(x)))/8)/2
Unión de expresiones racionales
[src]
/ ___ \
___ |\/ 2 *(-1 - cos(x) + 3*sin(x))|
\/ 2 *atan|------------------------------|
\ 4*(1 + cos(x)) /
------------------------------------------
2
$$\frac{\sqrt{2} \operatorname{atan}{\left(\frac{\sqrt{2} \left(3 \sin{\left(x \right)} - \cos{\left(x \right)} - 1\right)}{4 \left(\cos{\left(x \right)} + 1\right)} \right)}}{2}$$
sqrt(2)*atan(sqrt(2)*(-1 - cos(x) + 3*sin(x))/(4*(1 + cos(x))))/2