Descomposición de una fracción atan(((6*sin(x))/(1+cos(x))+2)/2^(5/2))/sqrt(2) (arco tangente de gente de (((6 multiplicar por seno de (x)) dividir por (1 más coseno de (x)) más 2) dividir por 2 en el grado (5 dividir por 2)) dividir por raíz cuadrada de (2))

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)

Descomposición de una fracción [src]

sqrt(2)*atan(2*sqrt(2)/8 + 6*(sqrt(2)/8)*sin(x)/(1 + cos(x)))/2

\frac{\sqrt{2} \operatorname{atan}{\left(\frac{2 \sqrt{2}}{8} + \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

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

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))

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

Unión de expresiones racionales [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

Potencias [src]

  ___     /  ___ /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}

          /      /        /   -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}

sqrt(2)*atan(sqrt(2)*(2 - 3*i*(-exp(-i*x) + exp(i*x))/(1 + exp(i*x)/2 + exp(-i*x)/2))/8)/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

Abrimos la expresión [src]

          /              ___       \
          |            \/ 2        |
  ___     |    ___   6*-----*sin(x)|
\/ 2      |2*\/ 2        8         |
-----*atan|------- + --------------|
  2       \   8        1 + cos(x)  /

\frac{\sqrt{2}}{2} \operatorname{atan}{\left(\frac{2 \sqrt{2}}{8} + \frac{6 \frac{\sqrt{2}}{8} \sin{\left(x \right)}}{\cos{\left(x \right)} + 1} \right)}

(sqrt(2)/2)*atan(2*sqrt(2)/8 + 6*(sqrt(2)/8)*sin(x)/(1 + cos(x)))

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

Parte trigonométrica [src]

          /  ___ /             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}

          /  ___ /               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}

          /      /         /    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            \\
          |\/ 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}

          /  ___ /     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}

          /  ___ /        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}

          /      /                     /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}

          /      /                     /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}

sqrt(2)*atan(sqrt(2)*(2 + 12*cot(x/2)/((1 + cot(x/2)^2)*(1 + (-1 + cot(x/2)^2)/(1 + cot(x/2)^2))))/8)/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

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¿Cómo vas a descomponer esta atan(((6*sin(x))/(1+cos(x))+2)/2^(5/2))/sqrt(2) expresión en fracciones?

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