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Descomponer al cuadrado:
-y^4+8*y^2+2
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Expresiones idénticas
cos(x)^atan(x+pi/ cuatro)*(log(cos(x))/(uno +(x+pi/ cuatro)^ dos)-atan(x+pi/ cuatro)*sin(x)/cos(x))
coseno de (x) en el grado arco tangente de gente de (x más número pi dividir por 4) multiplicar por ( logaritmo de ( coseno de (x)) dividir por (1 más (x más número pi dividir por 4) al cuadrado ) menos arco tangente de gente de (x más número pi dividir por 4) multiplicar por seno de (x) dividir por coseno de (x))
coseno de (x) en el grado arco tangente de gente de (x más número pi dividir por cuatro) multiplicar por ( logaritmo de ( coseno de (x)) dividir por (uno más (x más número pi dividir por cuatro) en el grado dos) menos arco tangente de gente de (x más número pi dividir por cuatro) multiplicar por seno de (x) dividir por coseno de (x))
cos(x)atan(x+pi/4)*(log(cos(x))/(1+(x+pi/4)2)-atan(x+pi/4)*sin(x)/cos(x))
cosxatanx+pi/4*logcosx/1+x+pi/42-atanx+pi/4*sinx/cosx
cos(x)^atan(x+pi/4)*(log(cos(x))/(1+(x+pi/4)²)-atan(x+pi/4)*sin(x)/cos(x))
cos(x) en el grado atan(x+pi/4)*(log(cos(x))/(1+(x+pi/4) en el grado 2)-atan(x+pi/4)*sin(x)/cos(x))
cos(x)^atan(x+pi/4)(log(cos(x))/(1+(x+pi/4)^2)-atan(x+pi/4)sin(x)/cos(x))
cos(x)atan(x+pi/4)(log(cos(x))/(1+(x+pi/4)2)-atan(x+pi/4)sin(x)/cos(x))
cosxatanx+pi/4logcosx/1+x+pi/42-atanx+pi/4sinx/cosx
cosx^atanx+pi/4logcosx/1+x+pi/4^2-atanx+pi/4sinx/cosx
cos(x)^atan(x+pi dividir por 4)*(log(cos(x)) dividir por (1+(x+pi dividir por 4)^2)-atan(x+pi dividir por 4)*sin(x) dividir por cos(x))
Expresiones semejantes
cos(x)^atan(x+pi/4)*(log(cos(x))/(1+(x+pi/4)^2)+atan(x+pi/4)*sin(x)/cos(x))
cos(x)^atan(x+pi/4)*(log(cos(x))/(1+(x-pi/4)^2)-atan(x+pi/4)*sin(x)/cos(x))
cos(x)^atan(x+pi/4)*(log(cos(x))/(1-(x+pi/4)^2)-atan(x+pi/4)*sin(x)/cos(x))
cos(x)^atan(x+pi/4)*(log(cos(x))/(1+(x+pi/4)^2)-atan(x-pi/4)*sin(x)/cos(x))
cos(x)^atan(x-pi/4)*(log(cos(x))/(1+(x+pi/4)^2)-atan(x+pi/4)*sin(x)/cos(x))
cos(x)^arctan(x+pi/4)*(log(cos(x))/(1+(x+pi/4)^2)-arctan(x+pi/4)*sin(x)/cos(x))
cosx^atan(x+pi/4)*(log(cosx)/(1+(x+pi/4)^2)-atan(x+pi/4)*sinx/cosx)
Expresiones con funciones
Coseno cos
cos(3*pi/(2+a))/sin(a)
cos(2*t)*x/(cos(t)+sin(x))-cos(t)
cos(x)/(cos(x+pi/6))
cos(x-pi/2)^(2)*cot(x+pi/2)^(2)/(cos(x+pi/2)+cot(x-pi/2)*cot(x-pi/2)-cos(x+pi/2))
cos(x)^atan(x)*(log(cos(x))/(1+x^2)-atan(x)*sin(x)/cos(x))
Arcotangente arctan
atan(x)+x/(1+x^2)-1/(x+1)-atan(x)/(x^2+1)
atan((4*x-2)/(2*sqrt(5)))/sqrt(5)
atan(2*x)/x+2*log(x)/(1+4*x^2)
atan((2*x+4)/(2*sqrt(3)))/sqrt(3)
atan((2*x-2*l)/(2*a))/a
Logaritmo log
log(x+1)/4+(3*log(x-1))/4+3/(2+2*x)
log(sqrt(x))/sqrt(1-x^2)+asin(x)/(2*x)
log(x)^(3/(x+3))*log(x)^2*log(x/4)/x
log(x^2+6*x+4)/2-(3*log((2*x-2*sqrt(5)+6)/(2*x+2*sqrt(5)+6)))/(2*sqrt(5))
log(x^2+3)/8-(3*log(x+1))/8+atan(x/sqrt(3))/(2*sqrt(3))+log(x-1)/8
Coseno cos
cos(3*pi/(2+a))/sin(a)
cos(2*t)*x/(cos(t)+sin(x))-cos(t)
cos(x)/(cos(x+pi/6))
cos(x-pi/2)^(2)*cot(x+pi/2)^(2)/(cos(x+pi/2)+cot(x-pi/2)*cot(x-pi/2)-cos(x+pi/2))
cos(x)^atan(x)*(log(cos(x))/(1+x^2)-atan(x)*sin(x)/cos(x))
Arcotangente arctan
atan(x)+x/(1+x^2)-1/(x+1)-atan(x)/(x^2+1)
atan((4*x-2)/(2*sqrt(5)))/sqrt(5)
atan(2*x)/x+2*log(x)/(1+4*x^2)
atan((2*x+4)/(2*sqrt(3)))/sqrt(3)
atan((2*x-2*l)/(2*a))/a
Seno sin
sin(x+y)/((sin(x)*sin(y)))
sin(x)*(sin(x)/(1-cos(x))-1/tan(x))
sin(x+y)/(cosx*cosy)+tgy
sin*(x)/(cos(x)-1)
sin(x)-cos(3*pi/(2-x))+cot(3*pi/(2+x))+cot(x)
Coseno cos
cos(3*pi/(2+a))/sin(a)
cos(2*t)*x/(cos(t)+sin(x))-cos(t)
cos(x)/(cos(x+pi/6))
cos(x-pi/2)^(2)*cot(x+pi/2)^(2)/(cos(x+pi/2)+cot(x-pi/2)*cot(x-pi/2)-cos(x+pi/2))
cos(x)^atan(x)*(log(cos(x))/(1+x^2)-atan(x)*sin(x)/cos(x))

Simplificación de expresiones/ Descomposición en fracciones simples/ cos(x)^atan(x+pi/4)*(log(cos(x))/(1+(x+pi/4)^2)-atan(x+pi/4)*sin(x)/cos(x))

¿Cómo vas a descomponer esta cos(x)^atan(x+pi/4)(log(cos(x))/(1+(x+pi/4)^2)-atan(x+pi/4)sin(x)/cos(x)) expresión en fracciones?

Solución

Ha introducido [src]

            /    pi\ /                    /    pi\       \
        atan|x + --| |                atan|x + --|*sin(x)|
            \    4 / | log(cos(x))        \    4 /       |
(cos(x))            *|------------- - -------------------|
                     |            2          cos(x)      |
                     |    /    pi\                       |
                     |1 + |x + --|                       |
                     \    \    4 /                       /

$$\left(- \frac{\sin{\left(x \right)} \operatorname{atan}{\left(x + \frac{\pi}{4} \right)}}{\cos{\left(x \right)}} + \frac{\log{\left(\cos{\left(x \right)} \right)}}{\left(x + \frac{\pi}{4}\right)^{2} + 1}\right) \cos^{\operatorname{atan}{\left(x + \frac{\pi}{4} \right)}}{\left(x \right)}$$

cos(x)^atan(x + pi/4)*(log(cos(x))/(1 + (x + pi/4)^2) - atan(x + pi/4)*sin(x)/cos(x))

Simplificación general [src]

                 /    pi\                                                                 
        -1 + atan|x + --|                                                                 
                 \    4 / /                        /               2\     /    pi\       \
(cos(x))                 *|16*cos(x)*log(cos(x)) - \16 + (pi + 4*x) /*atan|x + --|*sin(x)|
                          \                                               \    4 /       /
------------------------------------------------------------------------------------------
                                                    2                                     
                                     16 + (pi + 4*x)

$$\frac{\left(- \left(\left(4 x + \pi\right)^{2} + 16\right) \sin{\left(x \right)} \operatorname{atan}{\left(x + \frac{\pi}{4} \right)} + 16 \log{\left(\cos{\left(x \right)} \right)} \cos{\left(x \right)}\right) \cos^{\operatorname{atan}{\left(x + \frac{\pi}{4} \right)} - 1}{\left(x \right)}}{\left(4 x + \pi\right)^{2} + 16}$$

cos(x)^(-1 + atan(x + pi/4))*(16*cos(x)*log(cos(x)) - (16 + (pi + 4*x)^2)*atan(x + pi/4)*sin(x))/(16 + (pi + 4*x)^2)

Denominador racional [src]

                  /    pi\                                                                                     
         -1 + atan|x + --|                                                                                     
                  \    4 / /                                /    pi\                    2     /    pi\       \ 
-(cos(x))                 *|-16*cos(x)*log(cos(x)) + 16*atan|x + --|*sin(x) + (pi + 4*x) *atan|x + --|*sin(x)| 
                           \                                \    4 /                          \    4 /       / 
---------------------------------------------------------------------------------------------------------------
                                                  2       2                                                    
                                           16 + pi  + 16*x  + 8*pi*x

$$- \frac{\left(\left(4 x + \pi\right)^{2} \sin{\left(x \right)} \operatorname{atan}{\left(x + \frac{\pi}{4} \right)} - 16 \log{\left(\cos{\left(x \right)} \right)} \cos{\left(x \right)} + 16 \sin{\left(x \right)} \operatorname{atan}{\left(x + \frac{\pi}{4} \right)}\right) \cos^{\operatorname{atan}{\left(x + \frac{\pi}{4} \right)} - 1}{\left(x \right)}}{16 x^{2} + 8 \pi x + \pi^{2} + 16}$$

-cos(x)^(-1 + atan(x + pi/4))*(-16*cos(x)*log(cos(x)) + 16*atan(x + pi/4)*sin(x) + (pi + 4*x)^2*atan(x + pi/4)*sin(x))/(16 + pi^2 + 16*x^2 + 8*pi*x)

Denominador común [src]

 /                 /    pi\                                     /    pi\                                       /    pi\                                         /    pi\                                          /    pi\                    \ 
 |             atan|x + --|                                 atan|x + --|                                   atan|x + --|                                     atan|x + --|                                      atan|x + --|                    | 
 |                 \    4 /                                     \    4 /     /    pi\            2             \    4 /     /    pi\              2             \    4 /     /    pi\                             \    4 /     /    pi\       | 
-|- 16*(cos(x))            *cos(x)*log(cos(x)) + 16*(cos(x))            *atan|x + --|*sin(x) + pi *(cos(x))            *atan|x + --|*sin(x) + 16*x *(cos(x))            *atan|x + --|*sin(x) + 8*pi*x*(cos(x))            *atan|x + --|*sin(x)| 
 \                                                                           \    4 /                                       \    4 /                                         \    4 /                                          \    4 /       / 
------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                                           2              2                                                                                                                     
                                                                                             16*cos(x) + pi *cos(x) + 16*x *cos(x) + 8*pi*x*cos(x)

$$- \frac{16 x^{2} \sin{\left(x \right)} \cos^{\operatorname{atan}{\left(x + \frac{\pi}{4} \right)}}{\left(x \right)} \operatorname{atan}{\left(x + \frac{\pi}{4} \right)} + 8 \pi x \sin{\left(x \right)} \cos^{\operatorname{atan}{\left(x + \frac{\pi}{4} \right)}}{\left(x \right)} \operatorname{atan}{\left(x + \frac{\pi}{4} \right)} - 16 \log{\left(\cos{\left(x \right)} \right)} \cos{\left(x \right)} \cos^{\operatorname{atan}{\left(x + \frac{\pi}{4} \right)}}{\left(x \right)} + \pi^{2} \sin{\left(x \right)} \cos^{\operatorname{atan}{\left(x + \frac{\pi}{4} \right)}}{\left(x \right)} \operatorname{atan}{\left(x + \frac{\pi}{4} \right)} + 16 \sin{\left(x \right)} \cos^{\operatorname{atan}{\left(x + \frac{\pi}{4} \right)}}{\left(x \right)} \operatorname{atan}{\left(x + \frac{\pi}{4} \right)}}{16 x^{2} \cos{\left(x \right)} + 8 \pi x \cos{\left(x \right)} + \pi^{2} \cos{\left(x \right)} + 16 \cos{\left(x \right)}}$$

-(-16*cos(x)^atan(x + pi/4)*cos(x)*log(cos(x)) + 16*cos(x)^atan(x + pi/4)*atan(x + pi/4)*sin(x) + pi^2*cos(x)^atan(x + pi/4)*atan(x + pi/4)*sin(x) + 16*x^2*cos(x)^atan(x + pi/4)*atan(x + pi/4)*sin(x) + 8*pi*x*cos(x)^atan(x + pi/4)*atan(x + pi/4)*sin(x))/(16*cos(x) + pi^2*cos(x) + 16*x^2*cos(x) + 8*pi*x*cos(x))

Combinatoria [src]

             /    pi\                                                                                                                                      
         atan|x + --|                                                                                                                                      
             \    4 / /                                /    pi\            2     /    pi\              2     /    pi\                     /    pi\       \ 
-(cos(x))            *|-16*cos(x)*log(cos(x)) + 16*atan|x + --|*sin(x) + pi *atan|x + --|*sin(x) + 16*x *atan|x + --|*sin(x) + 8*pi*x*atan|x + --|*sin(x)| 
                      \                                \    4 /                  \    4 /                    \    4 /                     \    4 /       / 
-----------------------------------------------------------------------------------------------------------------------------------------------------------
                                                             /       2       2         \                                                                   
                                                             \16 + pi  + 16*x  + 8*pi*x/*cos(x)

$$- \frac{\left(16 x^{2} \sin{\left(x \right)} \operatorname{atan}{\left(x + \frac{\pi}{4} \right)} + 8 \pi x \sin{\left(x \right)} \operatorname{atan}{\left(x + \frac{\pi}{4} \right)} - 16 \log{\left(\cos{\left(x \right)} \right)} \cos{\left(x \right)} + \pi^{2} \sin{\left(x \right)} \operatorname{atan}{\left(x + \frac{\pi}{4} \right)} + 16 \sin{\left(x \right)} \operatorname{atan}{\left(x + \frac{\pi}{4} \right)}\right) \cos^{\operatorname{atan}{\left(x + \frac{\pi}{4} \right)}}{\left(x \right)}}{\left(16 x^{2} + 8 \pi x + \pi^{2} + 16\right) \cos{\left(x \right)}}$$

-cos(x)^atan(x + pi/4)*(-16*cos(x)*log(cos(x)) + 16*atan(x + pi/4)*sin(x) + pi^2*atan(x + pi/4)*sin(x) + 16*x^2*atan(x + pi/4)*sin(x) + 8*pi*x*atan(x + pi/4)*sin(x))/((16 + pi^2 + 16*x^2 + 8*pi*x)*cos(x))

Potencias [src]

                  /    pi\                                                      
              atan|x + --| /   / I*x    -I*x\                                  \
                  \    4 / |   |e      e    |     /   -I*x    I*x\     /    pi\|
/ I*x    -I*x\             |log|---- + -----|   I*\- e     + e   /*atan|x + --||
|e      e    |             |   \ 2       2  /                          \    4 /|
|---- + -----|            *|----------------- + -------------------------------|
\ 2       2  /             |              2               / I*x    -I*x\       |
                           |      /    pi\                |e      e    |       |
                           |  1 + |x + --|              2*|---- + -----|       |
                           \      \    4 /                \ 2       2  /       /

$$\left(\frac{i \left(e^{i x} - e^{- i x}\right) \operatorname{atan}{\left(x + \frac{\pi}{4} \right)}}{2 \left(\frac{e^{i x}}{2} + \frac{e^{- i x}}{2}\right)} + \frac{\log{\left(\frac{e^{i x}}{2} + \frac{e^{- i x}}{2} \right)}}{\left(x + \frac{\pi}{4}\right)^{2} + 1}\right) \left(\frac{e^{i x}}{2} + \frac{e^{- i x}}{2}\right)^{\operatorname{atan}{\left(x + \frac{\pi}{4} \right)}}$$

(exp(i*x)/2 + exp(-i*x)/2)^atan(x + pi/4)*(log(exp(i*x)/2 + exp(-i*x)/2)/(1 + (x + pi/4)^2) + i*(-exp(-i*x) + exp(i*x))*atan(x + pi/4)/(2*(exp(i*x)/2 + exp(-i*x)/2)))

Unión de expresiones racionales [src]

            /pi + 4*x\                                                                   
        atan|--------|                                                                   
            \   4    / /                        /               2\     /pi + 4*x\       \
(cos(x))              *|16*cos(x)*log(cos(x)) - \16 + (pi + 4*x) /*atan|--------|*sin(x)|
                       \                                               \   4    /       /
-----------------------------------------------------------------------------------------
                                /               2\                                       
                                \16 + (pi + 4*x) /*cos(x)

$$\frac{\left(- \left(\left(4 x + \pi\right)^{2} + 16\right) \sin{\left(x \right)} \operatorname{atan}{\left(\frac{4 x + \pi}{4} \right)} + 16 \log{\left(\cos{\left(x \right)} \right)} \cos{\left(x \right)}\right) \cos^{\operatorname{atan}{\left(\frac{4 x + \pi}{4} \right)}}{\left(x \right)}}{\left(\left(4 x + \pi\right)^{2} + 16\right) \cos{\left(x \right)}}$$

cos(x)^atan((pi + 4*x)/4)*(16*cos(x)*log(cos(x)) - (16 + (pi + 4*x)^2)*atan((pi + 4*x)/4)*sin(x))/((16 + (pi + 4*x)^2)*cos(x))

Parte trigonométrica [src]

                           /   /        2/x\\               \
                  /    pi\ |   |-1 + cot |-||               |
              atan|x + --| |   |         \2/|               |
                  \    4 / |log|------------|               |
/        2/x\\             |   |       2/x\ |       /    pi\|
|-1 + cot |-||             |   |1 + cot |-| |   atan|x + --||
|         \2/|             |   \        \2/ /       \    4 /|
|------------|            *|----------------- - ------------|
|       2/x\ |             |              2        cot(x)   |
|1 + cot |-| |             |      /    pi\                  |
\        \2/ /             |  1 + |x + --|                  |
                           \      \    4 /                  /

$$\left(\frac{\cot^{2}{\left(\frac{x}{2} \right)} - 1}{\cot^{2}{\left(\frac{x}{2} \right)} + 1}\right)^{\operatorname{atan}{\left(x + \frac{\pi}{4} \right)}} \left(- \frac{\operatorname{atan}{\left(x + \frac{\pi}{4} \right)}}{\cot{\left(x \right)}} + \frac{\log{\left(\frac{\cot^{2}{\left(\frac{x}{2} \right)} - 1}{\cot^{2}{\left(\frac{x}{2} \right)} + 1} \right)}}{\left(x + \frac{\pi}{4}\right)^{2} + 1}\right)$$

                          /   /       2/x\\                      \
                 /    pi\ |   |1 - tan |-||                      |
             atan|x + --| |   |        \2/|                      |
                 \    4 / |log|-----------|                      |
/       2/x\\             |   |       2/x\|                      |
|1 - tan |-||             |   |1 + tan |-||                      |
|        \2/|             |   \        \2//       /    pi\       |
|-----------|            *|---------------- - atan|x + --|*tan(x)|
|       2/x\|             |             2         \    4 /       |
|1 + tan |-||             |     /    pi\                         |
\        \2//             | 1 + |x + --|                         |
                          \     \    4 /                         /

$$\left(\frac{1 - \tan^{2}{\left(\frac{x}{2} \right)}}{\tan^{2}{\left(\frac{x}{2} \right)} + 1}\right)^{\operatorname{atan}{\left(x + \frac{\pi}{4} \right)}} \left(- \tan{\left(x \right)} \operatorname{atan}{\left(x + \frac{\pi}{4} \right)} + \frac{\log{\left(\frac{1 - \tan^{2}{\left(\frac{x}{2} \right)}}{\tan^{2}{\left(\frac{x}{2} \right)} + 1} \right)}}{\left(x + \frac{\pi}{4}\right)^{2} + 1}\right)$$

                 /    pi\                                            
             atan|x + --| /   /   /    pi\\        2        /    pi\\
                 \    4 / |log|sin|x + --||   2*sin (x)*atan|x + --||
/   /    pi\\             |   \   \    2 //                 \    4 /|
|sin|x + --||            *|---------------- - ----------------------|
\   \    2 //             |             2            sin(2*x)       |
                          |     /    pi\                            |
                          | 1 + |x + --|                            |
                          \     \    4 /                            /

$$\left(- \frac{2 \sin^{2}{\left(x \right)} \operatorname{atan}{\left(x + \frac{\pi}{4} \right)}}{\sin{\left(2 x \right)}} + \frac{\log{\left(\sin{\left(x + \frac{\pi}{2} \right)} \right)}}{\left(x + \frac{\pi}{4}\right)^{2} + 1}\right) \sin^{\operatorname{atan}{\left(x + \frac{\pi}{4} \right)}}{\left(x + \frac{\pi}{2} \right)}$$

            /    pi\                                      
        atan|x + --| /    /  1   \        /    pi\       \
            \    4 / | log|------|    atan|x + --|*sec(x)|
/  1   \             |    \sec(x)/        \    4 /       |
|------|            *|------------- - -------------------|
\sec(x)/             |            2          csc(x)      |
                     |    /    pi\                       |
                     |1 + |x + --|                       |
                     \    \    4 /                       /

$$\left(- \frac{\operatorname{atan}{\left(x + \frac{\pi}{4} \right)} \sec{\left(x \right)}}{\csc{\left(x \right)}} + \frac{\log{\left(\frac{1}{\sec{\left(x \right)}} \right)}}{\left(x + \frac{\pi}{4}\right)^{2} + 1}\right) \left(\frac{1}{\sec{\left(x \right)}}\right)^{\operatorname{atan}{\left(x + \frac{\pi}{4} \right)}}$$

                          /   /     1     \                           \
                 /    pi\ |log|-----------|                           |
             atan|x + --| |   |   /pi    \|       /    pi\    /pi    \|
                 \    4 / |   |csc|-- - x||   atan|x + --|*csc|-- - x||
/     1     \             |   \   \2     //       \    4 /    \2     /|
|-----------|            *|---------------- - ------------------------|
|   /pi    \|             |             2              csc(x)         |
|csc|-- - x||             |     /    pi\                              |
\   \2     //             | 1 + |x + --|                              |
                          \     \    4 /                              /

$$\left(- \frac{\operatorname{atan}{\left(x + \frac{\pi}{4} \right)} \csc{\left(- x + \frac{\pi}{2} \right)}}{\csc{\left(x \right)}} + \frac{\log{\left(\frac{1}{\csc{\left(- x + \frac{\pi}{2} \right)}} \right)}}{\left(x + \frac{\pi}{4}\right)^{2} + 1}\right) \left(\frac{1}{\csc{\left(- x + \frac{\pi}{2} \right)}}\right)^{\operatorname{atan}{\left(x + \frac{\pi}{4} \right)}}$$

                 /    pi\                                         
             atan|x + --| /   /   /    pi\\       /    pi\       \
                 \    4 / |log|sin|x + --||   atan|x + --|*sin(x)|
/   /    pi\\             |   \   \    2 //       \    4 /       |
|sin|x + --||            *|---------------- - -------------------|
\   \    2 //             |             2            /    pi\    |
                          |     /    pi\          sin|x + --|    |
                          | 1 + |x + --|             \    2 /    |
                          \     \    4 /                         /

$$\left(- \frac{\sin{\left(x \right)} \operatorname{atan}{\left(x + \frac{\pi}{4} \right)}}{\sin{\left(x + \frac{\pi}{2} \right)}} + \frac{\log{\left(\sin{\left(x + \frac{\pi}{2} \right)} \right)}}{\left(x + \frac{\pi}{4}\right)^{2} + 1}\right) \sin^{\operatorname{atan}{\left(x + \frac{\pi}{4} \right)}}{\left(x + \frac{\pi}{2} \right)}$$

                          /   /       2/x\\                        \
                 /    pi\ |   |1 - tan |-||                        |
             atan|x + --| |   |        \2/|                        |
                 \    4 / |log|-----------|                        |
/       2/x\\             |   |       2/x\|         /    pi\    /x\|
|1 - tan |-||             |   |1 + tan |-||   2*atan|x + --|*tan|-||
|        \2/|             |   \        \2//         \    4 /    \2/|
|-----------|            *|---------------- - ---------------------|
|       2/x\|             |             2                 2/x\     |
|1 + tan |-||             |     /    pi\           1 - tan |-|     |
\        \2//             | 1 + |x + --|                   \2/     |
                          \     \    4 /                           /

$$\left(\frac{1 - \tan^{2}{\left(\frac{x}{2} \right)}}{\tan^{2}{\left(\frac{x}{2} \right)} + 1}\right)^{\operatorname{atan}{\left(x + \frac{\pi}{4} \right)}} \left(\frac{\log{\left(\frac{1 - \tan^{2}{\left(\frac{x}{2} \right)}}{\tan^{2}{\left(\frac{x}{2} \right)} + 1} \right)}}{\left(x + \frac{\pi}{4}\right)^{2} + 1} - \frac{2 \tan{\left(\frac{x}{2} \right)} \operatorname{atan}{\left(x + \frac{\pi}{4} \right)}}{1 - \tan^{2}{\left(\frac{x}{2} \right)}}\right)$$

            /    pi\ /                    /    pi\    /    pi\\
        atan|x + --| |                atan|x + --|*cos|x - --||
            \    4 / | log(cos(x))        \    4 /    \    2 /|
(cos(x))            *|------------- - ------------------------|
                     |            2            cos(x)         |
                     |    /    pi\                            |
                     |1 + |x + --|                            |
                     \    \    4 /                            /

$$\left(- \frac{\cos{\left(x - \frac{\pi}{2} \right)} \operatorname{atan}{\left(x + \frac{\pi}{4} \right)}}{\cos{\left(x \right)}} + \frac{\log{\left(\cos{\left(x \right)} \right)}}{\left(x + \frac{\pi}{4}\right)^{2} + 1}\right) \cos^{\operatorname{atan}{\left(x + \frac{\pi}{4} \right)}}{\left(x \right)}$$

            /    pi\                                      
        atan|x + --| /    /  1   \        /    pi\       \
            \    4 / | log|------|    atan|x + --|*sec(x)|
/  1   \             |    \sec(x)/        \    4 /       |
|------|            *|------------- - -------------------|
\sec(x)/             |            2          /    pi\    |
                     |    /    pi\        sec|x - --|    |
                     |1 + |x + --|           \    2 /    |
                     \    \    4 /                       /

$$\left(- \frac{\operatorname{atan}{\left(x + \frac{\pi}{4} \right)} \sec{\left(x \right)}}{\sec{\left(x - \frac{\pi}{2} \right)}} + \frac{\log{\left(\frac{1}{\sec{\left(x \right)}} \right)}}{\left(x + \frac{\pi}{4}\right)^{2} + 1}\right) \left(\frac{1}{\sec{\left(x \right)}}\right)^{\operatorname{atan}{\left(x + \frac{\pi}{4} \right)}}$$

                           /   /        2/x\\                        \
                  /    pi\ |   |-1 + cot |-||                        |
              atan|x + --| |   |         \2/|                        |
                  \    4 / |log|------------|                        |
/        2/x\\             |   |       2/x\ |         /    pi\    /x\|
|-1 + cot |-||             |   |1 + cot |-| |   2*atan|x + --|*cot|-||
|         \2/|             |   \        \2/ /         \    4 /    \2/|
|------------|            *|----------------- - ---------------------|
|       2/x\ |             |              2                  2/x\    |
|1 + cot |-| |             |      /    pi\           -1 + cot |-|    |
\        \2/ /             |  1 + |x + --|                    \2/    |
                           \      \    4 /                           /

$$\left(\frac{\cot^{2}{\left(\frac{x}{2} \right)} - 1}{\cot^{2}{\left(\frac{x}{2} \right)} + 1}\right)^{\operatorname{atan}{\left(x + \frac{\pi}{4} \right)}} \left(- \frac{2 \cot{\left(\frac{x}{2} \right)} \operatorname{atan}{\left(x + \frac{\pi}{4} \right)}}{\cot^{2}{\left(\frac{x}{2} \right)} - 1} + \frac{\log{\left(\frac{\cot^{2}{\left(\frac{x}{2} \right)} - 1}{\cot^{2}{\left(\frac{x}{2} \right)} + 1} \right)}}{\left(x + \frac{\pi}{4}\right)^{2} + 1}\right)$$

            /    pi\                                      
        atan|x + --|                                      
            \    4 / / log(cos(x))        /    pi\       \
(cos(x))            *|------------- - atan|x + --|*tan(x)|
                     |            2       \    4 /       |
                     |    /    pi\                       |
                     |1 + |x + --|                       |
                     \    \    4 /                       /

$$\left(- \tan{\left(x \right)} \operatorname{atan}{\left(x + \frac{\pi}{4} \right)} + \frac{\log{\left(\cos{\left(x \right)} \right)}}{\left(x + \frac{\pi}{4}\right)^{2} + 1}\right) \cos^{\operatorname{atan}{\left(x + \frac{\pi}{4} \right)}}{\left(x \right)}$$

cos(x)^atan(x + pi/4)*(log(cos(x))/(1 + (x + pi/4)^2) - atan(x + pi/4)*tan(x))

Respuesta numérica [src]

cos(x)^atan(x + pi/4)*(log(cos(x))/(1.0 + (0.785398163397448 + x)^2) - atan(x + pi/4)*sin(x)/cos(x))

cos(x)^atan(x + pi/4)*(log(cos(x))/(1.0 + (0.785398163397448 + x)^2) - atan(x + pi/4)*sin(x)/cos(x))

Abrimos la expresión [src]

                                               /    pi\                    
            /    pi\                       atan|x + --|                    
        atan|x + --|                           \    4 /     /    pi\       
            \    4 /               (cos(x))            *atan|x + --|*sin(x)
(cos(x))            *log(cos(x))                            \    4 /       
-------------------------------- - ----------------------------------------
                 2                                  cos(x)                 
           2   pi    pi*x                                                  
      1 + x  + --- + ----                                                  
                16    2

$$- \frac{\sin{\left(x \right)} \cos^{\operatorname{atan}{\left(x + \frac{\pi}{4} \right)}}{\left(x \right)} \operatorname{atan}{\left(x + \frac{\pi}{4} \right)}}{\cos{\left(x \right)}} + \frac{\log{\left(\cos{\left(x \right)} \right)} \cos^{\operatorname{atan}{\left(x + \frac{\pi}{4} \right)}}{\left(x \right)}}{x^{2} + \frac{\pi x}{2} + \frac{\pi^{2}}{16} + 1}$$

cos(x)^atan(x + pi/4)*log(cos(x))/(1 + x^2 + pi^2/16 + pi*x/2) - cos(x)^atan(x + pi/4)*atan(x + pi/4)*sin(x)/cos(x)

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¿Cómo vas a descomponer esta cos(x)^atan(x+pi/4)*(log(cos(x))/(1+(x+pi/4)^2)-atan(x+pi/4)*sin(x)/cos(x)) expresión en fracciones?

Solución

¿Cómo vas a descomponer esta cos(x)^atan(x+pi/4)(log(cos(x))/(1+(x+pi/4)^2)-atan(x+pi/4)sin(x)/cos(x)) expresión en fracciones?