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¿cómo vas a descomponer esta expresión en fracciones?:
1/(3,94436∙〖10〗^(-7))
((3*c+1)/(c-1)+c)/(c+1)
-1/(5*x^5)
(49*b/a-25*a/b)/(7*a+5*b)
Factorizar el polinomio:
y^4-25
y^5-y^3-y+1
y^5+y+1
-y^3+y^2-1
Descomponer al cuadrado:
-y^4-8*y^2-8
-y^4+9*y^2-3
-y^4+8*y^2+4
-y^4-8*y^2-3
Expresiones idénticas
(uno +cos(x))^(sqrt(x))*(log(uno +cos(x))/(dos *sqrt(x))-sqrt(x)*sin(x)/(uno +cos(x)))
(1 más coseno de (x)) en el grado ( raíz cuadrada de (x)) multiplicar por ( logaritmo de (1 más coseno de (x)) dividir por (2 multiplicar por raíz cuadrada de (x)) menos raíz cuadrada de (x) multiplicar por seno de (x) dividir por (1 más coseno de (x)))
(uno más coseno de (x)) en el grado ( raíz cuadrada de (x)) multiplicar por ( logaritmo de (uno más coseno de (x)) dividir por (dos multiplicar por raíz cuadrada de (x)) menos raíz cuadrada de (x) multiplicar por seno de (x) dividir por (uno más coseno de (x)))
(1+cos(x))^(√(x))*(log(1+cos(x))/(2*√(x))-√(x)*sin(x)/(1+cos(x)))
(1+cos(x))(sqrt(x))*(log(1+cos(x))/(2*sqrt(x))-sqrt(x)*sin(x)/(1+cos(x)))
1+cosxsqrtx*log1+cosx/2*sqrtx-sqrtx*sinx/1+cosx
(1+cos(x))^(sqrt(x))(log(1+cos(x))/(2sqrt(x))-sqrt(x)sin(x)/(1+cos(x)))
(1+cos(x))(sqrt(x))(log(1+cos(x))/(2sqrt(x))-sqrt(x)sin(x)/(1+cos(x)))
1+cosxsqrtxlog1+cosx/2sqrtx-sqrtxsinx/1+cosx
1+cosx^sqrtxlog1+cosx/2sqrtx-sqrtxsinx/1+cosx
(1+cos(x))^(sqrt(x))*(log(1+cos(x)) dividir por (2*sqrt(x))-sqrt(x)*sin(x) dividir por (1+cos(x)))
Expresiones semejantes
(1+cos(x))^(sqrt(x))*(log(1-cos(x))/(2*sqrt(x))-sqrt(x)*sin(x)/(1+cos(x)))
(1-cos(x))^(sqrt(x))*(log(1+cos(x))/(2*sqrt(x))-sqrt(x)*sin(x)/(1+cos(x)))
(1+cos(x))^(sqrt(x))*(log(1+cos(x))/(2*sqrt(x))-sqrt(x)*sin(x)/(1-cos(x)))
(1+cos(x))^(sqrt(x))*(log(1+cos(x))/(2*sqrt(x))+sqrt(x)*sin(x)/(1+cos(x)))
(1+cosx)^(sqrt(x))*(log(1+cosx)/(2*sqrt(x))-sqrt(x)*sinx/(1+cosx))
Expresiones con funciones
Coseno cos
cos(10*a)/(sin(5*a)-cos(5*a))
cos(x)*(-sin(x)-(cos(x)*sin(x)))/sqrt(1+cos(x)^(2))/(cos(x)+sqrt(1+cos(x)^(2)))
cos(x)+t*sin(x)/(1-t*(x^2)/2)*x
cos(x)/(x+1)^3-3*sin(x)/(x+1)^4
cos(x)/(cos(x)+1)+sin(x)^2/(cos(x)+1)^2
Raíz cuadrada sqrt
Sqrt(2b+2*sqrt(b^2-4))/(sqrt(b^2-4)+b+2)
sqrt(x/(x-a^2))/((2*x^2-2*a^2)/a^2)
sqrt(x)/(-(x^7))
sqrt(x*(x-1)/(x-2))*(x-2)*((-1+2*x)/(2*(x-2))-x*(x-1)/(2*(x-2)^2))/(x*(x-1))
sqrt(x)/(m-16)-sqrt(m)/(4-sqrt(m))^2
Logaritmo log
log(x+9)/81-log(x)/81-1/(9*x)
log(x^2+1)/2-log(x+1)+atan(x)-1/(1+x)
log(x^2+2*x+2)/2-(5*atan((2*x+2)/2))/2+(x-2)/(4+4*x+2*x^2)
log(x^2+1)/(1+x^2)+2*x*atan(x)/(x^2+1)
log(x+1)/4-x/(2*x^2-2)-log(x-1)/4
Coseno cos
cos(10*a)/(sin(5*a)-cos(5*a))
cos(x)*(-sin(x)-(cos(x)*sin(x)))/sqrt(1+cos(x)^(2))/(cos(x)+sqrt(1+cos(x)^(2)))
cos(x)+t*sin(x)/(1-t*(x^2)/2)*x
cos(x)/(x+1)^3-3*sin(x)/(x+1)^4
cos(x)/(cos(x)+1)+sin(x)^2/(cos(x)+1)^2
Raíz cuadrada sqrt
Sqrt(2b+2*sqrt(b^2-4))/(sqrt(b^2-4)+b+2)
sqrt(x/(x-a^2))/((2*x^2-2*a^2)/a^2)
sqrt(x)/(-(x^7))
sqrt(x*(x-1)/(x-2))*(x-2)*((-1+2*x)/(2*(x-2))-x*(x-1)/(2*(x-2)^2))/(x*(x-1))
sqrt(x)/(m-16)-sqrt(m)/(4-sqrt(m))^2
Raíz cuadrada sqrt
Sqrt(2b+2*sqrt(b^2-4))/(sqrt(b^2-4)+b+2)
sqrt(x/(x-a^2))/((2*x^2-2*a^2)/a^2)
sqrt(x)/(-(x^7))
sqrt(x*(x-1)/(x-2))*(x-2)*((-1+2*x)/(2*(x-2))-x*(x-1)/(2*(x-2)^2))/(x*(x-1))
sqrt(x)/(m-16)-sqrt(m)/(4-sqrt(m))^2
Seno sin
sin^2/(cos-1)
sin^2a(cos4a-cos2a)/(sina-2sin3a+sin5a)
sin20/(2*cos10)
sin(2*x)/(1+cos(2*x))
sin(x)/(2*sqrt(cos(x)))
Coseno cos
cos(10*a)/(sin(5*a)-cos(5*a))
cos(x)*(-sin(x)-(cos(x)*sin(x)))/sqrt(1+cos(x)^(2))/(cos(x)+sqrt(1+cos(x)^(2)))
cos(x)+t*sin(x)/(1-t*(x^2)/2)*x
cos(x)/(x+1)^3-3*sin(x)/(x+1)^4
cos(x)/(cos(x)+1)+sin(x)^2/(cos(x)+1)^2

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

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

Solución

Ha introducido [src]

              ___ /                    ___       \
            \/ x  |log(1 + cos(x))   \/ x *sin(x)|
(1 + cos(x))     *|--------------- - ------------|
                  |        ___        1 + cos(x) |
                  \    2*\/ x                    /

\left(- \frac{\sqrt{x} \sin{\left(x \right)}}{\cos{\left(x \right)} + 1} + \frac{\log{\left(\cos{\left(x \right)} + 1 \right)}}{2 \sqrt{x}}\right) \left(\cos{\left(x \right)} + 1\right)^{\sqrt{x}}

(1 + cos(x))^(sqrt(x))*(log(1 + cos(x))/((2*sqrt(x))) - sqrt(x)*sin(x)/(1 + cos(x)))

Simplificación general [src]

                   ___                                          
            -1 + \/ x  /(1 + cos(x))*log(1 + cos(x))           \
(1 + cos(x))          *|---------------------------- - x*sin(x)|
                       \             2                         /
----------------------------------------------------------------
                               ___                              
                             \/ x

\frac{\left(- x \sin{\left(x \right)} + \frac{\left(\cos{\left(x \right)} + 1\right) \log{\left(\cos{\left(x \right)} + 1 \right)}}{2}\right) \left(\cos{\left(x \right)} + 1\right)^{\sqrt{x} - 1}}{\sqrt{x}}

(1 + cos(x))^(-1 + sqrt(x))*((1 + cos(x))*log(1 + cos(x))/2 - x*sin(x))/sqrt(x)

Respuesta numérica [src]

(1.0 + cos(x))^(x^0.5)*(0.5*x^(-0.5)*log(1 + cos(x)) - x^0.5*sin(x)/(1.0 + cos(x)))

(1.0 + cos(x))^(x^0.5)*(0.5*x^(-0.5)*log(1 + cos(x)) - x^0.5*sin(x)/(1.0 + cos(x)))

Denominador común [src]

 /                ___                                 ___                                            ___       \ 
 |              \/ x                                \/ x                                           \/ x        | 
-\- (1 + cos(x))     *log(1 + cos(x)) - (1 + cos(x))     *cos(x)*log(1 + cos(x)) + 2*x*(1 + cos(x))     *sin(x)/ 
-----------------------------------------------------------------------------------------------------------------
                                                 ___       ___                                                   
                                             2*\/ x  + 2*\/ x *cos(x)

- \frac{2 x \left(\cos{\left(x \right)} + 1\right)^{\sqrt{x}} \sin{\left(x \right)} - \left(\cos{\left(x \right)} + 1\right)^{\sqrt{x}} \log{\left(\cos{\left(x \right)} + 1 \right)} \cos{\left(x \right)} - \left(\cos{\left(x \right)} + 1\right)^{\sqrt{x}} \log{\left(\cos{\left(x \right)} + 1 \right)}}{2 \sqrt{x} \cos{\left(x \right)} + 2 \sqrt{x}}

-(-(1 + cos(x))^(sqrt(x))*log(1 + cos(x)) - (1 + cos(x))^(sqrt(x))*cos(x)*log(1 + cos(x)) + 2*x*(1 + cos(x))^(sqrt(x))*sin(x))/(2*sqrt(x) + 2*sqrt(x)*cos(x))

Unión de expresiones racionales [src]

              ___                                            
            \/ x                                             
(1 + cos(x))     *((1 + cos(x))*log(1 + cos(x)) - 2*x*sin(x))
-------------------------------------------------------------
                         ___                                 
                     2*\/ x *(1 + cos(x))

\frac{\left(- 2 x \sin{\left(x \right)} + \left(\cos{\left(x \right)} + 1\right) \log{\left(\cos{\left(x \right)} + 1 \right)}\right) \left(\cos{\left(x \right)} + 1\right)^{\sqrt{x}}}{2 \sqrt{x} \left(\cos{\left(x \right)} + 1\right)}

(1 + cos(x))^(sqrt(x))*((1 + cos(x))*log(1 + cos(x)) - 2*x*sin(x))/(2*sqrt(x)*(1 + cos(x)))

Potencias [src]

                    ___ /   /     I*x    -I*x\                           \
                  \/ x  |   |    e      e    |                           |
/     I*x    -I*x\      |log|1 + ---- + -----|       ___ /   -I*x    I*x\|
|    e      e    |      |   \     2       2  /   I*\/ x *\- e     + e   /|
|1 + ---- + -----|     *|--------------------- + ------------------------|
\     2       2  /      |           ___              /     I*x    -I*x\  |
                        |       2*\/ x               |    e      e    |  |
                        |                          2*|1 + ---- + -----|  |
                        \                            \     2       2  /  /

\left(\frac{i \sqrt{x} \left(e^{i x} - e^{- i x}\right)}{2 \left(\frac{e^{i x}}{2} + 1 + \frac{e^{- i x}}{2}\right)} + \frac{\log{\left(\frac{e^{i x}}{2} + 1 + \frac{e^{- i x}}{2} \right)}}{2 \sqrt{x}}\right) \left(\frac{e^{i x}}{2} + 1 + \frac{e^{- i x}}{2}\right)^{\sqrt{x}}

(1 + exp(i*x)/2 + exp(-i*x)/2)^(sqrt(x))*(log(1 + exp(i*x)/2 + exp(-i*x)/2)/(2*sqrt(x)) + i*sqrt(x)*(-exp(-i*x) + exp(i*x))/(2*(1 + exp(i*x)/2 + exp(-i*x)/2)))

Denominador racional [src]

                   ___                                      ___                                                 ___       
            -1 + \/ x                                -1 + \/ x                                           -1 + \/ x        
(1 + cos(x))          *log(1 + cos(x)) + (1 + cos(x))          *cos(x)*log(1 + cos(x)) - 2*x*(1 + cos(x))          *sin(x)
--------------------------------------------------------------------------------------------------------------------------
                                                             ___                                                          
                                                         2*\/ x

\frac{- 2 x \left(\cos{\left(x \right)} + 1\right)^{\sqrt{x} - 1} \sin{\left(x \right)} + \left(\cos{\left(x \right)} + 1\right)^{\sqrt{x} - 1} \log{\left(\cos{\left(x \right)} + 1 \right)} \cos{\left(x \right)} + \left(\cos{\left(x \right)} + 1\right)^{\sqrt{x} - 1} \log{\left(\cos{\left(x \right)} + 1 \right)}}{2 \sqrt{x}}

((1 + cos(x))^(-1 + sqrt(x))*log(1 + cos(x)) + (1 + cos(x))^(-1 + sqrt(x))*cos(x)*log(1 + cos(x)) - 2*x*(1 + cos(x))^(-1 + sqrt(x))*sin(x))/(2*sqrt(x))

Combinatoria [src]

               ___                                                          
             \/ x                                                           
-(1 + cos(x))     *(-log(1 + cos(x)) - cos(x)*log(1 + cos(x)) + 2*x*sin(x)) 
----------------------------------------------------------------------------
                                ___                                         
                            2*\/ x *(1 + cos(x))

- \frac{\left(\cos{\left(x \right)} + 1\right)^{\sqrt{x}} \left(2 x \sin{\left(x \right)} - \log{\left(\cos{\left(x \right)} + 1 \right)} \cos{\left(x \right)} - \log{\left(\cos{\left(x \right)} + 1 \right)}\right)}{2 \sqrt{x} \left(\cos{\left(x \right)} + 1\right)}

-(1 + cos(x))^(sqrt(x))*(-log(1 + cos(x)) - cos(x)*log(1 + cos(x)) + 2*x*sin(x))/(2*sqrt(x)*(1 + cos(x)))

Parte trigonométrica [src]

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

\left(- \frac{\sqrt{x} \cos{\left(x - \frac{\pi}{2} \right)}}{\cos{\left(x \right)} + 1} + \frac{\log{\left(\cos{\left(x \right)} + 1 \right)}}{2 \sqrt{x}}\right) \left(\cos{\left(x \right)} + 1\right)^{\sqrt{x}}

              ___ /   /      1   \                      \
            \/ x  |log|1 + ------|            ___       |
/      1   \      |   \    sec(x)/          \/ x        |
|1 + ------|     *|--------------- - -------------------|
\    sec(x)/      |        ___       /      1   \       |
                  |    2*\/ x        |1 + ------|*csc(x)|
                  \                  \    sec(x)/       /

\left(1 + \frac{1}{\sec{\left(x \right)}}\right)^{\sqrt{x}} \left(- \frac{\sqrt{x}}{\left(1 + \frac{1}{\sec{\left(x \right)}}\right) \csc{\left(x \right)}} + \frac{\log{\left(1 + \frac{1}{\sec{\left(x \right)}} \right)}}{2 \sqrt{x}}\right)

                       /   /           2/x\\                                  \
                       |   |    1 - tan |-||                                  |
                   ___ |   |            \2/|                                  |
                 \/ x  |log|1 + -----------|                                  |
/           2/x\\      |   |           2/x\|                ___    /x\        |
|    1 - tan |-||      |   |    1 + tan |-||            2*\/ x *tan|-|        |
|            \2/|      |   \            \2//                       \2/        |
|1 + -----------|     *|-------------------- - -------------------------------|
|           2/x\|      |          ___                        /           2/x\\|
|    1 + tan |-||      |      2*\/ x                         |    1 - tan |-|||
\            \2//      |                       /       2/x\\ |            \2/||
                       |                       |1 + tan |-||*|1 + -----------||
                       |                       \        \2// |           2/x\||
                       |                                     |    1 + tan |-|||
                       \                                     \            \2///

\left(\frac{1 - \tan^{2}{\left(\frac{x}{2} \right)}}{\tan^{2}{\left(\frac{x}{2} \right)} + 1} + 1\right)^{\sqrt{x}} \left(- \frac{2 \sqrt{x} \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)} + \frac{\log{\left(\frac{1 - \tan^{2}{\left(\frac{x}{2} \right)}}{\tan^{2}{\left(\frac{x}{2} \right)} + 1} + 1 \right)}}{2 \sqrt{x}}\right)

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

\left(1 + \frac{1}{\csc{\left(- x + \frac{\pi}{2} \right)}}\right)^{\sqrt{x}} \left(- \frac{\sqrt{x}}{\left(1 + \frac{1}{\csc{\left(- x + \frac{\pi}{2} \right)}}\right) \csc{\left(x \right)}} + \frac{\log{\left(1 + \frac{1}{\csc{\left(- x + \frac{\pi}{2} \right)}} \right)}}{2 \sqrt{x}}\right)

              ___ /                            ___       \
            \/ x  |   1                      \/ x *sin(x)|
(1 + cos(x))     *|-------*log(1 + cos(x)) - ------------|
                  |    ___                    1 + cos(x) |
                  \2*\/ x                                /

\left(\frac{1}{2 \sqrt{x}} \log{\left(\cos{\left(x \right)} + 1 \right)} - \frac{\sqrt{x} \sin{\left(x \right)}}{\cos{\left(x \right)} + 1}\right) \left(\cos{\left(x \right)} + 1\right)^{\sqrt{x}}

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

\left(- \frac{\sqrt{x} \sin{\left(x \right)}}{\sin{\left(x + \frac{\pi}{2} \right)} + 1} + \frac{\log{\left(\sin{\left(x + \frac{\pi}{2} \right)} + 1 \right)}}{2 \sqrt{x}}\right) \left(\sin{\left(x + \frac{\pi}{2} \right)} + 1\right)^{\sqrt{x}}

                        /   /            2/x\\                                   \
                        |   |    -1 + cot |-||                                   |
                    ___ |   |             \2/|                                   |
                  \/ x  |log|1 + ------------|                                   |
/            2/x\\      |   |           2/x\ |                ___    /x\         |
|    -1 + cot |-||      |   |    1 + cot |-| |            2*\/ x *cot|-|         |
|             \2/|      |   \            \2/ /                       \2/         |
|1 + ------------|     *|--------------------- - --------------------------------|
|           2/x\ |      |           ___                        /            2/x\\|
|    1 + cot |-| |      |       2*\/ x                         |    -1 + cot |-|||
\            \2/ /      |                        /       2/x\\ |             \2/||
                        |                        |1 + cot |-||*|1 + ------------||
                        |                        \        \2// |           2/x\ ||
                        |                                      |    1 + cot |-| ||
                        \                                      \            \2/ //

\left(\frac{\cot^{2}{\left(\frac{x}{2} \right)} - 1}{\cot^{2}{\left(\frac{x}{2} \right)} + 1} + 1\right)^{\sqrt{x}} \left(- \frac{2 \sqrt{x} \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)} + \frac{\log{\left(\frac{\cot^{2}{\left(\frac{x}{2} \right)} - 1}{\cot^{2}{\left(\frac{x}{2} \right)} + 1} + 1 \right)}}{2 \sqrt{x}}\right)

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

\left(1 + \frac{1}{\sec{\left(x \right)}}\right)^{\sqrt{x}} \left(- \frac{\sqrt{x}}{\left(1 + \frac{1}{\sec{\left(x \right)}}\right) \sec{\left(x - \frac{\pi}{2} \right)}} + \frac{\log{\left(1 + \frac{1}{\sec{\left(x \right)}} \right)}}{2 \sqrt{x}}\right)

(1 + 1/sec(x))^(sqrt(x))*(log(1 + 1/sec(x))/(2*sqrt(x)) - sqrt(x)/((1 + 1/sec(x))*sec(x - pi/2)))

Abrimos la expresión [src]

              ___                                       ___       
            \/ x                      ___             \/ x        
(1 + cos(x))     *log(1 + cos(x))   \/ x *(1 + cos(x))     *sin(x)
--------------------------------- - ------------------------------
                 ___                          1 + cos(x)          
             2*\/ x

- \frac{\sqrt{x} \left(\cos{\left(x \right)} + 1\right)^{\sqrt{x}} \sin{\left(x \right)}}{\cos{\left(x \right)} + 1} + \frac{\left(\cos{\left(x \right)} + 1\right)^{\sqrt{x}} \log{\left(\cos{\left(x \right)} + 1 \right)}}{2 \sqrt{x}}

(1 + cos(x))^(sqrt(x))*log(1 + cos(x))/(2*sqrt(x)) - sqrt(x)*(1 + cos(x))^(sqrt(x))*sin(x)/(1 + cos(x))

Otras calculadoras

¿Cómo usar?

Expresiones idénticas

Expresiones semejantes

Expresiones con funciones

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

Solución

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