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(z^2-4*z+16)/(16*z^2-1)*(4*z^2+z)/(z^3+64)-(z+4)/(4*z^2-z)/7/(z^2+4*z)-(20*z+13)/(7-28*z)
y/(y-3)+3/(3-y)
((z^2-z)/(z^2-9))^-1/((z^2-3*z)/(z-1))
(a^(7*a))^2/(-a)^15
Factorizar el polinomio:
y^x*y^3-y-1+y^x*y
y^8-1
y^4+y^3
y^3-x*y^2+y-x
Descomponer al cuadrado:
y^4-8*y^2-9
-y^4-8*y^2+7
-y^4+8*y^2+3
y^4-9*y^2+15
Expresiones idénticas
log(x^ dos +x+ uno)/ nueve +(dos *atan((dos *x+ uno)/sqrt(tres)))/ tres ^(tres / dos)-(dos *log(x- uno))/ nueve -x/(tres *x^ tres - tres)
logaritmo de (x al cuadrado más x más 1) dividir por 9 más (2 multiplicar por arco tangente de gente de ((2 multiplicar por x más 1) dividir por raíz cuadrada de (3))) dividir por 3 en el grado (3 dividir por 2) menos (2 multiplicar por logaritmo de (x menos 1)) dividir por 9 menos x dividir por (3 multiplicar por x al cubo menos 3)
logaritmo de (x en el grado dos más x más uno) dividir por nueve más (dos multiplicar por arco tangente de gente de ((dos multiplicar por x más uno) dividir por raíz cuadrada de (tres))) dividir por tres en el grado (tres dividir por dos) menos (dos multiplicar por logaritmo de (x menos uno)) dividir por nueve menos x dividir por (tres multiplicar por x en el grado tres menos tres)
log(x^2+x+1)/9+(2*atan((2*x+1)/√(3)))/3^(3/2)-(2*log(x-1))/9-x/(3*x^3-3)
log(x2+x+1)/9+(2*atan((2*x+1)/sqrt(3)))/3(3/2)-(2*log(x-1))/9-x/(3*x3-3)
logx2+x+1/9+2*atan2*x+1/sqrt3/33/2-2*logx-1/9-x/3*x3-3
log(x²+x+1)/9+(2*atan((2*x+1)/sqrt(3)))/3^(3/2)-(2*log(x-1))/9-x/(3*x³-3)
log(x en el grado 2+x+1)/9+(2*atan((2*x+1)/sqrt(3)))/3 en el grado (3/2)-(2*log(x-1))/9-x/(3*x en el grado 3-3)
log(x^2+x+1)/9+(2atan((2x+1)/sqrt(3)))/3^(3/2)-(2log(x-1))/9-x/(3x^3-3)
log(x2+x+1)/9+(2atan((2x+1)/sqrt(3)))/3(3/2)-(2log(x-1))/9-x/(3x3-3)
logx2+x+1/9+2atan2x+1/sqrt3/33/2-2logx-1/9-x/3x3-3
logx^2+x+1/9+2atan2x+1/sqrt3/3^3/2-2logx-1/9-x/3x^3-3
log(x^2+x+1) dividir por 9+(2*atan((2*x+1) dividir por sqrt(3))) dividir por 3^(3 dividir por 2)-(2*log(x-1)) dividir por 9-x dividir por (3*x^3-3)
Expresiones semejantes
log(x^2+x+1)/9-(2*atan((2*x+1)/sqrt(3)))/3^(3/2)-(2*log(x-1))/9-x/(3*x^3-3)
log(x^2+x+1)/9+(2*atan((2*x+1)/sqrt(3)))/3^(3/2)-(2*log(x-1))/9-x/(3*x^3+3)
log(x^2+x+1)/9+(2*atan((2*x+1)/sqrt(3)))/3^(3/2)-(2*log(x-1))/9+x/(3*x^3-3)
log(x^2+x+1)/9+(2*atan((2*x+1)/sqrt(3)))/3^(3/2)+(2*log(x-1))/9-x/(3*x^3-3)
log(x^2+x+1)/9+(2*atan((2*x+1)/sqrt(3)))/3^(3/2)-(2*log(x+1))/9-x/(3*x^3-3)
log(x^2+x-1)/9+(2*atan((2*x+1)/sqrt(3)))/3^(3/2)-(2*log(x-1))/9-x/(3*x^3-3)
log(x^2-x+1)/9+(2*atan((2*x+1)/sqrt(3)))/3^(3/2)-(2*log(x-1))/9-x/(3*x^3-3)
log(x^2+x+1)/9+(2*atan((2*x-1)/sqrt(3)))/3^(3/2)-(2*log(x-1))/9-x/(3*x^3-3)
log(x^2+x+1)/9+(2*arctan((2*x+1)/sqrt(3)))/3^(3/2)-(2*log(x-1))/9-x/(3*x^3-3)
Expresiones con funciones
Logaritmo log
log(z)*(-2)+2*c^i*2*z-1/(2*z^2)+cos(2*z)/((2*z^2))-sin(2*z)/z+log(z^2)
log(x)^sin(x)*(cos(x)*log(log(x))+sin(x)/(x*log(x)))
log(x-5*x^2)/(2*sqrt(x+2))+sqrt(x+2)*(1-10*x)/(x-5*x^2)
log(x)/log(5)/5*((x+exp(-x)*x)^(1/5))+(x+5)/(2*sin(x)+x)
log(x^2+2)/9-atan(x/sqrt(2))/(9*sqrt(2))-(2*log(x-1))/9-1/(3*x-3)
Arcotangente arctan
atan(x)/2+x/(2+2*x^2)
atan(sin(x)/(2*(1+cos(x))))/2
atan((4*x-4)/(2*sqrt(6)))/sqrt(6)
atan((2*x+4)/(2*sqrt(3)))/sqrt(3)
atan(x/sqrt(2))/2^(3/2)-x/(4+2*x^2)
Raíz cuadrada sqrt
sqrt((x^2+10^8)/(1+25*x^2))
sqrt((49)/(169^x^196))
sqrt(x/(x+1))*(x+1)*(1/(2*(x+1))-x/(2*(x+1)^2))/(x*sqrt(1-x/(x+1)))
sqrt(x)*exp(x/2)/2+exp(x/2)/(2*sqrt(x))
Sqrt(2b+2*sqrt(b^2-4))/(sqrt(b^2-4)+b+2)
Logaritmo log
log(z)*(-2)+2*c^i*2*z-1/(2*z^2)+cos(2*z)/((2*z^2))-sin(2*z)/z+log(z^2)
log(x)^sin(x)*(cos(x)*log(log(x))+sin(x)/(x*log(x)))
log(x-5*x^2)/(2*sqrt(x+2))+sqrt(x+2)*(1-10*x)/(x-5*x^2)
log(x)/log(5)/5*((x+exp(-x)*x)^(1/5))+(x+5)/(2*sin(x)+x)
log(x^2+2)/9-atan(x/sqrt(2))/(9*sqrt(2))-(2*log(x-1))/9-1/(3*x-3)

Simplificación de expresiones/ Descomposición en fracciones simples/ log(x^2+x+1)/9+(2*atan((2*x+1)/sqrt(3)))/3^(3/2)-(2*log(x-1))/9-x/(3*x^3-3)

¿Cómo vas a descomponer esta log(x^2+x+1)/9+(2atan((2x+1)/sqrt(3)))/3^(3/2)-(2log(x-1))/9-x/(3x^3-3) expresión en fracciones?

Solución

Ha introducido [src]

                        /2*x + 1\                          
                  2*atan|-------|                          
   / 2        \         |   ___ |                          
log\x  + x + 1/         \ \/ 3  /   2*log(x - 1)      x    
--------------- + --------------- - ------------ - --------
       9                 3/2             9            3    
                        3                          3*x  - 3

- \frac{x}{3 x^{3} - 3} + \left(\left(\frac{\log{\left(\left(x^{2} + x\right) + 1 \right)}}{9} + \frac{2 \operatorname{atan}{\left(\frac{2 x + 1}{\sqrt{3}} \right)}}{3^{\frac{3}{2}}}\right) - \frac{2 \log{\left(x - 1 \right)}}{9}\right)

log(x^2 + x + 1)/9 + (2*atan((2*x + 1)/sqrt(3)))/3^(3/2) - 2*log(x - 1)/9 - x/(3*x^3 - 3)

Simplificación general [src]

                 /                             /  ___          \                  \
       /      3\ |                     ___     |\/ 3 *(1 + 2*x)|      /         2\|
-3*x + \-1 + x /*|-2*log(-1 + x) + 2*\/ 3 *atan|---------------| + log\1 + x + x /|
                 \                             \       3       /                  /
-----------------------------------------------------------------------------------
                                      /      3\                                    
                                    9*\-1 + x /

\frac{- 3 x + \left(x^{3} - 1\right) \left(- 2 \log{\left(x - 1 \right)} + \log{\left(x^{2} + x + 1 \right)} + 2 \sqrt{3} \operatorname{atan}{\left(\frac{\sqrt{3} \left(2 x + 1\right)}{3} \right)}\right)}{9 \left(x^{3} - 1\right)}

(-3*x + (-1 + x^3)*(-2*log(-1 + x) + 2*sqrt(3)*atan(sqrt(3)*(1 + 2*x)/3) + log(1 + x + x^2)))/(9*(-1 + x^3))

Unión de expresiones racionales [src]

                 /                             /  ___          \                     \
       /      3\ |                     ___     |\/ 3 *(1 + 2*x)|                     |
-3*x + \-1 + x /*|-2*log(-1 + x) + 2*\/ 3 *atan|---------------| + log(1 + x*(1 + x))|
                 \                             \       3       /                     /
--------------------------------------------------------------------------------------
                                       /      3\                                      
                                     9*\-1 + x /

\frac{- 3 x + \left(x^{3} - 1\right) \left(- 2 \log{\left(x - 1 \right)} + \log{\left(x \left(x + 1\right) + 1 \right)} + 2 \sqrt{3} \operatorname{atan}{\left(\frac{\sqrt{3} \left(2 x + 1\right)}{3} \right)}\right)}{9 \left(x^{3} - 1\right)}

(-3*x + (-1 + x^3)*(-2*log(-1 + x) + 2*sqrt(3)*atan(sqrt(3)*(1 + 2*x)/3) + log(1 + x*(1 + x))))/(9*(-1 + x^3))

Potencias [src]

                                                            /  ___          \
                                                    ___     |\/ 3 *(1 + 2*x)|
                     /         2\               2*\/ 3 *atan|---------------|
  2*log(-1 + x)   log\1 + x + x /       x                   \       3       /
- ------------- + --------------- - --------- + -----------------------------
        9                9                  3                 9              
                                    -3 + 3*x

- \frac{x}{3 x^{3} - 3} - \frac{2 \log{\left(x - 1 \right)}}{9} + \frac{\log{\left(x^{2} + x + 1 \right)}}{9} + \frac{2 \sqrt{3} \operatorname{atan}{\left(\frac{\sqrt{3} \left(2 x + 1\right)}{3} \right)}}{9}

                                                    ___     /  ___ /1   2*x\\
                     /         2\               2*\/ 3 *atan|\/ 3 *|- + ---||
  2*log(-1 + x)   log\1 + x + x /       x                   \      \3    3 //
- ------------- + --------------- - --------- + -----------------------------
        9                9                  3                 9              
                                    -3 + 3*x

- \frac{x}{3 x^{3} - 3} - \frac{2 \log{\left(x - 1 \right)}}{9} + \frac{\log{\left(x^{2} + x + 1 \right)}}{9} + \frac{2 \sqrt{3} \operatorname{atan}{\left(\sqrt{3} \left(\frac{2 x}{3} + \frac{1}{3}\right) \right)}}{9}

-2*log(-1 + x)/9 + log(1 + x + x^2)/9 - x/(-3 + 3*x^3) + 2*sqrt(3)*atan(sqrt(3)*(1/3 + 2*x/3))/9

Compilar la expresión [src]

                                                   ___     /2*x + 1\
                                               2*\/ 3 *atan|-------|
                    / 2        \                           |   ___ |
  2*log(x - 1)   log\x  + x + 1/       x                   \ \/ 3  /
- ------------ + --------------- - --------- + ---------------------
       9                9                  3             9          
                                   -3 + 3*x

- \frac{x}{3 x^{3} - 3} - \frac{2 \log{\left(x - 1 \right)}}{9} + \frac{\log{\left(\left(x^{2} + x\right) + 1 \right)}}{9} + \frac{2 \sqrt{3} \operatorname{atan}{\left(\frac{2 x + 1}{\sqrt{3}} \right)}}{9}

-2*log(x - 1)/9 + log(x^2 + x + 1)/9 - x/(-3 + 3*x^3) + 2*sqrt(3)*atan((2*x + 1)/sqrt(3))/9

Denominador racional [src]

                                                                           /  ___         ___\                                     /  ___         ___\
     /         2\                          3    /         2\       ___     |\/ 3    2*x*\/ 3 |      3                   ___  3     |\/ 3    2*x*\/ 3 |
- log\1 + x + x / - 3*x + 2*log(-1 + x) + x *log\1 + x + x / - 2*\/ 3 *atan|----- + ---------| - 2*x *log(-1 + x) + 2*\/ 3 *x *atan|----- + ---------|
                                                                           \  3         3    /                                     \  3         3    /
------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                              3                                                                       
                                                                      -9 + 9*x

\frac{- 2 x^{3} \log{\left(x - 1 \right)} + x^{3} \log{\left(x^{2} + x + 1 \right)} + 2 \sqrt{3} x^{3} \operatorname{atan}{\left(\frac{2 \sqrt{3} x}{3} + \frac{\sqrt{3}}{3} \right)} - 3 x + 2 \log{\left(x - 1 \right)} - \log{\left(x^{2} + x + 1 \right)} - 2 \sqrt{3} \operatorname{atan}{\left(\frac{2 \sqrt{3} x}{3} + \frac{\sqrt{3}}{3} \right)}}{9 x^{3} - 9}

(-log(1 + x + x^2) - 3*x + 2*log(-1 + x) + x^3*log(1 + x + x^2) - 2*sqrt(3)*atan(sqrt(3)/3 + 2*x*sqrt(3)/3) - 2*x^3*log(-1 + x) + 2*sqrt(3)*x^3*atan(sqrt(3)/3 + 2*x*sqrt(3)/3))/(-9 + 9*x^3)

Respuesta numérica [src]

0.111111111111111*log(x^2 + x + 1) + 0.384900179459751*atan((2*x + 1)/sqrt(3)) - 0.222222222222222*log(x - 1) - x/(-3.0 + 3.0*x^3)

0.111111111111111*log(x^2 + x + 1) + 0.384900179459751*atan((2*x + 1)/sqrt(3)) - 0.222222222222222*log(x - 1) - x/(-3.0 + 3.0*x^3)

Combinatoria [src]

                                                                           /  ___         ___\                                     /  ___         ___\
     /         2\                          3    /         2\       ___     |\/ 3    2*x*\/ 3 |      3                   ___  3     |\/ 3    2*x*\/ 3 |
- log\1 + x + x / - 3*x + 2*log(-1 + x) + x *log\1 + x + x / - 2*\/ 3 *atan|----- + ---------| - 2*x *log(-1 + x) + 2*\/ 3 *x *atan|----- + ---------|
                                                                           \  3         3    /                                     \  3         3    /
------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                          /         2\                                                                
                                                               9*(-1 + x)*\1 + x + x /

\frac{- 2 x^{3} \log{\left(x - 1 \right)} + x^{3} \log{\left(x^{2} + x + 1 \right)} + 2 \sqrt{3} x^{3} \operatorname{atan}{\left(\frac{2 \sqrt{3} x}{3} + \frac{\sqrt{3}}{3} \right)} - 3 x + 2 \log{\left(x - 1 \right)} - \log{\left(x^{2} + x + 1 \right)} - 2 \sqrt{3} \operatorname{atan}{\left(\frac{2 \sqrt{3} x}{3} + \frac{\sqrt{3}}{3} \right)}}{9 \left(x - 1\right) \left(x^{2} + x + 1\right)}

(-log(1 + x + x^2) - 3*x + 2*log(-1 + x) + x^3*log(1 + x + x^2) - 2*sqrt(3)*atan(sqrt(3)/3 + 2*x*sqrt(3)/3) - 2*x^3*log(-1 + x) + 2*sqrt(3)*x^3*atan(sqrt(3)/3 + 2*x*sqrt(3)/3))/(9*(-1 + x)*(1 + x + x^2))

Denominador común [src]

                                                            /  ___         ___\
                                                    ___     |\/ 3    2*x*\/ 3 |
                     /         2\               2*\/ 3 *atan|----- + ---------|
  2*log(-1 + x)   log\1 + x + x /       x                   \  3         3    /
- ------------- + --------------- - --------- + -------------------------------
        9                9                  3                  9               
                                    -3 + 3*x

- \frac{x}{3 x^{3} - 3} - \frac{2 \log{\left(x - 1 \right)}}{9} + \frac{\log{\left(x^{2} + x + 1 \right)}}{9} + \frac{2 \sqrt{3} \operatorname{atan}{\left(\frac{2 \sqrt{3} x}{3} + \frac{\sqrt{3}}{3} \right)}}{9}

-2*log(-1 + x)/9 + log(1 + x + x^2)/9 - x/(-3 + 3*x^3) + 2*sqrt(3)*atan(sqrt(3)/3 + 2*x*sqrt(3)/3)/9

Parte trigonométrica [src]

                                                            /  ___          \
                                                    ___     |\/ 3 *(1 + 2*x)|
                     /         2\               2*\/ 3 *atan|---------------|
  2*log(-1 + x)   log\1 + x + x /       x                   \       3       /
- ------------- + --------------- - --------- + -----------------------------
        9                9                  3                 9              
                                    -3 + 3*x

- \frac{x}{3 x^{3} - 3} - \frac{2 \log{\left(x - 1 \right)}}{9} + \frac{\log{\left(x^{2} + x + 1 \right)}}{9} + \frac{2 \sqrt{3} \operatorname{atan}{\left(\frac{\sqrt{3} \left(2 x + 1\right)}{3} \right)}}{9}

-2*log(-1 + x)/9 + log(1 + x + x^2)/9 - x/(-3 + 3*x^3) + 2*sqrt(3)*atan(sqrt(3)*(1 + 2*x)/3)/9

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¿Cómo usar?

Expresiones idénticas

Expresiones semejantes

Expresiones con funciones

¿Cómo vas a descomponer esta log(x^2+x+1)/9+(2*atan((2*x+1)/sqrt(3)))/3^(3/2)-(2*log(x-1))/9-x/(3*x^3-3) expresión en fracciones?

Solución

¿Cómo vas a descomponer esta log(x^2+x+1)/9+(2atan((2x+1)/sqrt(3)))/3^(3/2)-(2log(x-1))/9-x/(3x^3-3) expresión en fracciones?