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45*x*y^2/(75*y^2)
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z-2/4*z^2+16*z+16/(z/2*z-4-z^2+4/2*z^2-8-2/z^2+2*z)
Factorizar el polinomio:
y^7-2*y^5
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y*x^2+i*y^3/3
y^8-1
Descomponer al cuadrado:
y^4-9*y^2+10
y^4-9*y^2-15
y^4-9*y^2+4
y^4-9*y^2+2
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(y)/(2*x)
log(x-5*x^2)/(2*sqrt(x+2))+sqrt(x+2)*(1-10*x)/(x-5*x^2)
log(x+a)/(2*a)-log(x-a)/(2*a)
log(x^2+2)/9-atan(x/sqrt(2))/(9*sqrt(2))-(2*log(x-1))/9-1/(3*x-3)
log((sqrt(1-a^2/x^2)-1)/(sqrt(1-a^2/x^2)+1))
Arcotangente arctan
atan(3*pi/2)/(9*pi^2)
atan(x)/2+x/(2+2*x^2)
atan(sin(2*x)/(sqrt(5)*(1+cos(2*x))))/sqrt(5)
atan(5*x)/(x^3)-5/(2*x^2*(25*x^2+1))-125/(2+50*x^2)
atan(x/2)/16+x/(32+8*x^2)
Raíz cuadrada sqrt
Sqrt(2b+2*sqrt(b^2-4))/(sqrt(b^2-4)+(b+2))
sqrt(16*x^2*(1-5/(16*x)))
sqrt(x-x^2)/2+1/(4*sqrt(1-(2*x-1)^2))+(1/2-x)*(2*x-1)/(4*sqrt(x-x^2))
sqrt(x^3*cos(x))*(-x^3*sin(x)/2+3*x^2*cos(x)/2)/(x^3*cos(x))
sqrt(m)/((m-16))-sqrt(m)/(((4-sqrt(m))^2))еслиm=1/3
Logaritmo log
log(y)/(2*x)
log(x-5*x^2)/(2*sqrt(x+2))+sqrt(x+2)*(1-10*x)/(x-5*x^2)
log(x+a)/(2*a)-log(x-a)/(2*a)
log(x^2+2)/9-atan(x/sqrt(2))/(9*sqrt(2))-(2*log(x-1))/9-1/(3*x-3)
log((sqrt(1-a^2/x^2)-1)/(sqrt(1-a^2/x^2)+1))

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 /

(-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

-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

Otras calculadoras

¿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?