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

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

Solución

Ha introducido [src]

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

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

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

Simplificación general [src]

              /                                           /    ___\\
              |                      /     2\     ___     |x*\/ 2 ||
-6 + (-1 + x)*|-4*log(-1 + x) + 2*log\2 + x / - \/ 2 *atan|-------||
              \                                           \   2   //
--------------------------------------------------------------------
                            18*(-1 + x)

$$\frac{\left(x - 1\right) \left(- 4 \log{\left(x - 1 \right)} + 2 \log{\left(x^{2} + 2 \right)} - \sqrt{2} \operatorname{atan}{\left(\frac{\sqrt{2} x}{2} \right)}\right) - 6}{18 \left(x - 1\right)}$$

(-6 + (-1 + x)*(-4*log(-1 + x) + 2*log(2 + x^2) - sqrt(2)*atan(x*sqrt(2)/2)))/(18*(-1 + x))

Respuesta numérica [src]

-1/(-3.0 + 3.0*x) + 0.111111111111111*log(x^2 + 2) - 0.222222222222222*log(x - 1) - 0.0785674201318386*atan(x/sqrt(2))

-1/(-3.0 + 3.0*x) + 0.111111111111111*log(x^2 + 2) - 0.222222222222222*log(x - 1) - 0.0785674201318386*atan(x/sqrt(2))

Combinatoria [src]

 /                                              /    ___\                                                   /    ___\\ 
 |                         /     2\     ___     |x*\/ 2 |          /     2\                         ___     |x*\/ 2 || 
-|6 - 4*log(-1 + x) + 2*log\2 + x / - \/ 2 *atan|-------| - 2*x*log\2 + x / + 4*x*log(-1 + x) + x*\/ 2 *atan|-------|| 
 \                                              \   2   /                                                   \   2   // 
-----------------------------------------------------------------------------------------------------------------------
                                                      18*(-1 + x)

$$- \frac{4 x \log{\left(x - 1 \right)} - 2 x \log{\left(x^{2} + 2 \right)} + \sqrt{2} x \operatorname{atan}{\left(\frac{\sqrt{2} x}{2} \right)} - 4 \log{\left(x - 1 \right)} + 2 \log{\left(x^{2} + 2 \right)} - \sqrt{2} \operatorname{atan}{\left(\frac{\sqrt{2} x}{2} \right)} + 6}{18 \left(x - 1\right)}$$

-(6 - 4*log(-1 + x) + 2*log(2 + x^2) - sqrt(2)*atan(x*sqrt(2)/2) - 2*x*log(2 + x^2) + 4*x*log(-1 + x) + x*sqrt(2)*atan(x*sqrt(2)/2))/(18*(-1 + x))

Unión de expresiones racionales [src]

              /                                           /    ___\\
              |                      /     2\     ___     |x*\/ 2 ||
-6 + (-1 + x)*|-4*log(-1 + x) + 2*log\2 + x / - \/ 2 *atan|-------||
              \                                           \   2   //
--------------------------------------------------------------------
                            18*(-1 + x)

(-6 + (-1 + x)*(-4*log(-1 + x) + 2*log(2 + x^2) - sqrt(2)*atan(x*sqrt(2)/2)))/(18*(-1 + x))

Parte trigonométrica [src]

                                                     /    ___\
                                             ___     |x*\/ 2 |
                                /     2\   \/ 2 *atan|-------|
     1       2*log(-1 + x)   log\2 + x /             \   2   /
- -------- - ------------- + ----------- - -------------------
  -3 + 3*x         9              9                 18

$$- \frac{2 \log{\left(x - 1 \right)}}{9} + \frac{\log{\left(x^{2} + 2 \right)}}{9} - \frac{\sqrt{2} \operatorname{atan}{\left(\frac{\sqrt{2} x}{2} \right)}}{18} - \frac{1}{3 x - 3}$$

-1/(-3 + 3*x) - 2*log(-1 + x)/9 + log(2 + x^2)/9 - sqrt(2)*atan(x*sqrt(2)/2)/18

Denominador común [src]

                                                     /    ___\
                                             ___     |x*\/ 2 |
                                /     2\   \/ 2 *atan|-------|
     1       2*log(-1 + x)   log\2 + x /             \   2   /
- -------- - ------------- + ----------- - -------------------
  -3 + 3*x         9              9                 18

$$- \frac{2 \log{\left(x - 1 \right)}}{9} + \frac{\log{\left(x^{2} + 2 \right)}}{9} - \frac{\sqrt{2} \operatorname{atan}{\left(\frac{\sqrt{2} x}{2} \right)}}{18} - \frac{1}{3 x - 3}$$

-1/(-3 + 3*x) - 2*log(-1 + x)/9 + log(2 + x^2)/9 - sqrt(2)*atan(x*sqrt(2)/2)/18

Potencias [src]

                                                     /    ___\
                                             ___     |x*\/ 2 |
                                /     2\   \/ 2 *atan|-------|
     1       2*log(-1 + x)   log\2 + x /             \   2   /
- -------- - ------------- + ----------- - -------------------
  -3 + 3*x         9              9                 18

$$- \frac{2 \log{\left(x - 1 \right)}}{9} + \frac{\log{\left(x^{2} + 2 \right)}}{9} - \frac{\sqrt{2} \operatorname{atan}{\left(\frac{\sqrt{2} x}{2} \right)}}{18} - \frac{1}{3 x - 3}$$

-1/(-3 + 3*x) - 2*log(-1 + x)/9 + log(2 + x^2)/9 - sqrt(2)*atan(x*sqrt(2)/2)/18

Denominador racional [src]

                                               /    ___\                                                   /    ___\
          /     2\                     ___     |x*\/ 2 |                            /     2\       ___     |x*\/ 2 |
-6 - 2*log\2 + x / + 4*log(-1 + x) + \/ 2 *atan|-------| - 4*x*log(-1 + x) + 2*x*log\2 + x / - x*\/ 2 *atan|-------|
                                               \   2   /                                                   \   2   /
--------------------------------------------------------------------------------------------------------------------
                                                     -18 + 18*x

$$\frac{- 4 x \log{\left(x - 1 \right)} + 2 x \log{\left(x^{2} + 2 \right)} - \sqrt{2} x \operatorname{atan}{\left(\frac{\sqrt{2} x}{2} \right)} + 4 \log{\left(x - 1 \right)} - 2 \log{\left(x^{2} + 2 \right)} + \sqrt{2} \operatorname{atan}{\left(\frac{\sqrt{2} x}{2} \right)} - 6}{18 x - 18}$$

(-6 - 2*log(2 + x^2) + 4*log(-1 + x) + sqrt(2)*atan(x*sqrt(2)/2) - 4*x*log(-1 + x) + 2*x*log(2 + x^2) - x*sqrt(2)*atan(x*sqrt(2)/2))/(-18 + 18*x)

Abrimos la expresión [src]

                                           ___     /  x  \
                                         \/ 2 *atan|-----|
               / 2    \                            |  ___|
     1      log\x  + 2/   2*log(x - 1)             \\/ 2 /
- ------- + ----------- - ------------ - -----------------
  3*x - 3        9             9                 18

$$- \frac{2 \log{\left(x - 1 \right)}}{9} + \frac{\log{\left(x^{2} + 2 \right)}}{9} - \frac{\sqrt{2} \operatorname{atan}{\left(\frac{x}{\sqrt{2}} \right)}}{18} - \frac{1}{3 x - 3}$$

-1/(3*x - 3) + log(x^2 + 2)/9 - 2*log(x - 1)/9 - sqrt(2)*atan(x/sqrt(2))/18

Compilar la expresión [src]

                                            ___     /  x  \
                                          \/ 2 *atan|-----|
                               / 2    \             |  ___|
     1       2*log(x - 1)   log\x  + 2/             \\/ 2 /
- -------- - ------------ + ----------- - -----------------
  -3 + 3*x        9              9                18

$$- \frac{2 \log{\left(x - 1 \right)}}{9} + \frac{\log{\left(x^{2} + 2 \right)}}{9} - \frac{\sqrt{2} \operatorname{atan}{\left(\frac{x}{\sqrt{2}} \right)}}{18} - \frac{1}{3 x - 3}$$

-1/(-3 + 3*x) - 2*log(x - 1)/9 + log(x^2 + 2)/9 - sqrt(2)*atan(x/sqrt(2))/18

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Expresiones con funciones

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

Solución

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