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

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

Expresión a simplificar:

Solución

Ha introducido [src] 
    /2*x + 1\                  
atan|-------|                  
    |   ___ |      / 2        \
    \ \/ 3  /   log\x  + x + 1/
------------- - ---------------
      ___         2*(1 + 2*x)  
    \/ 3
atan⁡(2x+13)3−log⁡((x2+x)+1)2(2x+1)\frac{\operatorname{atan}{\left(\frac{2 x + 1}{\sqrt{3}} \right)}}{\sqrt{3}} - \frac{\log{\left(\left(x^{2} + x\right) + 1 \right)}}{2 \left(2 x + 1\right)} 
atan((2*x + 1)/sqrt(3))/sqrt(3) - log(x^2 + x + 1)/(2*(1 + 2*x))
Simplificación general [src] 
                                            /  ___          \
       /         2\       ___               |\/ 3 *(1 + 2*x)|
- 3*log\1 + x + x / + 2*\/ 3 *(1 + 2*x)*atan|---------------|
                                            \       3       /
-------------------------------------------------------------
                         6*(1 + 2*x)
23(2x+1)atan⁡(3(2x+1)3)−3log⁡(x2+x+1)6(2x+1)\frac{2 \sqrt{3} \left(2 x + 1\right) \operatorname{atan}{\left(\frac{\sqrt{3} \left(2 x + 1\right)}{3} \right)} - 3 \log{\left(x^{2} + x + 1 \right)}}{6 \left(2 x + 1\right)} 
(-3*log(1 + x + x^2) + 2*sqrt(3)*(1 + 2*x)*atan(sqrt(3)*(1 + 2*x)/3))/(6*(1 + 2*x))
Respuesta numérica [src] 
0.577350269189626*atan((2*x + 1)/sqrt(3)) - log(x^2 + x + 1)/(2.0 + 4.0*x)
0.577350269189626*atan((2*x + 1)/sqrt(3)) - log(x^2 + x + 1)/(2.0 + 4.0*x)
Unión de expresiones racionales [src] 
                                              /  ___          \
                            ___               |\/ 3 *(1 + 2*x)|
-3*log(1 + x*(1 + x)) + 2*\/ 3 *(1 + 2*x)*atan|---------------|
                                              \       3       /
---------------------------------------------------------------
                          6*(1 + 2*x)
23(2x+1)atan⁡(3(2x+1)3)−3log⁡(x(x+1)+1)6(2x+1)\frac{2 \sqrt{3} \left(2 x + 1\right) \operatorname{atan}{\left(\frac{\sqrt{3} \left(2 x + 1\right)}{3} \right)} - 3 \log{\left(x \left(x + 1\right) + 1 \right)}}{6 \left(2 x + 1\right)} 
(-3*log(1 + x*(1 + x)) + 2*sqrt(3)*(1 + 2*x)*atan(sqrt(3)*(1 + 2*x)/3))/(6*(1 + 2*x))
Denominador común [src] 
                              /  ___         ___\
                      ___     |\/ 3    2*x*\/ 3 |
     /         2\   \/ 3 *atan|----- + ---------|
  log\1 + x + x /             \  3         3    /
- --------------- + -----------------------------
      2 + 4*x                     3
3atan⁡(23x3+33)3−log⁡(x2+x+1)4x+2\frac{\sqrt{3} \operatorname{atan}{\left(\frac{2 \sqrt{3} x}{3} + \frac{\sqrt{3}}{3} \right)}}{3} - \frac{\log{\left(x^{2} + x + 1 \right)}}{4 x + 2} 
-log(1 + x + x^2)/(2 + 4*x) + sqrt(3)*atan(sqrt(3)/3 + 2*x*sqrt(3)/3)/3
Combinatoria [src] 
                                  /  ___         ___\                 /  ___         ___\
       /         2\       ___     |\/ 3    2*x*\/ 3 |         ___     |\/ 3    2*x*\/ 3 |
- 3*log\1 + x + x / + 2*\/ 3 *atan|----- + ---------| + 4*x*\/ 3 *atan|----- + ---------|
                                  \  3         3    /                 \  3         3    /
-----------------------------------------------------------------------------------------
                                       6*(1 + 2*x)
43xatan⁡(23x3+33)−3log⁡(x2+x+1)+23atan⁡(23x3+33)6(2x+1)\frac{4 \sqrt{3} x \operatorname{atan}{\left(\frac{2 \sqrt{3} x}{3} + \frac{\sqrt{3}}{3} \right)} - 3 \log{\left(x^{2} + x + 1 \right)} + 2 \sqrt{3} \operatorname{atan}{\left(\frac{2 \sqrt{3} x}{3} + \frac{\sqrt{3}}{3} \right)}}{6 \left(2 x + 1\right)} 
(-3*log(1 + x + x^2) + 2*sqrt(3)*atan(sqrt(3)/3 + 2*x*sqrt(3)/3) + 4*x*sqrt(3)*atan(sqrt(3)/3 + 2*x*sqrt(3)/3))/(6*(1 + 2*x))
Denominador racional [src] 
                                  /  ___         ___\                 /  ___         ___\
       /         2\       ___     |\/ 3    2*x*\/ 3 |         ___     |\/ 3    2*x*\/ 3 |
- 3*log\1 + x + x / + 2*\/ 3 *atan|----- + ---------| + 4*x*\/ 3 *atan|----- + ---------|
                                  \  3         3    /                 \  3         3    /
-----------------------------------------------------------------------------------------
                                         6 + 12*x
43xatan⁡(23x3+33)−3log⁡(x2+x+1)+23atan⁡(23x3+33)12x+6\frac{4 \sqrt{3} x \operatorname{atan}{\left(\frac{2 \sqrt{3} x}{3} + \frac{\sqrt{3}}{3} \right)} - 3 \log{\left(x^{2} + x + 1 \right)} + 2 \sqrt{3} \operatorname{atan}{\left(\frac{2 \sqrt{3} x}{3} + \frac{\sqrt{3}}{3} \right)}}{12 x + 6} 
(-3*log(1 + x + x^2) + 2*sqrt(3)*atan(sqrt(3)/3 + 2*x*sqrt(3)/3) + 4*x*sqrt(3)*atan(sqrt(3)/3 + 2*x*sqrt(3)/3))/(6 + 12*x)
Potencias [src] 
                      ___     /  ___ /1   2*x\\
     /         2\   \/ 3 *atan|\/ 3 *|- + ---||
  log\1 + x + x /             \      \3    3 //
- --------------- + ---------------------------
      2 + 4*x                    3
3atan⁡(3(2x3+13))3−log⁡(x2+x+1)4x+2\frac{\sqrt{3} \operatorname{atan}{\left(\sqrt{3} \left(\frac{2 x}{3} + \frac{1}{3}\right) \right)}}{3} - \frac{\log{\left(x^{2} + x + 1 \right)}}{4 x + 2} 
                              /  ___          \
                      ___     |\/ 3 *(1 + 2*x)|
     /         2\   \/ 3 *atan|---------------|
  log\1 + x + x /             \       3       /
- --------------- + ---------------------------
      2 + 4*x                    3
3atan⁡(3(2x+1)3)3−log⁡(x2+x+1)4x+2\frac{\sqrt{3} \operatorname{atan}{\left(\frac{\sqrt{3} \left(2 x + 1\right)}{3} \right)}}{3} - \frac{\log{\left(x^{2} + x + 1 \right)}}{4 x + 2} 
-log(1 + x + x^2)/(2 + 4*x) + sqrt(3)*atan(sqrt(3)*(1 + 2*x)/3)/3
Parte trigonométrica [src] 
                              /  ___          \
                      ___     |\/ 3 *(1 + 2*x)|
     /         2\   \/ 3 *atan|---------------|
  log\1 + x + x /             \       3       /
- --------------- + ---------------------------
      2 + 4*x                    3
3atan⁡(3(2x+1)3)3−log⁡(x2+x+1)4x+2\frac{\sqrt{3} \operatorname{atan}{\left(\frac{\sqrt{3} \left(2 x + 1\right)}{3} \right)}}{3} - \frac{\log{\left(x^{2} + x + 1 \right)}}{4 x + 2} 
-log(1 + x + x^2)/(2 + 4*x) + sqrt(3)*atan(sqrt(3)*(1 + 2*x)/3)/3
Compilar la expresión [src] 
                      ___     /2*x + 1\
                    \/ 3 *atan|-------|
     / 2        \             |   ___ |
  log\x  + x + 1/             \ \/ 3  /
- --------------- + -------------------
      2 + 4*x                3
3atan⁡(2x+13)3−log⁡((x2+x)+1)4x+2\frac{\sqrt{3} \operatorname{atan}{\left(\frac{2 x + 1}{\sqrt{3}} \right)}}{3} - \frac{\log{\left(\left(x^{2} + x\right) + 1 \right)}}{4 x + 2} 
-log(x^2 + x + 1)/(2 + 4*x) + sqrt(3)*atan((2*x + 1)/sqrt(3))/3
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