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¿cómo vas a descomponer esta expresión en fracciones?:
((y-9)/(y-8))*((y^2-64)/(y^2-16*y+64))
(z-(5*z)/z+1)/(z-4)/(z+1)
(s+3)/(5*s+15)
c^(k+5)*c^k/(c^2)^k
Factorizar el polinomio:
y^3+y
y^3+4^3
z^3-5*z^2+9*z-45
y^3-3*y+3^3
Descomponer al cuadrado:
-y^4+8*y^2+2
-y^4+8*y^2+9
-y^4-7*y^2-9
y^4-7*y^2+4
Expresiones idénticas
exp(x^ dos *(- tres))*(cinco ^(x+ cuatro)*((dos *x+ uno)^ tres)^(uno / cuatro)*log(cinco)+ tres * cinco ^(x+ cuatro)*((dos *x+ uno)^ tres)^(uno / cuatro)/((dos *(dos *x+ uno))))/cot(x/ dos)+ cinco ^(x+ cuatro)*((dos *x+ uno)^ tres)^(uno / cuatro)*(exp(tres *x^ dos)*(uno / dos +cot(x/ dos)^ dos / dos)- seis *x*cot(x/ dos)*exp(tres *x^ dos))*exp(x^ dos *(- seis))/cot(x/ dos)^ dos
exponente de (x al cuadrado multiplicar por ( menos 3)) multiplicar por (5 en el grado (x más 4) multiplicar por ((2 multiplicar por x más 1) al cubo ) en el grado (1 dividir por 4) multiplicar por logaritmo de (5) más 3 multiplicar por 5 en el grado (x más 4) multiplicar por ((2 multiplicar por x más 1) al cubo ) en el grado (1 dividir por 4) dividir por ((2 multiplicar por (2 multiplicar por x más 1)))) dividir por cotangente de (x dividir por 2) más 5 en el grado (x más 4) multiplicar por ((2 multiplicar por x más 1) al cubo ) en el grado (1 dividir por 4) multiplicar por ( exponente de (3 multiplicar por x al cuadrado ) multiplicar por (1 dividir por 2 más cotangente de (x dividir por 2) al cuadrado dividir por 2) menos 6 multiplicar por x multiplicar por cotangente de (x dividir por 2) multiplicar por exponente de (3 multiplicar por x al cuadrado )) multiplicar por exponente de (x al cuadrado multiplicar por ( menos 6)) dividir por cotangente de (x dividir por 2) al cuadrado
exponente de (x en el grado dos multiplicar por ( menos tres)) multiplicar por (cinco en el grado (x más cuatro) multiplicar por ((dos multiplicar por x más uno) en el grado tres) en el grado (uno dividir por cuatro) multiplicar por logaritmo de (cinco) más tres multiplicar por cinco en el grado (x más cuatro) multiplicar por ((dos multiplicar por x más uno) en el grado tres) en el grado (uno dividir por cuatro) dividir por ((dos multiplicar por (dos multiplicar por x más uno)))) dividir por cotangente de (x dividir por dos) más cinco en el grado (x más cuatro) multiplicar por ((dos multiplicar por x más uno) en el grado tres) en el grado (uno dividir por cuatro) multiplicar por ( exponente de (tres multiplicar por x en el grado dos) multiplicar por (uno dividir por dos más cotangente de (x dividir por dos) en el grado dos dividir por dos) menos seis multiplicar por x multiplicar por cotangente de (x dividir por dos) multiplicar por exponente de (tres multiplicar por x en el grado dos)) multiplicar por exponente de (x en el grado dos multiplicar por ( menos seis)) dividir por cotangente de (x dividir por dos) en el grado dos
exp(x2*(-3))*(5(x+4)*((2*x+1)3)(1/4)*log(5)+3*5(x+4)*((2*x+1)3)(1/4)/((2*(2*x+1))))/cot(x/2)+5(x+4)*((2*x+1)3)(1/4)*(exp(3*x2)*(1/2+cot(x/2)2/2)-6*x*cot(x/2)*exp(3*x2))*exp(x2*(-6))/cot(x/2)2
expx2*-3*5x+4*2*x+131/4*log5+3*5x+4*2*x+131/4/2*2*x+1/cotx/2+5x+4*2*x+131/4*exp3*x2*1/2+cotx/22/2-6*x*cotx/2*exp3*x2*expx2*-6/cotx/22
exp(x²*(-3))*(5^(x+4)*((2*x+1)³)^(1/4)*log(5)+3*5^(x+4)*((2*x+1)³)^(1/4)/((2*(2*x+1))))/cot(x/2)+5^(x+4)*((2*x+1)³)^(1/4)*(exp(3*x²)*(1/2+cot(x/2)²/2)-6*x*cot(x/2)*exp(3*x²))*exp(x²*(-6))/cot(x/2)²
exp(x en el grado 2*(-3))*(5 en el grado (x+4)*((2*x+1) en el grado 3) en el grado (1/4)*log(5)+3*5 en el grado (x+4)*((2*x+1) en el grado 3) en el grado (1/4)/((2*(2*x+1))))/cot(x/2)+5 en el grado (x+4)*((2*x+1) en el grado 3) en el grado (1/4)*(exp(3*x en el grado 2)*(1/2+cot(x/2) en el grado 2/2)-6*x*cot(x/2)*exp(3*x en el grado 2))*exp(x en el grado 2*(-6))/cot(x/2) en el grado 2
exp(x^2(-3))(5^(x+4)((2x+1)^3)^(1/4)log(5)+35^(x+4)((2x+1)^3)^(1/4)/((2(2x+1))))/cot(x/2)+5^(x+4)((2x+1)^3)^(1/4)(exp(3x^2)(1/2+cot(x/2)^2/2)-6xcot(x/2)exp(3x^2))exp(x^2(-6))/cot(x/2)^2
exp(x2(-3))(5(x+4)((2x+1)3)(1/4)log(5)+35(x+4)((2x+1)3)(1/4)/((2(2x+1))))/cot(x/2)+5(x+4)((2x+1)3)(1/4)(exp(3x2)(1/2+cot(x/2)2/2)-6xcot(x/2)exp(3x2))exp(x2(-6))/cot(x/2)2
expx2-35x+42x+131/4log5+35x+42x+131/4/22x+1/cotx/2+5x+42x+131/4exp3x21/2+cotx/22/2-6xcotx/2exp3x2expx2-6/cotx/22
expx^2-35^x+42x+1^3^1/4log5+35^x+42x+1^3^1/4/22x+1/cotx/2+5^x+42x+1^3^1/4exp3x^21/2+cotx/2^2/2-6xcotx/2exp3x^2expx^2-6/cotx/2^2
exp(x^2*(-3))*(5^(x+4)*((2*x+1)^3)^(1 dividir por 4)*log(5)+3*5^(x+4)*((2*x+1)^3)^(1 dividir por 4) dividir por ((2*(2*x+1)))) dividir por cot(x dividir por 2)+5^(x+4)*((2*x+1)^3)^(1 dividir por 4)*(exp(3*x^2)*(1 dividir por 2+cot(x dividir por 2)^2 dividir por 2)-6*x*cot(x dividir por 2)*exp(3*x^2))*exp(x^2*(-6)) dividir por cot(x dividir por 2)^2
Expresiones semejantes
exp(x^2*(-3))*(5^(x+4)*((2*x+1)^3)^(1/4)*log(5)+3*5^(x+4)*((2*x+1)^3)^(1/4)/((2*(2*x+1))))/cot(x/2)+5^(x+4)*((2*x-1)^3)^(1/4)*(exp(3*x^2)*(1/2+cot(x/2)^2/2)-6*x*cot(x/2)*exp(3*x^2))*exp(x^2*(-6))/cot(x/2)^2
exp(x^2*(-3))*(5^(x+4)*((2*x+1)^3)^(1/4)*log(5)-3*5^(x+4)*((2*x+1)^3)^(1/4)/((2*(2*x+1))))/cot(x/2)+5^(x+4)*((2*x+1)^3)^(1/4)*(exp(3*x^2)*(1/2+cot(x/2)^2/2)-6*x*cot(x/2)*exp(3*x^2))*exp(x^2*(-6))/cot(x/2)^2
exp(x^2*(-3))*(5^(x+4)*((2*x+1)^3)^(1/4)*log(5)+3*5^(x+4)*((2*x-1)^3)^(1/4)/((2*(2*x+1))))/cot(x/2)+5^(x+4)*((2*x+1)^3)^(1/4)*(exp(3*x^2)*(1/2+cot(x/2)^2/2)-6*x*cot(x/2)*exp(3*x^2))*exp(x^2*(-6))/cot(x/2)^2
exp(x^2*(-3))*(5^(x+4)*((2*x+1)^3)^(1/4)*log(5)+3*5^(x+4)*((2*x+1)^3)^(1/4)/((2*(2*x+1))))/cot(x/2)+5^(x+4)*((2*x+1)^3)^(1/4)*(exp(3*x^2)*(1/2-cot(x/2)^2/2)-6*x*cot(x/2)*exp(3*x^2))*exp(x^2*(-6))/cot(x/2)^2
exp(x^2*(-3))*(5^(x+4)*((2*x+1)^3)^(1/4)*log(5)+3*5^(x+4)*((2*x+1)^3)^(1/4)/((2*(2*x+1))))/cot(x/2)+5^(x-4)*((2*x+1)^3)^(1/4)*(exp(3*x^2)*(1/2+cot(x/2)^2/2)-6*x*cot(x/2)*exp(3*x^2))*exp(x^2*(-6))/cot(x/2)^2
exp(x^2*(-3))*(5^(x+4)*((2*x+1)^3)^(1/4)*log(5)+3*5^(x+4)*((2*x+1)^3)^(1/4)/((2*(2*x+1))))/cot(x/2)+5^(x+4)*((2*x+1)^3)^(1/4)*(exp(3*x^2)*(1/2+cot(x/2)^2/2)-6*x*cot(x/2)*exp(3*x^2))*exp(x^2*(6))/cot(x/2)^2
exp(x^2*(-3))*(5^(x+4)*((2*x+1)^3)^(1/4)*log(5)+3*5^(x+4)*((2*x+1)^3)^(1/4)/((2*(2*x-1))))/cot(x/2)+5^(x+4)*((2*x+1)^3)^(1/4)*(exp(3*x^2)*(1/2+cot(x/2)^2/2)-6*x*cot(x/2)*exp(3*x^2))*exp(x^2*(-6))/cot(x/2)^2
exp(x^2*(3))*(5^(x+4)*((2*x+1)^3)^(1/4)*log(5)+3*5^(x+4)*((2*x+1)^3)^(1/4)/((2*(2*x+1))))/cot(x/2)+5^(x+4)*((2*x+1)^3)^(1/4)*(exp(3*x^2)*(1/2+cot(x/2)^2/2)-6*x*cot(x/2)*exp(3*x^2))*exp(x^2*(-6))/cot(x/2)^2
exp(x^2*(-3))*(5^(x+4)*((2*x+1)^3)^(1/4)*log(5)+3*5^(x+4)*((2*x+1)^3)^(1/4)/((2*(2*x+1))))/cot(x/2)-5^(x+4)*((2*x+1)^3)^(1/4)*(exp(3*x^2)*(1/2+cot(x/2)^2/2)-6*x*cot(x/2)*exp(3*x^2))*exp(x^2*(-6))/cot(x/2)^2
exp(x^2*(-3))*(5^(x+4)*((2*x+1)^3)^(1/4)*log(5)+3*5^(x+4)*((2*x+1)^3)^(1/4)/((2*(2*x+1))))/cot(x/2)+5^(x+4)*((2*x+1)^3)^(1/4)*(exp(3*x^2)*(1/2+cot(x/2)^2/2)+6*x*cot(x/2)*exp(3*x^2))*exp(x^2*(-6))/cot(x/2)^2
exp(x^2*(-3))*(5^(x+4)*((2*x+1)^3)^(1/4)*log(5)+3*5^(x-4)*((2*x+1)^3)^(1/4)/((2*(2*x+1))))/cot(x/2)+5^(x+4)*((2*x+1)^3)^(1/4)*(exp(3*x^2)*(1/2+cot(x/2)^2/2)-6*x*cot(x/2)*exp(3*x^2))*exp(x^2*(-6))/cot(x/2)^2
exp(x^2*(-3))*(5^(x+4)*((2*x-1)^3)^(1/4)*log(5)+3*5^(x+4)*((2*x+1)^3)^(1/4)/((2*(2*x+1))))/cot(x/2)+5^(x+4)*((2*x+1)^3)^(1/4)*(exp(3*x^2)*(1/2+cot(x/2)^2/2)-6*x*cot(x/2)*exp(3*x^2))*exp(x^2*(-6))/cot(x/2)^2
exp(x^2*(-3))*(5^(x-4)*((2*x+1)^3)^(1/4)*log(5)+3*5^(x+4)*((2*x+1)^3)^(1/4)/((2*(2*x+1))))/cot(x/2)+5^(x+4)*((2*x+1)^3)^(1/4)*(exp(3*x^2)*(1/2+cot(x/2)^2/2)-6*x*cot(x/2)*exp(3*x^2))*exp(x^2*(-6))/cot(x/2)^2
Expresiones con funciones
Exponente exp
exp(x)/(4*(1+(e^x-3)^2/4))
exp(x+3)/(x+3)-exp(x+3)/(x+3)^2
exp(x)/(x^2+1)-2*x*exp(x)/(x^2+1)^2
exp(-x)/(1+exp(x))^2
exp(1/(x-3))/((x-3)^2*(x-3)^2)-(6-2*x)*exp(1/(x-3))/(x-3)^4
Logaritmo log
log(x+1)/4+(3*log(x-1))/4+3/(2+2*x)
log(x)^5100+2*log(x)^(101/2)/(a*x-1)-1/(a*x+1)
log(sqrt(1-1/e^(2*x))+1)/(2*log(e))-log(sqrt(1-1/e^(2*x))-1)/(2*log(e))
log(tan(x)^2+1)/8-log(tan(x)+1)/4+(tan(x)-1)/(4*tan(x)^2+4)
log((sqrt(x^2+2)-x*sqrt(3))/(sqrt(x^2+2)+x*sqrt(3)))/log(10)
Exponente exp
exp(x)/(4*(1+(e^x-3)^2/4))
exp(x+3)/(x+3)-exp(x+3)/(x+3)^2
exp(x)/(x^2+1)-2*x*exp(x)/(x^2+1)^2
exp(-x)/(1+exp(x))^2
exp(1/(x-3))/((x-3)^2*(x-3)^2)-(6-2*x)*exp(1/(x-3))/(x-3)^4
Exponente exp
exp(x)/(4*(1+(e^x-3)^2/4))
exp(x+3)/(x+3)-exp(x+3)/(x+3)^2
exp(x)/(x^2+1)-2*x*exp(x)/(x^2+1)^2
exp(-x)/(1+exp(x))^2
exp(1/(x-3))/((x-3)^2*(x-3)^2)-(6-2*x)*exp(1/(x-3))/(x-3)^4
Exponente exp
exp(x)/(4*(1+(e^x-3)^2/4))
exp(x+3)/(x+3)-exp(x+3)/(x+3)^2
exp(x)/(x^2+1)-2*x*exp(x)/(x^2+1)^2
exp(-x)/(1+exp(x))^2
exp(1/(x-3))/((x-3)^2*(x-3)^2)-(6-2*x)*exp(1/(x-3))/(x-3)^4

Simplificación de expresiones/ Descomposición en fracciones simples/ exp(x^2*(-3))*(5^(x+4)*((2*x+1)^3)^(1/4)*log(5)+3*5^(x+4)*((2*x+1)^3)^(1/4)/((2*(2*x+1))))/cot(x/2)+5^(x+4)*((2*x+1)^3)^(1/4)*(exp(3*x^2)*(1/2+cot(x/2)^2/2)-6*x*cot(x/2)*exp(3*x^2))*exp(x^2*(-6))/cot(x/2)^2

¿Cómo vas a descomponer esta exp(x^2(-3))(5^(x+4)((2x+1)^3)^(1/4)log(5)+35^(x+4)((2x+1)^3)^(1/4)/((2(2x+1))))/cot(x/2)+5^(x+4)((2x+1)^3)^(1/4)(exp(3x^2)(1/2+cot(x/2)^2/2)-6x*cot(x/2)exp(3x^2))exp(x^2(-6))/cot(x/2)^2 expresión en fracciones?

Solución

Ha introducido [src]

         /                                            ____________\                          /      /       2/x\\                   \         
  2      |          ____________             x + 4 4 /          3 |             ____________ |    2 |    cot |-||                  2|   2     
 x *(-3) | x + 4 4 /          3           3*5     *\/  (2*x + 1)  |    x + 4 4 /          3  | 3*x  |1       \2/|          /x\  3*x |  x *(-6)
e       *|5     *\/  (2*x + 1)  *log(5) + ------------------------|   5     *\/  (2*x + 1)  *|e    *|- + -------| - 6*x*cot|-|*e    |*e       
         \                                      2*(2*x + 1)       /                          \      \2      2   /          \2/      /         
------------------------------------------------------------------- + ------------------------------------------------------------------------
                                  /x\                                                                    2/x\                                 
                               cot|-|                                                                 cot |-|                                 
                                  \2/                                                                     \2/

\frac{5^{x + 4} \sqrt[4]{\left(2 x + 1\right)^{3}} \left(- 6 x \cot{\left(\frac{x}{2} \right)} e^{3 x^{2}} + \left(\frac{\cot^{2}{\left(\frac{x}{2} \right)}}{2} + \frac{1}{2}\right) e^{3 x^{2}}\right) e^{\left(-6\right) x^{2}}}{\cot^{2}{\left(\frac{x}{2} \right)}} + \frac{\left(5^{x + 4} \sqrt[4]{\left(2 x + 1\right)^{3}} \log{\left(5 \right)} + \frac{3 \cdot 5^{x + 4} \sqrt[4]{\left(2 x + 1\right)^{3}}}{2 \left(2 x + 1\right)}\right) e^{\left(-3\right) x^{2}}}{\cot{\left(\frac{x}{2} \right)}}

(exp(x^2*(-3))*((5^(x + 4)*((2*x + 1)^3)^(1/4))*log(5) + ((3*5^(x + 4))*((2*x + 1)^3)^(1/4))/((2*(2*x + 1)))))/cot(x/2) + (((5^(x + 4)*((2*x + 1)^3)^(1/4))*(exp(3*x^2)*(1/2 + cot(x/2)^2/2) - (6*x)*cot(x/2)*exp(3*x^2)))*exp(x^2*(-6)))/cot(x/2)^2

Simplificación general [src]

          ____________                                                                                        2
     x 4 /          3     2/x\ /                           /x\             /        2/x\           /x\\\  -3*x 
625*5 *\/  (1 + 2*x)  *tan |-|*|(3 + (1 + 2*x)*log(25))*cot|-| - (1 + 2*x)*|-1 - cot |-| + 12*x*cot|-|||*e     
                           \2/ \                           \2/             \         \2/           \2///       
---------------------------------------------------------------------------------------------------------------
                                                  2*(1 + 2*x)

\frac{625 \cdot 5^{x} \left(- \left(2 x + 1\right) \left(12 x \cot{\left(\frac{x}{2} \right)} - \cot^{2}{\left(\frac{x}{2} \right)} - 1\right) + \left(\left(2 x + 1\right) \log{\left(25 \right)} + 3\right) \cot{\left(\frac{x}{2} \right)}\right) \sqrt[4]{\left(2 x + 1\right)^{3}} e^{- 3 x^{2}} \tan^{2}{\left(\frac{x}{2} \right)}}{2 \left(2 x + 1\right)}

625*5^x*((1 + 2*x)^3)^(1/4)*tan(x/2)^2*((3 + (1 + 2*x)*log(25))*cot(x/2) - (1 + 2*x)*(-1 - cot(x/2)^2 + 12*x*cot(x/2)))*exp(-3*x^2)/(2*(1 + 2*x))

Respuesta numérica [src]

(2.70674114227851*5.0^(4.0 + x)*((0.5 + x)^3)^0.25 + 5.04537849152229*5.0^(4.0 + x)*((0.5 + x)^3)^0.25/(2.0 + 4.0*x))*exp(x^2*(-3))/cot(x/2) + 1.68179283050743*5.0^(4.0 + x)*((0.5 + x)^3)^0.25*((0.5 + 0.5*cot(x/2)^2)*exp(3*x^2) - 6.0*x*cot(x/2)*exp(3*x^2))*exp(x^2*(-6))/cot(x/2)^2

(2.70674114227851*5.0^(4.0 + x)*((0.5 + x)^3)^0.25 + 5.04537849152229*5.0^(4.0 + x)*((0.5 + x)^3)^0.25/(2.0 + 4.0*x))*exp(x^2*(-3))/cot(x/2) + 1.68179283050743*5.0^(4.0 + x)*((0.5 + x)^3)^0.25*((0.5 + 0.5*cot(x/2)^2)*exp(3*x^2) - 6.0*x*cot(x/2)*exp(3*x^2))*exp(x^2*(-6))/cot(x/2)^2

Denominador racional [src]

            ____________              2               ____________             2                ____________              2                   ____________              2                  ____________              2                 ____________              2                 ____________             2               ____________              2                         ____________              2       
   4 + x 4 /          3     3/x\  -3*x       4 + x 4 /          3     /x\  -3*x        4 + x 4 /          3     2/x\  -3*x        4 + x  2 4 /          3     2/x\  -3*x          4 + x 4 /          3     2/x\  -3*x         4 + x 4 /          3     3/x\  -3*x         4 + x 4 /          3     /x\  -3*x       4 + x 4 /          3     2/x\  -3*x                 4 + x 4 /          3     2/x\  -3*x        
4*5     *\/  (1 + 2*x)  *cot |-|*e      + 4*5     *\/  (1 + 2*x)  *cot|-|*e      + 12*5     *\/  (1 + 2*x)  *cot |-|*e      - 96*5     *x *\/  (1 + 2*x)  *cot |-|*e      - 48*x*5     *\/  (1 + 2*x)  *cot |-|*e      + 8*x*5     *\/  (1 + 2*x)  *cot |-|*e      + 8*x*5     *\/  (1 + 2*x)  *cot|-|*e      + 8*5     *\/  (1 + 2*x)  *cot |-|*e     *log(5) + 16*x*5     *\/  (1 + 2*x)  *cot |-|*e     *log(5)
                             \2/                                      \2/                                        \2/                                           \2/                                          \2/                                         \2/                                        \2/                                       \2/                                                 \2/              
------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                                                                                                                                              3/x\                                                                                                                                                                                                
                                                                                                                                                                                               4*(2 + 4*x)*cot |-|                                                                                                                                                                                                
                                                                                                                                                                                                               \2/

\frac{- 96 \cdot 5^{x + 4} x^{2} \sqrt[4]{\left(2 x + 1\right)^{3}} e^{- 3 x^{2}} \cot^{2}{\left(\frac{x}{2} \right)} + 8 \cdot 5^{x + 4} x \sqrt[4]{\left(2 x + 1\right)^{3}} e^{- 3 x^{2}} \cot^{3}{\left(\frac{x}{2} \right)} - 48 \cdot 5^{x + 4} x \sqrt[4]{\left(2 x + 1\right)^{3}} e^{- 3 x^{2}} \cot^{2}{\left(\frac{x}{2} \right)} + 16 \cdot 5^{x + 4} x \sqrt[4]{\left(2 x + 1\right)^{3}} e^{- 3 x^{2}} \log{\left(5 \right)} \cot^{2}{\left(\frac{x}{2} \right)} + 8 \cdot 5^{x + 4} x \sqrt[4]{\left(2 x + 1\right)^{3}} e^{- 3 x^{2}} \cot{\left(\frac{x}{2} \right)} + 4 \cdot 5^{x + 4} \sqrt[4]{\left(2 x + 1\right)^{3}} e^{- 3 x^{2}} \cot^{3}{\left(\frac{x}{2} \right)} + 12 \cdot 5^{x + 4} \sqrt[4]{\left(2 x + 1\right)^{3}} e^{- 3 x^{2}} \cot^{2}{\left(\frac{x}{2} \right)} + 8 \cdot 5^{x + 4} \sqrt[4]{\left(2 x + 1\right)^{3}} e^{- 3 x^{2}} \log{\left(5 \right)} \cot^{2}{\left(\frac{x}{2} \right)} + 4 \cdot 5^{x + 4} \sqrt[4]{\left(2 x + 1\right)^{3}} e^{- 3 x^{2}} \cot{\left(\frac{x}{2} \right)}}{4 \left(4 x + 2\right) \cot^{3}{\left(\frac{x}{2} \right)}}

(4*5^(4 + x)*((1 + 2*x)^3)^(1/4)*cot(x/2)^3*exp(-3*x^2) + 4*5^(4 + x)*((1 + 2*x)^3)^(1/4)*cot(x/2)*exp(-3*x^2) + 12*5^(4 + x)*((1 + 2*x)^3)^(1/4)*cot(x/2)^2*exp(-3*x^2) - 96*5^(4 + x)*x^2*((1 + 2*x)^3)^(1/4)*cot(x/2)^2*exp(-3*x^2) - 48*x*5^(4 + x)*((1 + 2*x)^3)^(1/4)*cot(x/2)^2*exp(-3*x^2) + 8*x*5^(4 + x)*((1 + 2*x)^3)^(1/4)*cot(x/2)^3*exp(-3*x^2) + 8*x*5^(4 + x)*((1 + 2*x)^3)^(1/4)*cot(x/2)*exp(-3*x^2) + 8*5^(4 + x)*((1 + 2*x)^3)^(1/4)*cot(x/2)^2*exp(-3*x^2)*log(5) + 16*x*5^(4 + x)*((1 + 2*x)^3)^(1/4)*cot(x/2)^2*exp(-3*x^2)*log(5))/(4*(2 + 4*x)*cot(x/2)^3)

Potencias [src]

/                                            ____________\                                 //       2/x\\                         \       
|          ____________             4 + x 4 /          3 |      2             ____________ ||    cot |-||     2                  2|      2
| 4 + x 4 /          3           3*5     *\/  (1 + 2*x)  |  -3*x     4 + x 4 /          3  ||1       \2/|  3*x           /x\  3*x |  -6*x 
|5     *\/  (1 + 2*x)  *log(5) + ------------------------|*e        5     *\/  (1 + 2*x)  *||- + -------|*e     - 6*x*cot|-|*e    |*e     
\                                        2 + 4*x         /                                 \\2      2   /                \2/      /       
----------------------------------------------------------------- + ----------------------------------------------------------------------
                                 /x\                                                                  2/x\                                
                              cot|-|                                                               cot |-|                                
                                 \2/                                                                   \2/

\frac{5^{x + 4} \left(- 6 x e^{3 x^{2}} \cot{\left(\frac{x}{2} \right)} + \left(\frac{\cot^{2}{\left(\frac{x}{2} \right)}}{2} + \frac{1}{2}\right) e^{3 x^{2}}\right) \sqrt[4]{\left(2 x + 1\right)^{3}} e^{- 6 x^{2}}}{\cot^{2}{\left(\frac{x}{2} \right)}} + \frac{\left(5^{x + 4} \sqrt[4]{\left(2 x + 1\right)^{3}} \log{\left(5 \right)} + \frac{3 \cdot 5^{x + 4} \sqrt[4]{\left(2 x + 1\right)^{3}}}{4 x + 2}\right) e^{- 3 x^{2}}}{\cot{\left(\frac{x}{2} \right)}}

(5^(4 + x)*((1 + 2*x)^3)^(1/4)*log(5) + 3*5^(4 + x)*((1 + 2*x)^3)^(1/4)/(2 + 4*x))*exp(-3*x^2)/cot(x/2) + 5^(4 + x)*((1 + 2*x)^3)^(1/4)*((1/2 + cot(x/2)^2/2)*exp(3*x^2) - 6*x*cot(x/2)*exp(3*x^2))*exp(-6*x^2)/cot(x/2)^2

Unión de expresiones racionales [src]

          ____________                                                                                2
 4 + x 4 /          3  /          /       2/x\           /x\\                               /x\\  -3*x 
5     *\/  (1 + 2*x)  *|(1 + 2*x)*|1 + cot |-| - 12*x*cot|-|| + (3 + 2*(1 + 2*x)*log(5))*cot|-||*e     
                       \          \        \2/           \2//                               \2//       
-------------------------------------------------------------------------------------------------------
                                                         2/x\                                          
                                          2*(1 + 2*x)*cot |-|                                          
                                                          \2/

\frac{5^{x + 4} \left(\left(2 x + 1\right) \left(- 12 x \cot{\left(\frac{x}{2} \right)} + \cot^{2}{\left(\frac{x}{2} \right)} + 1\right) + \left(2 \left(2 x + 1\right) \log{\left(5 \right)} + 3\right) \cot{\left(\frac{x}{2} \right)}\right) \sqrt[4]{\left(2 x + 1\right)^{3}} e^{- 3 x^{2}}}{2 \left(2 x + 1\right) \cot^{2}{\left(\frac{x}{2} \right)}}

5^(4 + x)*((1 + 2*x)^3)^(1/4)*((1 + 2*x)*(1 + cot(x/2)^2 - 12*x*cot(x/2)) + (3 + 2*(1 + 2*x)*log(5))*cot(x/2))*exp(-3*x^2)/(2*(1 + 2*x)*cot(x/2)^2)

Combinatoria [src]

           ____________                                                                                                                       2 
  4 + x 4 /          3  /        2/x\        /x\                2/x\        /x\                  /x\       2    /x\          /x\       \  -3*x  
-5     *\/  (1 + 2*x)  *|-1 - cot |-| - 3*cot|-| - 2*x - 2*x*cot |-| - 2*cot|-|*log(5) + 12*x*cot|-| + 24*x *cot|-| - 4*x*cot|-|*log(5)|*e      
                        \         \2/        \2/                 \2/        \2/                  \2/            \2/          \2/       /        
------------------------------------------------------------------------------------------------------------------------------------------------
                                                                             2/x\                                                               
                                                              2*(1 + 2*x)*cot |-|                                                               
                                                                              \2/

- \frac{5^{x + 4} \left(24 x^{2} \cot{\left(\frac{x}{2} \right)} - 2 x \cot^{2}{\left(\frac{x}{2} \right)} - 4 x \log{\left(5 \right)} \cot{\left(\frac{x}{2} \right)} + 12 x \cot{\left(\frac{x}{2} \right)} - 2 x - \cot^{2}{\left(\frac{x}{2} \right)} - 2 \log{\left(5 \right)} \cot{\left(\frac{x}{2} \right)} - 3 \cot{\left(\frac{x}{2} \right)} - 1\right) \sqrt[4]{\left(2 x + 1\right)^{3}} e^{- 3 x^{2}}}{2 \left(2 x + 1\right) \cot^{2}{\left(\frac{x}{2} \right)}}

-5^(4 + x)*((1 + 2*x)^3)^(1/4)*(-1 - cot(x/2)^2 - 3*cot(x/2) - 2*x - 2*x*cot(x/2)^2 - 2*cot(x/2)*log(5) + 12*x*cot(x/2) + 24*x^2*cot(x/2) - 4*x*cot(x/2)*log(5))*exp(-3*x^2)/(2*(1 + 2*x)*cot(x/2)^2)

Denominador común [src]

 /            ________________________              ________________________                       ________________________             ________________________                        ________________________                      ________________________                              ________________________                         ________________________                       ________________________              \ 
 |       x 4 /              3       2          x 4 /              3       2     /x\           x 4 /              3       2         x 4 /              3       2     2/x\           x 4 /              3       2     2/x\         x 4 /              3       2     /x\                  x 4 /              3       2     /x\          x  2 4 /              3       2     /x\           x 4 /              3       2     /x\       | 
-|- 625*5 *\/  1 + 6*x + 8*x  + 12*x   - 1875*5 *\/  1 + 6*x + 8*x  + 12*x  *cot|-| - 1250*x*5 *\/  1 + 6*x + 8*x  + 12*x   - 625*5 *\/  1 + 6*x + 8*x  + 12*x  *cot |-| - 1250*x*5 *\/  1 + 6*x + 8*x  + 12*x  *cot |-| - 1250*5 *\/  1 + 6*x + 8*x  + 12*x  *cot|-|*log(5) + 7500*x*5 *\/  1 + 6*x + 8*x  + 12*x  *cot|-| + 15000*5 *x *\/  1 + 6*x + 8*x  + 12*x  *cot|-| - 2500*x*5 *\/  1 + 6*x + 8*x  + 12*x  *cot|-|*log(5)| 
 \                                                                              \2/                                                                                  \2/                                             \2/                                          \2/                                                   \2/                                              \2/                                            \2/       / 
------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                                                                                                                                              2                   2                                                                                                                                                                                                 
                                                                                                                                                                                                     2/x\  3*x           2/x\  3*x                                                                                                                                                                                                  
                                                                                                                                                                                                2*cot |-|*e     + 4*x*cot |-|*e                                                                                                                                                                                                     
                                                                                                                                                                                                      \2/                 \2/

- \frac{15000 \cdot 5^{x} x^{2} \sqrt[4]{8 x^{3} + 12 x^{2} + 6 x + 1} \cot{\left(\frac{x}{2} \right)} - 1250 \cdot 5^{x} x \sqrt[4]{8 x^{3} + 12 x^{2} + 6 x + 1} \cot^{2}{\left(\frac{x}{2} \right)} - 2500 \cdot 5^{x} x \sqrt[4]{8 x^{3} + 12 x^{2} + 6 x + 1} \log{\left(5 \right)} \cot{\left(\frac{x}{2} \right)} + 7500 \cdot 5^{x} x \sqrt[4]{8 x^{3} + 12 x^{2} + 6 x + 1} \cot{\left(\frac{x}{2} \right)} - 1250 \cdot 5^{x} x \sqrt[4]{8 x^{3} + 12 x^{2} + 6 x + 1} - 625 \cdot 5^{x} \sqrt[4]{8 x^{3} + 12 x^{2} + 6 x + 1} \cot^{2}{\left(\frac{x}{2} \right)} - 1250 \cdot 5^{x} \sqrt[4]{8 x^{3} + 12 x^{2} + 6 x + 1} \log{\left(5 \right)} \cot{\left(\frac{x}{2} \right)} - 1875 \cdot 5^{x} \sqrt[4]{8 x^{3} + 12 x^{2} + 6 x + 1} \cot{\left(\frac{x}{2} \right)} - 625 \cdot 5^{x} \sqrt[4]{8 x^{3} + 12 x^{2} + 6 x + 1}}{4 x e^{3 x^{2}} \cot^{2}{\left(\frac{x}{2} \right)} + 2 e^{3 x^{2}} \cot^{2}{\left(\frac{x}{2} \right)}}

-(-625*5^x*(1 + 6*x + 8*x^3 + 12*x^2)^(1/4) - 1875*5^x*(1 + 6*x + 8*x^3 + 12*x^2)^(1/4)*cot(x/2) - 1250*x*5^x*(1 + 6*x + 8*x^3 + 12*x^2)^(1/4) - 625*5^x*(1 + 6*x + 8*x^3 + 12*x^2)^(1/4)*cot(x/2)^2 - 1250*x*5^x*(1 + 6*x + 8*x^3 + 12*x^2)^(1/4)*cot(x/2)^2 - 1250*5^x*(1 + 6*x + 8*x^3 + 12*x^2)^(1/4)*cot(x/2)*log(5) + 7500*x*5^x*(1 + 6*x + 8*x^3 + 12*x^2)^(1/4)*cot(x/2) + 15000*5^x*x^2*(1 + 6*x + 8*x^3 + 12*x^2)^(1/4)*cot(x/2) - 2500*x*5^x*(1 + 6*x + 8*x^3 + 12*x^2)^(1/4)*cot(x/2)*log(5))/(2*cot(x/2)^2*exp(3*x^2) + 4*x*cot(x/2)^2*exp(3*x^2))

Abrimos la expresión [src]

           ________________________   2                  ________________________     2   2                  ________________________   2                         ________________________     2   2                     ________________________     2   2     
      x 4 /              3       2   x *(-3)        x 4 /              3       2   3*x   x *(-6)        x 4 /              3       2   x *(-3)               x 4 /              3       2   3*x   x *(-6)           x 4 /              3       2   3*x   x *(-6)
1875*5 *\/  1 + 6*x + 8*x  + 12*x  *e          625*5 *\/  1 + 6*x + 8*x  + 12*x  *e    *e          625*5 *\/  1 + 6*x + 8*x  + 12*x  *e       *log(5)   625*5 *\/  1 + 6*x + 8*x  + 12*x  *e    *e          3750*x*5 *\/  1 + 6*x + 8*x  + 12*x  *e    *e       
-------------------------------------------- + ------------------------------------------------- + -------------------------------------------------- + ------------------------------------------------- - ----------------------------------------------------
                /x\          /x\                                       2                                                    /x\                                                  2/x\                                                 /x\                       
           2*cot|-| + 4*x*cot|-|                                                                                         cot|-|                                             2*cot |-|                                              cot|-|                       
                \2/          \2/                                                                                            \2/                                                   \2/                                                 \2/

- \frac{3750 \cdot 5^{x} x \sqrt[4]{8 x^{3} + 12 x^{2} + 6 x + 1} e^{3 x^{2}} e^{\left(-6\right) x^{2}}}{\cot{\left(\frac{x}{2} \right)}} + \frac{625 \cdot 5^{x} \sqrt[4]{8 x^{3} + 12 x^{2} + 6 x + 1} e^{3 x^{2}} e^{\left(-6\right) x^{2}}}{2} + \frac{625 \cdot 5^{x} \sqrt[4]{8 x^{3} + 12 x^{2} + 6 x + 1} e^{3 x^{2}} e^{\left(-6\right) x^{2}}}{2 \cot^{2}{\left(\frac{x}{2} \right)}} + \frac{625 \cdot 5^{x} \sqrt[4]{8 x^{3} + 12 x^{2} + 6 x + 1} e^{\left(-3\right) x^{2}} \log{\left(5 \right)}}{\cot{\left(\frac{x}{2} \right)}} + \frac{1875 \cdot 5^{x} \sqrt[4]{8 x^{3} + 12 x^{2} + 6 x + 1} e^{\left(-3\right) x^{2}}}{4 x \cot{\left(\frac{x}{2} \right)} + 2 \cot{\left(\frac{x}{2} \right)}}

                       /      /       2/x\\                   \            /                                            ____________\         
          ____________ |    2 |    cot |-||                  2|   2        |          ____________             x + 4 4 /          3 |   2     
 x + 4 4 /          3  | 3*x  |1       \2/|          /x\  3*x |  x *(-6)   | x + 4 4 /          3           3*5     *\/  (2*x + 1)  |  x *(-3)
5     *\/  (2*x + 1)  *|e    *|- + -------| - 6*x*cot|-|*e    |*e          |5     *\/  (2*x + 1)  *log(5) + ------------------------|*e       
                       \      \2      2   /          \2/      /            \                                      2*(2*x + 1)       /         
------------------------------------------------------------------------ + -------------------------------------------------------------------
                                   2/x\                                                                      /x\                              
                                cot |-|                                                                   cot|-|                              
                                    \2/                                                                      \2/

\frac{5^{x + 4} \sqrt[4]{\left(2 x + 1\right)^{3}} \left(- 6 x \cot{\left(\frac{x}{2} \right)} e^{3 x^{2}} + \left(\frac{\cot^{2}{\left(\frac{x}{2} \right)}}{2} + \frac{1}{2}\right) e^{3 x^{2}}\right) e^{\left(-6\right) x^{2}}}{\cot^{2}{\left(\frac{x}{2} \right)}} + \frac{\left(\frac{3 \cdot 5^{x + 4} \sqrt[4]{\left(2 x + 1\right)^{3}}}{2 \left(2 x + 1\right)} + 5^{x + 4} \sqrt[4]{\left(2 x + 1\right)^{3}} \log{\left(5 \right)}\right) e^{\left(-3\right) x^{2}}}{\cot{\left(\frac{x}{2} \right)}}

(((5^(x + 4)*((2*x + 1)^3)^(1/4))*(exp(3*x^2)*(1/2 + cot(x/2)^2/2) - (6*x)*cot(x/2)*exp(3*x^2)))*exp(x^2*(-6)))/cot(x/2)^2 + ((5^(x + 4)*((2*x + 1)^3)^(1/4))*log(5) + 3*5^(x + 4)*((2*x + 1)^3)^(1/4)/(2*(2*x + 1)))*exp(x^2*(-3))/cot(x/2)

Compilar la expresión [src]

/                                            ____________\                                   //       2/x\\                         \         
|          ____________             x + 4 4 /          3 |   2                  ____________ ||    cot |-||     2                  2|   2     
| x + 4 4 /          3           3*5     *\/  (1 + 2*x)  |  x *(-3)    x + 4 4 /          3  ||1       \2/|  3*x           /x\  3*x |  x *(-6)
|5     *\/  (1 + 2*x)  *log(5) + ------------------------|*e          5     *\/  (1 + 2*x)  *||- + -------|*e     - 6*x*cot|-|*e    |*e       
\                                        2 + 4*x         /                                   \\2      2   /                \2/      /         
------------------------------------------------------------------- + ------------------------------------------------------------------------
                                  /x\                                                                    2/x\                                 
                               cot|-|                                                                 cot |-|                                 
                                  \2/                                                                     \2/

\frac{5^{x + 4} \left(- 6 x e^{3 x^{2}} \cot{\left(\frac{x}{2} \right)} + \left(\frac{\cot^{2}{\left(\frac{x}{2} \right)}}{2} + \frac{1}{2}\right) e^{3 x^{2}}\right) \sqrt[4]{\left(2 x + 1\right)^{3}} e^{\left(-6\right) x^{2}}}{\cot^{2}{\left(\frac{x}{2} \right)}} + \frac{\left(5^{x + 4} \sqrt[4]{\left(2 x + 1\right)^{3}} \log{\left(5 \right)} + \frac{3 \cdot 5^{x + 4} \sqrt[4]{\left(2 x + 1\right)^{3}}}{4 x + 2}\right) e^{\left(-3\right) x^{2}}}{\cot{\left(\frac{x}{2} \right)}}

(5^(x + 4)*((1 + 2*x)^3)^(1/4)*log(5) + 3*5^(x + 4)*((1 + 2*x)^3)^(1/4)/(2 + 4*x))*exp(x^2*(-3))/cot(x/2) + 5^(x + 4)*((1 + 2*x)^3)^(1/4)*((1/2 + cot(x/2)^2/2)*exp(3*x^2) - 6*x*cot(x/2)*exp(3*x^2))*exp(x^2*(-6))/cot(x/2)^2

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¿Cómo vas a descomponer esta exp(x^2(-3))(5^(x+4)((2x+1)^3)^(1/4)log(5)+35^(x+4)((2x+1)^3)^(1/4)/((2(2x+1))))/cot(x/2)+5^(x+4)((2x+1)^3)^(1/4)(exp(3x^2)(1/2+cot(x/2)^2/2)-6x*cot(x/2)exp(3x^2))exp(x^2(-6))/cot(x/2)^2 expresión en fracciones?