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Simplificación de expresiones/ Descomposición en fracciones simples/ atan((2*x)/15)/30+7*log(x-1)+3^(5*x+6)/(5*log(3))

¿Cómo vas a descomponer esta atan((2*x)/15)/30+7*log(x-1)+3^(5*x+6)/(5*log(3)) expresión en fracciones?

Expresión a simplificar:

Solución

Ha introducido [src] 
    /2*x\                          
atan|---|                   5*x + 6
    \ 15/                  3       
--------- + 7*log(x - 1) + --------
    30                     5*log(3)
35x+65log⁡(3)+(7log⁡(x−1)+atan⁡(2x15)30)\frac{3^{5 x + 6}}{5 \log{\left(3 \right)}} + \left(7 \log{\left(x - 1 \right)} + \frac{\operatorname{atan}{\left(\frac{2 x}{15} \right)}}{30}\right) 
atan((2*x)/15)/30 + 7*log(x - 1) + 3^(5*x + 6)/((5*log(3)))
Simplificación general [src] 
                    /2*x\           
                atan|---|        5*x
                    \ 15/   729*3   
7*log(-1 + x) + --------- + --------
                    30      5*log(3)
729⋅35x5log⁡(3)+7log⁡(x−1)+atan⁡(2x15)30\frac{729 \cdot 3^{5 x}}{5 \log{\left(3 \right)}} + 7 \log{\left(x - 1 \right)} + \frac{\operatorname{atan}{\left(\frac{2 x}{15} \right)}}{30} 
7*log(-1 + x) + atan(2*x/15)/30 + 729*3^(5*x)/(5*log(3))
Respuesta numérica [src] 
7.0*log(x - 1) + 0.0333333333333333*atan((2*x)/15) + 0.182047845325367*3.0^(6.0 + 5.0*x)
7.0*log(x - 1) + 0.0333333333333333*atan((2*x)/15) + 0.182047845325367*3.0^(6.0 + 5.0*x)
Potencias [src] 
                    /2*x\           
                atan|---|    6 + 5*x
                    \ 15/   3       
7*log(-1 + x) + --------- + --------
                    30      5*log(3)
35x+65log⁡(3)+7log⁡(x−1)+atan⁡(2x15)30\frac{3^{5 x + 6}}{5 \log{\left(3 \right)}} + 7 \log{\left(x - 1 \right)} + \frac{\operatorname{atan}{\left(\frac{2 x}{15} \right)}}{30} 
7*log(-1 + x) + atan(2*x/15)/30 + 3^(6 + 5*x)/(5*log(3))
Parte trigonométrica [src] 
                    /2*x\           
                atan|---|    6 + 5*x
                    \ 15/   3       
7*log(-1 + x) + --------- + --------
                    30      5*log(3)
35x+65log⁡(3)+7log⁡(x−1)+atan⁡(2x15)30\frac{3^{5 x + 6}}{5 \log{\left(3 \right)}} + 7 \log{\left(x - 1 \right)} + \frac{\operatorname{atan}{\left(\frac{2 x}{15} \right)}}{30} 
7*log(-1 + x) + atan(2*x/15)/30 + 3^(6 + 5*x)/(5*log(3))
Denominador común [src] 
                    /2*x\           
                atan|---|        5*x
                    \ 15/   729*3   
7*log(-1 + x) + --------- + --------
                    30      5*log(3)
729⋅35x5log⁡(3)+7log⁡(x−1)+atan⁡(2x15)30\frac{729 \cdot 3^{5 x}}{5 \log{\left(3 \right)}} + 7 \log{\left(x - 1 \right)} + \frac{\operatorname{atan}{\left(\frac{2 x}{15} \right)}}{30} 
7*log(-1 + x) + atan(2*x/15)/30 + 729*3^(5*x)/(5*log(3))
Denominador racional [src] 
    6 + 5*x         /2*x\                                 
30*3        + 5*atan|---|*log(3) + 1050*log(3)*log(-1 + x)
                    \ 15/                                 
----------------------------------------------------------
                        150*log(3)
30⋅35x+6+1050log⁡(3)log⁡(x−1)+5log⁡(3)atan⁡(2x15)150log⁡(3)\frac{30 \cdot 3^{5 x + 6} + 1050 \log{\left(3 \right)} \log{\left(x - 1 \right)} + 5 \log{\left(3 \right)} \operatorname{atan}{\left(\frac{2 x}{15} \right)}}{150 \log{\left(3 \right)}} 
(30*3^(6 + 5*x) + 5*atan(2*x/15)*log(3) + 1050*log(3)*log(-1 + x))/(150*log(3))
Combinatoria [src] 
      5*x       /2*x\                                
4374*3    + atan|---|*log(3) + 210*log(3)*log(-1 + x)
                \ 15/                                
-----------------------------------------------------
                      30*log(3)
4374⋅35x+210log⁡(3)log⁡(x−1)+log⁡(3)atan⁡(2x15)30log⁡(3)\frac{4374 \cdot 3^{5 x} + 210 \log{\left(3 \right)} \log{\left(x - 1 \right)} + \log{\left(3 \right)} \operatorname{atan}{\left(\frac{2 x}{15} \right)}}{30 \log{\left(3 \right)}} 
(4374*3^(5*x) + atan(2*x/15)*log(3) + 210*log(3)*log(-1 + x))/(30*log(3))
Unión de expresiones racionales [src] 
   6 + 5*x   /                      /2*x\\       
6*3        + |210*log(-1 + x) + atan|---||*log(3)
             \                      \ 15//       
-------------------------------------------------
                    30*log(3)
6⋅35x+6+(210log⁡(x−1)+atan⁡(2x15))log⁡(3)30log⁡(3)\frac{6 \cdot 3^{5 x + 6} + \left(210 \log{\left(x - 1 \right)} + \operatorname{atan}{\left(\frac{2 x}{15} \right)}\right) \log{\left(3 \right)}}{30 \log{\left(3 \right)}} 
(6*3^(6 + 5*x) + (210*log(-1 + x) + atan(2*x/15))*log(3))/(30*log(3))
Compilar la expresión [src] 
                   /2*x\           
               atan|---|    5*x + 6
                   \ 15/   3       
7*log(x - 1) + --------- + --------
                   30      5*log(3)
35x+65log⁡(3)+7log⁡(x−1)+atan⁡(2x15)30\frac{3^{5 x + 6}}{5 \log{\left(3 \right)}} + 7 \log{\left(x - 1 \right)} + \frac{\operatorname{atan}{\left(\frac{2 x}{15} \right)}}{30} 
7*log(x - 1) + atan((2*x)/15)/30 + 3^(5*x + 6)/(5*log(3))
Abrimos la expresión [src] 
                   /2*x\           
               atan|---|    5*x + 6
                   \ 15/   3       
7*log(x - 1) + --------- + --------
                   30      5*log(3)
35x+65log⁡(3)+7log⁡(x−1)+atan⁡(2x15)30\frac{3^{5 x + 6}}{5 \log{\left(3 \right)}} + 7 \log{\left(x - 1 \right)} + \frac{\operatorname{atan}{\left(\frac{2 x}{15} \right)}}{30} 
7*log(x - 1) + atan((2*x)/15)/30 + 3^(5*x + 6)/(5*log(3))
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