Sr Examen

Otras calculadoras

Simplificación de expresiones/ Descomposición en fracciones simples/ acos(3*x)/((x+5)*log(3))-3*log(x+5)/(sqrt(1-9*x^2)*log(3))

¿Cómo vas a descomponer esta acos(3*x)/((x+5)*log(3))-3*log(x+5)/(sqrt(1-9*x^2)*log(3)) expresión en fracciones?

Expresión a simplificar:

Solución

Ha introducido [src] 
  acos(3*x)          3*log(x + 5)    
-------------- - --------------------
(x + 5)*log(3)      __________       
                   /        2        
                 \/  1 - 9*x  *log(3)
acos⁡(3x)(x+5)log⁡(3)−3log⁡(x+5)1−9x2log⁡(3)\frac{\operatorname{acos}{\left(3 x \right)}}{\left(x + 5\right) \log{\left(3 \right)}} - \frac{3 \log{\left(x + 5 \right)}}{\sqrt{1 - 9 x^{2}} \log{\left(3 \right)}} 
acos(3*x)/(((x + 5)*log(3))) - 3*log(x + 5)/(sqrt(1 - 9*x^2)*log(3))
Simplificación general [src] 
   __________                                 
  /        2                                  
\/  1 - 9*x  *acos(3*x) - 3*(5 + x)*log(5 + x)
----------------------------------------------
            __________                        
           /        2                         
         \/  1 - 9*x  *(5 + x)*log(3)
1−9x2acos⁡(3x)−3(x+5)log⁡(x+5)1−9x2(x+5)log⁡(3)\frac{\sqrt{1 - 9 x^{2}} \operatorname{acos}{\left(3 x \right)} - 3 \left(x + 5\right) \log{\left(x + 5 \right)}}{\sqrt{1 - 9 x^{2}} \left(x + 5\right) \log{\left(3 \right)}} 
(sqrt(1 - 9*x^2)*acos(3*x) - 3*(5 + x)*log(5 + x))/(sqrt(1 - 9*x^2)*(5 + x)*log(3))
Denominador racional [src] 
                                                  __________                            __________                  
                       2                         /        2                            /        2                   
-acos(3*x)*log(3) + 9*x *acos(3*x)*log(3) + 15*\/  1 - 9*x  *log(3)*log(5 + x) + 3*x*\/  1 - 9*x  *log(3)*log(5 + x)
--------------------------------------------------------------------------------------------------------------------
                                            /        2\            2                                                
                                            \-1 + 9*x /*(5 + x)*log (3)
9x2log⁡(3)acos⁡(3x)+3x1−9x2log⁡(3)log⁡(x+5)+151−9x2log⁡(3)log⁡(x+5)−log⁡(3)acos⁡(3x)(x+5)(9x2−1)log⁡(3)2\frac{9 x^{2} \log{\left(3 \right)} \operatorname{acos}{\left(3 x \right)} + 3 x \sqrt{1 - 9 x^{2}} \log{\left(3 \right)} \log{\left(x + 5 \right)} + 15 \sqrt{1 - 9 x^{2}} \log{\left(3 \right)} \log{\left(x + 5 \right)} - \log{\left(3 \right)} \operatorname{acos}{\left(3 x \right)}}{\left(x + 5\right) \left(9 x^{2} - 1\right) \log{\left(3 \right)}^{2}} 
(-acos(3*x)*log(3) + 9*x^2*acos(3*x)*log(3) + 15*sqrt(1 - 9*x^2)*log(3)*log(5 + x) + 3*x*sqrt(1 - 9*x^2)*log(3)*log(5 + x))/((-1 + 9*x^2)*(5 + x)*log(3)^2)
Unión de expresiones racionales [src] 
   __________                                 
  /        2                                  
\/  1 - 9*x  *acos(3*x) - 3*(5 + x)*log(5 + x)
----------------------------------------------
            __________                        
           /        2                         
         \/  1 - 9*x  *(5 + x)*log(3)
1−9x2acos⁡(3x)−3(x+5)log⁡(x+5)1−9x2(x+5)log⁡(3)\frac{\sqrt{1 - 9 x^{2}} \operatorname{acos}{\left(3 x \right)} - 3 \left(x + 5\right) \log{\left(x + 5 \right)}}{\sqrt{1 - 9 x^{2}} \left(x + 5\right) \log{\left(3 \right)}} 
(sqrt(1 - 9*x^2)*acos(3*x) - 3*(5 + x)*log(5 + x))/(sqrt(1 - 9*x^2)*(5 + x)*log(3))
Combinatoria [src] 
 /                   __________                           \ 
 |                  /        2                            | 
-\15*log(5 + x) - \/  1 - 9*x  *acos(3*x) + 3*x*log(5 + x)/ 
------------------------------------------------------------
            _______________________                         
          \/ -(1 + 3*x)*(-1 + 3*x) *(5 + x)*log(3)
−3xlog⁡(x+5)−1−9x2acos⁡(3x)+15log⁡(x+5)−(3x−1)(3x+1)(x+5)log⁡(3)- \frac{3 x \log{\left(x + 5 \right)} - \sqrt{1 - 9 x^{2}} \operatorname{acos}{\left(3 x \right)} + 15 \log{\left(x + 5 \right)}}{\sqrt{- \left(3 x - 1\right) \left(3 x + 1\right)} \left(x + 5\right) \log{\left(3 \right)}} 
-(15*log(5 + x) - sqrt(1 - 9*x^2)*acos(3*x) + 3*x*log(5 + x))/(sqrt(-(1 + 3*x)*(-1 + 3*x))*(5 + x)*log(3))
Denominador común [src] 
 /                   __________                           \ 
 |                  /        2                            | 
-\15*log(5 + x) - \/  1 - 9*x  *acos(3*x) + 3*x*log(5 + x)/ 
------------------------------------------------------------
           __________               __________              
          /        2               /        2               
      5*\/  1 - 9*x  *log(3) + x*\/  1 - 9*x  *log(3)
−3xlog⁡(x+5)−1−9x2acos⁡(3x)+15log⁡(x+5)x1−9x2log⁡(3)+51−9x2log⁡(3)- \frac{3 x \log{\left(x + 5 \right)} - \sqrt{1 - 9 x^{2}} \operatorname{acos}{\left(3 x \right)} + 15 \log{\left(x + 5 \right)}}{x \sqrt{1 - 9 x^{2}} \log{\left(3 \right)} + 5 \sqrt{1 - 9 x^{2}} \log{\left(3 \right)}} 
-(15*log(5 + x) - sqrt(1 - 9*x^2)*acos(3*x) + 3*x*log(5 + x))/(5*sqrt(1 - 9*x^2)*log(3) + x*sqrt(1 - 9*x^2)*log(3))
Respuesta numérica [src] 
acos(3*x)/(5.49306144334055 + 1.09861228866811*x) - 0.910239226626837*(0.111111111111111 - x^2)^(-0.5)*log(x + 5)
acos(3*x)/(5.49306144334055 + 1.09861228866811*x) - 0.910239226626837*(0.111111111111111 - x^2)^(-0.5)*log(x + 5)
    © Sr Examen – Калькулятор