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Simplificación de expresiones/ Descomposición en fracciones simples/ asin(x)^(1/4)/x+20*(1-cos(x)^2)^9*cos(x)*sin(x)+log(x)/(4*sqrt(1-x^2)*asin(x)^(3/4))

¿Cómo vas a descomponer esta asin(x)^(1/4)/x+20*(1-cos(x)^2)^9*cos(x)*sin(x)+log(x)/(4*sqrt(1-x^2)*asin(x)^(3/4)) expresión en fracciones?

Expresión a simplificar:

Solución

Ha introducido [src] 
4 _________                   9                                         
\/ asin(x)       /       2   \                           log(x)         
----------- + 20*\1 - cos (x)/ *cos(x)*sin(x) + ------------------------
     x                                               ________           
                                                    /      2      3/4   
                                                4*\/  1 - x  *asin   (x)
(20(1−cos⁡2(x))9cos⁡(x)sin⁡(x)+asin⁡(x)4x)+log⁡(x)41−x2asin⁡34(x)\left(20 \left(1 - \cos^{2}{\left(x \right)}\right)^{9} \cos{\left(x \right)} \sin{\left(x \right)} + \frac{\sqrt[4]{\operatorname{asin}{\left(x \right)}}}{x}\right) + \frac{\log{\left(x \right)}}{4 \sqrt{1 - x^{2}} \operatorname{asin}^{\frac{3}{4}}{\left(x \right)}} 
asin(x)^(1/4)/x + ((20*(1 - cos(x)^2)^9)*cos(x))*sin(x) + log(x)/(((4*sqrt(1 - x^2))*asin(x)^(3/4)))
Simplificación general [src] 
4 _________                                                
\/ asin(x)          19                      log(x)         
----------- + 20*sin  (x)*cos(x) + ------------------------
     x                                  ________           
                                       /      2      3/4   
                                   4*\/  1 - x  *asin   (x)
20sin⁡19(x)cos⁡(x)+log⁡(x)41−x2asin⁡34(x)+asin⁡(x)4x20 \sin^{19}{\left(x \right)} \cos{\left(x \right)} + \frac{\log{\left(x \right)}}{4 \sqrt{1 - x^{2}} \operatorname{asin}^{\frac{3}{4}}{\left(x \right)}} + \frac{\sqrt[4]{\operatorname{asin}{\left(x \right)}}}{x} 
asin(x)^(1/4)/x + 20*sin(x)^19*cos(x) + log(x)/(4*sqrt(1 - x^2)*asin(x)^(3/4))
Respuesta numérica [src] 
asin(x)^0.25/x + 0.25*(1.0 - x^2)^(-0.5)*asin(x)^(-0.75)*log(x) + 20.0*(1.0 - cos(x)^2)^9*cos(x)*sin(x)
asin(x)^0.25/x + 0.25*(1.0 - x^2)^(-0.5)*asin(x)^(-0.75)*log(x) + 20.0*(1.0 - cos(x)^2)^9*cos(x)*sin(x)
Unión de expresiones racionales [src] 
                ________            /                                9              \
               /      2      3/4    |4 _________        /       2   \               |
x*log(x) + 4*\/  1 - x  *asin   (x)*\\/ asin(x)  + 20*x*\1 - cos (x)/ *cos(x)*sin(x)/
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                                     ________                                        
                                    /      2      3/4                                
                              4*x*\/  1 - x  *asin   (x)
xlog⁡(x)+41−x2(20x(1−cos⁡2(x))9sin⁡(x)cos⁡(x)+asin⁡(x)4)asin⁡34(x)4x1−x2asin⁡34(x)\frac{x \log{\left(x \right)} + 4 \sqrt{1 - x^{2}} \left(20 x \left(1 - \cos^{2}{\left(x \right)}\right)^{9} \sin{\left(x \right)} \cos{\left(x \right)} + \sqrt[4]{\operatorname{asin}{\left(x \right)}}\right) \operatorname{asin}^{\frac{3}{4}}{\left(x \right)}}{4 x \sqrt{1 - x^{2}} \operatorname{asin}^{\frac{3}{4}}{\left(x \right)}} 
(x*log(x) + 4*sqrt(1 - x^2)*asin(x)^(3/4)*(asin(x)^(1/4) + 20*x*(1 - cos(x)^2)^9*cos(x)*sin(x)))/(4*x*sqrt(1 - x^2)*asin(x)^(3/4))
Denominador común [src] 
                                                                                                                                                                                                                                          ________        
                                                                                                                                                                                                                                         /      2         
          11                     7                    15                    3                   19                                       17                    5                     13                     9             x*log(x) + 4*\/  1 - x  *asin(x)
- 2520*cos  (x)*sin(x) - 1680*cos (x)*sin(x) - 720*cos  (x)*sin(x) - 180*cos (x)*sin(x) - 20*cos  (x)*sin(x) + 20*cos(x)*sin(x) + 180*cos  (x)*sin(x) + 720*cos (x)*sin(x) + 1680*cos  (x)*sin(x) + 2520*cos (x)*sin(x) + --------------------------------
                                                                                                                                                                                                                                    ________              
                                                                                                                                                                                                                                   /      2      3/4      
                                                                                                                                                                                                                             4*x*\/  1 - x  *asin   (x)
−20sin⁡(x)cos⁡19(x)+180sin⁡(x)cos⁡17(x)−720sin⁡(x)cos⁡15(x)+1680sin⁡(x)cos⁡13(x)−2520sin⁡(x)cos⁡11(x)+2520sin⁡(x)cos⁡9(x)−1680sin⁡(x)cos⁡7(x)+720sin⁡(x)cos⁡5(x)−180sin⁡(x)cos⁡3(x)+20sin⁡(x)cos⁡(x)+xlog⁡(x)+41−x2asin⁡(x)4x1−x2asin⁡34(x)- 20 \sin{\left(x \right)} \cos^{19}{\left(x \right)} + 180 \sin{\left(x \right)} \cos^{17}{\left(x \right)} - 720 \sin{\left(x \right)} \cos^{15}{\left(x \right)} + 1680 \sin{\left(x \right)} \cos^{13}{\left(x \right)} - 2520 \sin{\left(x \right)} \cos^{11}{\left(x \right)} + 2520 \sin{\left(x \right)} \cos^{9}{\left(x \right)} - 1680 \sin{\left(x \right)} \cos^{7}{\left(x \right)} + 720 \sin{\left(x \right)} \cos^{5}{\left(x \right)} - 180 \sin{\left(x \right)} \cos^{3}{\left(x \right)} + 20 \sin{\left(x \right)} \cos{\left(x \right)} + \frac{x \log{\left(x \right)} + 4 \sqrt{1 - x^{2}} \operatorname{asin}{\left(x \right)}}{4 x \sqrt{1 - x^{2}} \operatorname{asin}^{\frac{3}{4}}{\left(x \right)}} 
-2520*cos(x)^11*sin(x) - 1680*cos(x)^7*sin(x) - 720*cos(x)^15*sin(x) - 180*cos(x)^3*sin(x) - 20*cos(x)^19*sin(x) + 20*cos(x)*sin(x) + 180*cos(x)^17*sin(x) + 720*cos(x)^5*sin(x) + 1680*cos(x)^13*sin(x) + 2520*cos(x)^9*sin(x) + (x*log(x) + 4*sqrt(1 - x^2)*asin(x))/(4*x*sqrt(1 - x^2)*asin(x)^(3/4))
Denominador racional [src] 
                                 ________                              9                                               9                         
                2               /      2               3 /        2   \      3/4                         /        2   \      3/4                 
-4*asin(x) + 4*x *asin(x) - x*\/  1 - x  *log(x) - 80*x *\-1 + cos (x)/ *asin   (x)*cos(x)*sin(x) + 80*x*\-1 + cos (x)/ *asin   (x)*cos(x)*sin(x)
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                                                                 /      2\     3/4                                                               
                                                             4*x*\-1 + x /*asin   (x)
−80x3(cos⁡2(x)−1)9sin⁡(x)cos⁡(x)asin⁡34(x)+4x2asin⁡(x)−x1−x2log⁡(x)+80x(cos⁡2(x)−1)9sin⁡(x)cos⁡(x)asin⁡34(x)−4asin⁡(x)4x(x2−1)asin⁡34(x)\frac{- 80 x^{3} \left(\cos^{2}{\left(x \right)} - 1\right)^{9} \sin{\left(x \right)} \cos{\left(x \right)} \operatorname{asin}^{\frac{3}{4}}{\left(x \right)} + 4 x^{2} \operatorname{asin}{\left(x \right)} - x \sqrt{1 - x^{2}} \log{\left(x \right)} + 80 x \left(\cos^{2}{\left(x \right)} - 1\right)^{9} \sin{\left(x \right)} \cos{\left(x \right)} \operatorname{asin}^{\frac{3}{4}}{\left(x \right)} - 4 \operatorname{asin}{\left(x \right)}}{4 x \left(x^{2} - 1\right) \operatorname{asin}^{\frac{3}{4}}{\left(x \right)}} 
(-4*asin(x) + 4*x^2*asin(x) - x*sqrt(1 - x^2)*log(x) - 80*x^3*(-1 + cos(x)^2)^9*asin(x)^(3/4)*cos(x)*sin(x) + 80*x*(-1 + cos(x)^2)^9*asin(x)^(3/4)*cos(x)*sin(x))/(4*x*(-1 + x^2)*asin(x)^(3/4))
Potencias [src] 
4 _________                   9                                         
\/ asin(x)       /       2   \                           log(x)         
----------- + 20*\1 - cos (x)/ *cos(x)*sin(x) + ------------------------
     x                                               ________           
                                                    /      2      3/4   
                                                4*\/  1 - x  *asin   (x)
20(1−cos⁡2(x))9sin⁡(x)cos⁡(x)+log⁡(x)41−x2asin⁡34(x)+asin⁡(x)4x20 \left(1 - \cos^{2}{\left(x \right)}\right)^{9} \sin{\left(x \right)} \cos{\left(x \right)} + \frac{\log{\left(x \right)}}{4 \sqrt{1 - x^{2}} \operatorname{asin}^{\frac{3}{4}}{\left(x \right)}} + \frac{\sqrt[4]{\operatorname{asin}{\left(x \right)}}}{x} 
                                                                   9                                
                                              /                  2\                                 
4 _________                                   |    / I*x    -I*x\ |  / I*x    -I*x\                 
\/ asin(x)             log(x)                 |    |e      e    | |  |e      e    | /   -I*x    I*x\
----------- + ------------------------ - 10*I*|1 - |---- + -----| | *|---- + -----|*\- e     + e   /
     x             ________                   \    \ 2       2  / /  \ 2       2  /                 
                  /      2      3/4                                                                 
              4*\/  1 - x  *asin   (x)
−10i(1−(eix2+e−ix2)2)9(eix2+e−ix2)(eix−e−ix)+log⁡(x)41−x2asin⁡34(x)+asin⁡(x)4x- 10 i \left(1 - \left(\frac{e^{i x}}{2} + \frac{e^{- i x}}{2}\right)^{2}\right)^{9} \left(\frac{e^{i x}}{2} + \frac{e^{- i x}}{2}\right) \left(e^{i x} - e^{- i x}\right) + \frac{\log{\left(x \right)}}{4 \sqrt{1 - x^{2}} \operatorname{asin}^{\frac{3}{4}}{\left(x \right)}} + \frac{\sqrt[4]{\operatorname{asin}{\left(x \right)}}}{x} 
asin(x)^(1/4)/x + log(x)/(4*sqrt(1 - x^2)*asin(x)^(3/4)) - 10*i*(1 - (exp(i*x)/2 + exp(-i*x)/2)^2)^9*(exp(i*x)/2 + exp(-i*x)/2)*(-exp(-i*x) + exp(i*x))
Combinatoria [src] 
 /                 ________                      ________                                       ________                                        ________                                      ________                                      ________                                    ________                                       ________                                       ________                                        ________                                        ________                           \ 
 |                /      2                      /      2      3/4       9                      /      2      3/4       13                      /      2      3/4       5                     /      2      3/4       17                    /      2      3/4                           /      2      3/4       19                     /      2      3/4       3                      /      2      3/4       15                      /      2      3/4       7                       /      2      3/4       11          | 
-\-x*log(x) - 4*\/  1 - x  *asin(x) - 10080*x*\/  1 - x  *asin   (x)*cos (x)*sin(x) - 6720*x*\/  1 - x  *asin   (x)*cos  (x)*sin(x) - 2880*x*\/  1 - x  *asin   (x)*cos (x)*sin(x) - 720*x*\/  1 - x  *asin   (x)*cos  (x)*sin(x) - 80*x*\/  1 - x  *asin   (x)*cos(x)*sin(x) + 80*x*\/  1 - x  *asin   (x)*cos  (x)*sin(x) + 720*x*\/  1 - x  *asin   (x)*cos (x)*sin(x) + 2880*x*\/  1 - x  *asin   (x)*cos  (x)*sin(x) + 6720*x*\/  1 - x  *asin   (x)*cos (x)*sin(x) + 10080*x*\/  1 - x  *asin   (x)*cos  (x)*sin(x)/ 
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                                                                                                                                                                                                                                                  ___________________     3/4                                                                                                                                                                                                                                              
                                                                                                                                                                                                                                            4*x*\/ -(1 + x)*(-1 + x) *asin   (x)
−80x1−x2sin⁡(x)cos⁡19(x)asin⁡34(x)−720x1−x2sin⁡(x)cos⁡17(x)asin⁡34(x)+2880x1−x2sin⁡(x)cos⁡15(x)asin⁡34(x)−6720x1−x2sin⁡(x)cos⁡13(x)asin⁡34(x)+10080x1−x2sin⁡(x)cos⁡11(x)asin⁡34(x)−10080x1−x2sin⁡(x)cos⁡9(x)asin⁡34(x)+6720x1−x2sin⁡(x)cos⁡7(x)asin⁡34(x)−2880x1−x2sin⁡(x)cos⁡5(x)asin⁡34(x)+720x1−x2sin⁡(x)cos⁡3(x)asin⁡34(x)−80x1−x2sin⁡(x)cos⁡(x)asin⁡34(x)−xlog⁡(x)−41−x2asin⁡(x)4x−(x−1)(x+1)asin⁡34(x)- \frac{80 x \sqrt{1 - x^{2}} \sin{\left(x \right)} \cos^{19}{\left(x \right)} \operatorname{asin}^{\frac{3}{4}}{\left(x \right)} - 720 x \sqrt{1 - x^{2}} \sin{\left(x \right)} \cos^{17}{\left(x \right)} \operatorname{asin}^{\frac{3}{4}}{\left(x \right)} + 2880 x \sqrt{1 - x^{2}} \sin{\left(x \right)} \cos^{15}{\left(x \right)} \operatorname{asin}^{\frac{3}{4}}{\left(x \right)} - 6720 x \sqrt{1 - x^{2}} \sin{\left(x \right)} \cos^{13}{\left(x \right)} \operatorname{asin}^{\frac{3}{4}}{\left(x \right)} + 10080 x \sqrt{1 - x^{2}} \sin{\left(x \right)} \cos^{11}{\left(x \right)} \operatorname{asin}^{\frac{3}{4}}{\left(x \right)} - 10080 x \sqrt{1 - x^{2}} \sin{\left(x \right)} \cos^{9}{\left(x \right)} \operatorname{asin}^{\frac{3}{4}}{\left(x \right)} + 6720 x \sqrt{1 - x^{2}} \sin{\left(x \right)} \cos^{7}{\left(x \right)} \operatorname{asin}^{\frac{3}{4}}{\left(x \right)} - 2880 x \sqrt{1 - x^{2}} \sin{\left(x \right)} \cos^{5}{\left(x \right)} \operatorname{asin}^{\frac{3}{4}}{\left(x \right)} + 720 x \sqrt{1 - x^{2}} \sin{\left(x \right)} \cos^{3}{\left(x \right)} \operatorname{asin}^{\frac{3}{4}}{\left(x \right)} - 80 x \sqrt{1 - x^{2}} \sin{\left(x \right)} \cos{\left(x \right)} \operatorname{asin}^{\frac{3}{4}}{\left(x \right)} - x \log{\left(x \right)} - 4 \sqrt{1 - x^{2}} \operatorname{asin}{\left(x \right)}}{4 x \sqrt{- \left(x - 1\right) \left(x + 1\right)} \operatorname{asin}^{\frac{3}{4}}{\left(x \right)}} 
-(-x*log(x) - 4*sqrt(1 - x^2)*asin(x) - 10080*x*sqrt(1 - x^2)*asin(x)^(3/4)*cos(x)^9*sin(x) - 6720*x*sqrt(1 - x^2)*asin(x)^(3/4)*cos(x)^13*sin(x) - 2880*x*sqrt(1 - x^2)*asin(x)^(3/4)*cos(x)^5*sin(x) - 720*x*sqrt(1 - x^2)*asin(x)^(3/4)*cos(x)^17*sin(x) - 80*x*sqrt(1 - x^2)*asin(x)^(3/4)*cos(x)*sin(x) + 80*x*sqrt(1 - x^2)*asin(x)^(3/4)*cos(x)^19*sin(x) + 720*x*sqrt(1 - x^2)*asin(x)^(3/4)*cos(x)^3*sin(x) + 2880*x*sqrt(1 - x^2)*asin(x)^(3/4)*cos(x)^15*sin(x) + 6720*x*sqrt(1 - x^2)*asin(x)^(3/4)*cos(x)^7*sin(x) + 10080*x*sqrt(1 - x^2)*asin(x)^(3/4)*cos(x)^11*sin(x))/(4*x*sqrt(-(1 + x)*(-1 + x))*asin(x)^(3/4))
Abrimos la expresión [src] 
4 _________                   9                                         
\/ asin(x)       /       2   \                           log(x)         
----------- + 20*\1 - cos (x)/ *cos(x)*sin(x) + ------------------------
     x                                               ________           
                                                    /      2      3/4   
                                                4*\/  1 - x  *asin   (x)
20(1−cos⁡2(x))9cos⁡(x)sin⁡(x)+log⁡(x)41−x2asin⁡34(x)+asin⁡(x)4x20 \left(1 - \cos^{2}{\left(x \right)}\right)^{9} \cos{\left(x \right)} \sin{\left(x \right)} + \frac{\log{\left(x \right)}}{4 \sqrt{1 - x^{2}} \operatorname{asin}^{\frac{3}{4}}{\left(x \right)}} + \frac{\sqrt[4]{\operatorname{asin}{\left(x \right)}}}{x} 
4 _________                                                                                                                                                                                                                                                   
\/ asin(x)            11                     7                    15                    3                   19                                       17                    5                     13                     9                      log(x)         
----------- - 2520*cos  (x)*sin(x) - 1680*cos (x)*sin(x) - 720*cos  (x)*sin(x) - 180*cos (x)*sin(x) - 20*cos  (x)*sin(x) + 20*cos(x)*sin(x) + 180*cos  (x)*sin(x) + 720*cos (x)*sin(x) + 1680*cos  (x)*sin(x) + 2520*cos (x)*sin(x) + ------------------------
     x                                                                                                                                                                                                                                     ________           
                                                                                                                                                                                                                                          /      2      3/4   
                                                                                                                                                                                                                                      4*\/  1 - x  *asin   (x)
−20sin⁡(x)cos⁡19(x)+180sin⁡(x)cos⁡17(x)−720sin⁡(x)cos⁡15(x)+1680sin⁡(x)cos⁡13(x)−2520sin⁡(x)cos⁡11(x)+2520sin⁡(x)cos⁡9(x)−1680sin⁡(x)cos⁡7(x)+720sin⁡(x)cos⁡5(x)−180sin⁡(x)cos⁡3(x)+20sin⁡(x)cos⁡(x)+log⁡(x)41−x2asin⁡34(x)+asin⁡(x)4x- 20 \sin{\left(x \right)} \cos^{19}{\left(x \right)} + 180 \sin{\left(x \right)} \cos^{17}{\left(x \right)} - 720 \sin{\left(x \right)} \cos^{15}{\left(x \right)} + 1680 \sin{\left(x \right)} \cos^{13}{\left(x \right)} - 2520 \sin{\left(x \right)} \cos^{11}{\left(x \right)} + 2520 \sin{\left(x \right)} \cos^{9}{\left(x \right)} - 1680 \sin{\left(x \right)} \cos^{7}{\left(x \right)} + 720 \sin{\left(x \right)} \cos^{5}{\left(x \right)} - 180 \sin{\left(x \right)} \cos^{3}{\left(x \right)} + 20 \sin{\left(x \right)} \cos{\left(x \right)} + \frac{\log{\left(x \right)}}{4 \sqrt{1 - x^{2}} \operatorname{asin}^{\frac{3}{4}}{\left(x \right)}} + \frac{\sqrt[4]{\operatorname{asin}{\left(x \right)}}}{x} 
asin(x)^(1/4)/x - 2520*cos(x)^11*sin(x) - 1680*cos(x)^7*sin(x) - 720*cos(x)^15*sin(x) - 180*cos(x)^3*sin(x) - 20*cos(x)^19*sin(x) + 20*cos(x)*sin(x) + 180*cos(x)^17*sin(x) + 720*cos(x)^5*sin(x) + 1680*cos(x)^13*sin(x) + 2520*cos(x)^9*sin(x) + log(x)/(4*sqrt(1 - x^2)*asin(x)^(3/4))
Compilar la expresión [src] 
4 _________                   9                                         
\/ asin(x)       /       2   \                           log(x)         
----------- + 20*\1 - cos (x)/ *cos(x)*sin(x) + ------------------------
     x                                               ________           
                                                    /      2      3/4   
                                                4*\/  1 - x  *asin   (x)
20(1−cos⁡2(x))9sin⁡(x)cos⁡(x)+log⁡(x)41−x2asin⁡34(x)+asin⁡(x)4x20 \left(1 - \cos^{2}{\left(x \right)}\right)^{9} \sin{\left(x \right)} \cos{\left(x \right)} + \frac{\log{\left(x \right)}}{4 \sqrt{1 - x^{2}} \operatorname{asin}^{\frac{3}{4}}{\left(x \right)}} + \frac{\sqrt[4]{\operatorname{asin}{\left(x \right)}}}{x} 
asin(x)^(1/4)/x + 20*(1 - cos(x)^2)^9*cos(x)*sin(x) + log(x)/(4*sqrt(1 - x^2)*asin(x)^(3/4))
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