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Simplificación de expresiones/ Descomposición en fracciones simples/ (-3*10^x*sin(2x))/(2*(cos(2x))^(1/4))-10^x*ln(10)*(cos(2x))^(3/4)

¿Cómo vas a descomponer esta (-3*10^x*sin(2x))/(2*(cos(2x))^(1/4))-10^x*ln(10)*(cos(2x))^(3/4) expresión en fracciones?

Expresión a simplificar:

Solución

Ha introducido [src] 
     x                                   
-3*10 *sin(2*x)     x            3/4     
--------------- - 10 *log(10)*cos   (2*x)
   4 __________                          
 2*\/ cos(2*x)
−10xlog⁡(10)cos⁡34(2x)+−3⋅10xsin⁡(2x)2cos⁡(2x)4- 10^{x} \log{\left(10 \right)} \cos^{\frac{3}{4}}{\left(2 x \right)} + \frac{- 3 \cdot 10^{x} \sin{\left(2 x \right)}}{2 \sqrt[4]{\cos{\left(2 x \right)}}} 
((-3*10^x)*sin(2*x))/((2*cos(2*x)^(1/4))) - 10^x*log(10)*cos(2*x)^(3/4)
Simplificación general [src] 
   x                                  
-10 *(3*sin(2*x) + cos(2*x)*log(100)) 
--------------------------------------
              4 __________            
            2*\/ cos(2*x)
−10x(3sin⁡(2x)+log⁡(100)cos⁡(2x))2cos⁡(2x)4- \frac{10^{x} \left(3 \sin{\left(2 x \right)} + \log{\left(100 \right)} \cos{\left(2 x \right)}\right)}{2 \sqrt[4]{\cos{\left(2 x \right)}}} 
-10^x*(3*sin(2*x) + cos(2*x)*log(100))/(2*cos(2*x)^(1/4))
Respuesta numérica [src] 
-2.30258509299405*10.0^x*cos(2*x)^0.75 - 1.5*10.0^x*cos(2*x)^(-0.25)*sin(2*x)
-2.30258509299405*10.0^x*cos(2*x)^0.75 - 1.5*10.0^x*cos(2*x)^(-0.25)*sin(2*x)
Denominador racional [src] 
      x                x                 
- 3*10 *sin(2*x) - 2*10 *cos(2*x)*log(10)
-----------------------------------------
                4 __________             
              2*\/ cos(2*x)
−3⋅10xsin⁡(2x)−2⋅10xlog⁡(10)cos⁡(2x)2cos⁡(2x)4\frac{- 3 \cdot 10^{x} \sin{\left(2 x \right)} - 2 \cdot 10^{x} \log{\left(10 \right)} \cos{\left(2 x \right)}}{2 \sqrt[4]{\cos{\left(2 x \right)}}} 
(-3*10^x*sin(2*x) - 2*10^x*cos(2*x)*log(10))/(2*cos(2*x)^(1/4))
Potencias [src] 
                        3/4                                       
      / -2*I*x    2*I*x\                    x /   -2*I*x    2*I*x\
    x |e         e     |              3*I*10 *\- e       + e     /
- 10 *|------- + ------|   *log(10) + ----------------------------
      \   2        2   /                      __________________  
                                             /  -2*I*x    2*I*x   
                                            /  e         e        
                                       4*4 /   ------- + ------   
                                         \/       2        2
−10x(e2ix2+e−2ix2)34log⁡(10)+3⋅10xi(e2ix−e−2ix)4e2ix2+e−2ix24- 10^{x} \left(\frac{e^{2 i x}}{2} + \frac{e^{- 2 i x}}{2}\right)^{\frac{3}{4}} \log{\left(10 \right)} + \frac{3 \cdot 10^{x} i \left(e^{2 i x} - e^{- 2 i x}\right)}{4 \sqrt[4]{\frac{e^{2 i x}}{2} + \frac{e^{- 2 i x}}{2}}} 
                                x         
    x    3/4                3*10 *sin(2*x)
- 10 *cos   (2*x)*log(10) - --------------
                              4 __________
                            2*\/ cos(2*x)
−3⋅10xsin⁡(2x)2cos⁡(2x)4−10xlog⁡(10)cos⁡34(2x)- \frac{3 \cdot 10^{x} \sin{\left(2 x \right)}}{2 \sqrt[4]{\cos{\left(2 x \right)}}} - 10^{x} \log{\left(10 \right)} \cos^{\frac{3}{4}}{\left(2 x \right)} 
-10^x*cos(2*x)^(3/4)*log(10) - 3*10^x*sin(2*x)/(2*cos(2*x)^(1/4))
Unión de expresiones racionales [src] 
  x                                   
10 *(-3*sin(2*x) - 2*cos(2*x)*log(10))
--------------------------------------
              4 __________            
            2*\/ cos(2*x)
10x(−3sin⁡(2x)−2log⁡(10)cos⁡(2x))2cos⁡(2x)4\frac{10^{x} \left(- 3 \sin{\left(2 x \right)} - 2 \log{\left(10 \right)} \cos{\left(2 x \right)}\right)}{2 \sqrt[4]{\cos{\left(2 x \right)}}} 
10^x*(-3*sin(2*x) - 2*cos(2*x)*log(10))/(2*cos(2*x)^(1/4))
Combinatoria [src] 
   x                                   
-10 *(3*sin(2*x) + 2*cos(2*x)*log(10)) 
---------------------------------------
               4 __________            
             2*\/ cos(2*x)
−10x(3sin⁡(2x)+2log⁡(10)cos⁡(2x))2cos⁡(2x)4- \frac{10^{x} \left(3 \sin{\left(2 x \right)} + 2 \log{\left(10 \right)} \cos{\left(2 x \right)}\right)}{2 \sqrt[4]{\cos{\left(2 x \right)}}} 
-10^x*(3*sin(2*x) + 2*cos(2*x)*log(10))/(2*cos(2*x)^(1/4))
Denominador común [src] 
 /    x                x                 \ 
-\3*10 *sin(2*x) + 2*10 *cos(2*x)*log(10)/ 
-------------------------------------------
                 4 __________              
               2*\/ cos(2*x)
−3⋅10xsin⁡(2x)+2⋅10xlog⁡(10)cos⁡(2x)2cos⁡(2x)4- \frac{3 \cdot 10^{x} \sin{\left(2 x \right)} + 2 \cdot 10^{x} \log{\left(10 \right)} \cos{\left(2 x \right)}}{2 \sqrt[4]{\cos{\left(2 x \right)}}} 
-(3*10^x*sin(2*x) + 2*10^x*cos(2*x)*log(10))/(2*cos(2*x)^(1/4))
Abrimos la expresión [src] 
                      3/4               x              
    x /          2   \              3*10 *cos(x)*sin(x)
- 10 *\-1 + 2*cos (x)/   *log(10) - -------------------
                                       ________________
                                    4 /           2    
                                    \/  -1 + 2*cos (x)
−10x(2cos⁡2(x)−1)34log⁡(10)−3⋅10xsin⁡(x)cos⁡(x)2cos⁡2(x)−14- 10^{x} \left(2 \cos^{2}{\left(x \right)} - 1\right)^{\frac{3}{4}} \log{\left(10 \right)} - \frac{3 \cdot 10^{x} \sin{\left(x \right)} \cos{\left(x \right)}}{\sqrt[4]{2 \cos^{2}{\left(x \right)} - 1}} 
                                x         
    x            3/4        3*10 *sin(2*x)
- 10 *log(10)*cos   (2*x) - --------------
                              4 __________
                            2*\/ cos(2*x)
−3⋅10xsin⁡(2x)2cos⁡(2x)4−10xlog⁡(10)cos⁡34(2x)- \frac{3 \cdot 10^{x} \sin{\left(2 x \right)}}{2 \sqrt[4]{\cos{\left(2 x \right)}}} - 10^{x} \log{\left(10 \right)} \cos^{\frac{3}{4}}{\left(2 x \right)} 
-10^x*log(10)*cos(2*x)^(3/4) - 3*10^x*sin(2*x)/(2*cos(2*x)^(1/4))
Compilar la expresión [src] 
                                x         
    x    3/4                3*10 *sin(2*x)
- 10 *cos   (2*x)*log(10) - --------------
                              4 __________
                            2*\/ cos(2*x)
−3⋅10xsin⁡(2x)2cos⁡(2x)4−10xlog⁡(10)cos⁡34(2x)- \frac{3 \cdot 10^{x} \sin{\left(2 x \right)}}{2 \sqrt[4]{\cos{\left(2 x \right)}}} - 10^{x} \log{\left(10 \right)} \cos^{\frac{3}{4}}{\left(2 x \right)} 
-10^x*cos(2*x)^(3/4)*log(10) - 3*10^x*sin(2*x)/(2*cos(2*x)^(1/4))
Parte trigonométrica [src] 
     /                           /      pi\\
     |                      3*cos|2*x - --||
   x |   3/4                     \      2 /|
-10 *|cos   (2*x)*log(10) + ---------------|
     |                         4 __________|
     \                       2*\/ cos(2*x) /
−10x(log⁡(10)cos⁡34(2x)+3cos⁡(2x−π2)2cos⁡(2x)4)- 10^{x} \left(\log{\left(10 \right)} \cos^{\frac{3}{4}}{\left(2 x \right)} + \frac{3 \cos{\left(2 x - \frac{\pi}{2} \right)}}{2 \sqrt[4]{\cos{\left(2 x \right)}}}\right) 
                3/4                         x          
    x /   1    \                        3*10           
- 10 *|--------|   *log(10) - -------------------------
      \sec(2*x)/                    __________         
                                   /    1              
                              2*4 /  -------- *csc(2*x)
                                \/   sec(2*x)
−10x(1sec⁡(2x))34log⁡(10)−3⋅10x21sec⁡(2x)4csc⁡(2x)- 10^{x} \left(\frac{1}{\sec{\left(2 x \right)}}\right)^{\frac{3}{4}} \log{\left(10 \right)} - \frac{3 \cdot 10^{x}}{2 \sqrt[4]{\frac{1}{\sec{\left(2 x \right)}}} \csc{\left(2 x \right)}} 
   x /   3/4                  3*sin(2*x)  \
-10 *|cos   (2*x)*log(10) + --------------|
     |                        4 __________|
     \                      2*\/ cos(2*x) /
−10x(3sin⁡(2x)2cos⁡(2x)4+log⁡(10)cos⁡34(2x))- 10^{x} \left(\frac{3 \sin{\left(2 x \right)}}{2 \sqrt[4]{\cos{\left(2 x \right)}}} + \log{\left(10 \right)} \cos^{\frac{3}{4}}{\left(2 x \right)}\right) 
                                x    /      pi\
                            3*10 *cos|2*x - --|
    x    3/4                         \      2 /
- 10 *cos   (2*x)*log(10) - -------------------
                                 4 __________  
                               2*\/ cos(2*x)
−10xlog⁡(10)cos⁡34(2x)−3⋅10xcos⁡(2x−π2)2cos⁡(2x)4- 10^{x} \log{\left(10 \right)} \cos^{\frac{3}{4}}{\left(2 x \right)} - \frac{3 \cdot 10^{x} \cos{\left(2 x - \frac{\pi}{2} \right)}}{2 \sqrt[4]{\cos{\left(2 x \right)}}} 
   x /   3/4/pi      \                 3*sin(2*x)     \
-10 *|sin   |-- + 2*x|*log(10) + ---------------------|
     |      \2       /                 _______________|
     |                                /    /pi      \ |
     |                           2*4 /  sin|-- + 2*x| |
     \                             \/      \2       / /
−10x(3sin⁡(2x)2sin⁡(2x+π2)4+log⁡(10)sin⁡34(2x+π2))- 10^{x} \left(\frac{3 \sin{\left(2 x \right)}}{2 \sqrt[4]{\sin{\left(2 x + \frac{\pi}{2} \right)}}} + \log{\left(10 \right)} \sin^{\frac{3}{4}}{\left(2 x + \frac{\pi}{2} \right)}\right) 
     /          3/4                                         \
   x |/   1    \                            3               |
-10 *||--------|   *log(10) + ------------------------------|
     |\sec(2*x)/                    __________              |
     |                             /    1         /      pi\|
     |                        2*4 /  -------- *sec|2*x - --||
     \                          \/   sec(2*x)     \      2 //
−10x((1sec⁡(2x))34log⁡(10)+321sec⁡(2x)4sec⁡(2x−π2))- 10^{x} \left(\left(\frac{1}{\sec{\left(2 x \right)}}\right)^{\frac{3}{4}} \log{\left(10 \right)} + \frac{3}{2 \sqrt[4]{\frac{1}{\sec{\left(2 x \right)}}} \sec{\left(2 x - \frac{\pi}{2} \right)}}\right) 
     /               3/4                                           \
   x |/      1      \                             3                |
-10 *||-------------|   *log(10) + --------------------------------|
     ||   /pi      \|                      _______________         |
     ||csc|-- - 2*x||                     /       1                |
     |\   \2       //              2*    /  ------------- *csc(2*x)|
     |                                  /      /pi      \          |
     |                               4 /    csc|-- - 2*x|          |
     \                               \/        \2       /          /
−10x((1csc⁡(−2x+π2))34log⁡(10)+321csc⁡(−2x+π2)4csc⁡(2x))- 10^{x} \left(\left(\frac{1}{\csc{\left(- 2 x + \frac{\pi}{2} \right)}}\right)^{\frac{3}{4}} \log{\left(10 \right)} + \frac{3}{2 \sqrt[4]{\frac{1}{\csc{\left(- 2 x + \frac{\pi}{2} \right)}}} \csc{\left(2 x \right)}}\right) 
     /             3/4                                            \
     |/       2   \                                               |
   x ||1 - tan (x)|                           3*tan(x)            |
-10 *||-----------|   *log(10) + ---------------------------------|
     ||       2   |                    _____________              |
     |\1 + tan (x)/                   /        2                  |
     |                               /  1 - tan (x)  /       2   \|
     |                              /   ----------- *\1 + tan (x)/|
     |                           4 /           2                  |
     \                           \/     1 + tan (x)               /
−10x((1−tan⁡2(x)tan⁡2(x)+1)34log⁡(10)+3tan⁡(x)1−tan⁡2(x)tan⁡2(x)+14(tan⁡2(x)+1))- 10^{x} \left(\left(\frac{1 - \tan^{2}{\left(x \right)}}{\tan^{2}{\left(x \right)} + 1}\right)^{\frac{3}{4}} \log{\left(10 \right)} + \frac{3 \tan{\left(x \right)}}{\sqrt[4]{\frac{1 - \tan^{2}{\left(x \right)}}{\tan^{2}{\left(x \right)} + 1}} \left(\tan^{2}{\left(x \right)} + 1\right)}\right) 
                                         x            
    x    3/4/pi      \               3*10 *sin(2*x)   
- 10 *sin   |-- + 2*x|*log(10) - ---------------------
            \2       /                 _______________
                                      /    /pi      \ 
                                 2*4 /  sin|-- + 2*x| 
                                   \/      \2       /
−3⋅10xsin⁡(2x)2sin⁡(2x+π2)4−10xlog⁡(10)sin⁡34(2x+π2)- \frac{3 \cdot 10^{x} \sin{\left(2 x \right)}}{2 \sqrt[4]{\sin{\left(2 x + \frac{\pi}{2} \right)}}} - 10^{x} \log{\left(10 \right)} \sin^{\frac{3}{4}}{\left(2 x + \frac{\pi}{2} \right)} 
                   3/4                                            
      /       2   \                             x                 
    x |1 - tan (x)|                         3*10 *tan(x)          
- 10 *|-----------|   *log(10) - ---------------------------------
      |       2   |                    _____________              
      \1 + tan (x)/                   /        2                  
                                     /  1 - tan (x)  /       2   \
                                    /   ----------- *\1 + tan (x)/
                                 4 /           2                  
                                 \/     1 + tan (x)
−10x(1−tan⁡2(x)tan⁡2(x)+1)34log⁡(10)−3⋅10xtan⁡(x)1−tan⁡2(x)tan⁡2(x)+14(tan⁡2(x)+1)- 10^{x} \left(\frac{1 - \tan^{2}{\left(x \right)}}{\tan^{2}{\left(x \right)} + 1}\right)^{\frac{3}{4}} \log{\left(10 \right)} - \frac{3 \cdot 10^{x} \tan{\left(x \right)}}{\sqrt[4]{\frac{1 - \tan^{2}{\left(x \right)}}{\tan^{2}{\left(x \right)} + 1}} \left(\tan^{2}{\left(x \right)} + 1\right)} 
                3/4                           x             
    x /   1    \                          3*10              
- 10 *|--------|   *log(10) - ------------------------------
      \sec(2*x)/                    __________              
                                   /    1         /      pi\
                              2*4 /  -------- *sec|2*x - --|
                                \/   sec(2*x)     \      2 /
−10x(1sec⁡(2x))34log⁡(10)−3⋅10x21sec⁡(2x)4sec⁡(2x−π2)- 10^{x} \left(\frac{1}{\sec{\left(2 x \right)}}\right)^{\frac{3}{4}} \log{\left(10 \right)} - \frac{3 \cdot 10^{x}}{2 \sqrt[4]{\frac{1}{\sec{\left(2 x \right)}}} \sec{\left(2 x - \frac{\pi}{2} \right)}} 
     /              3/4                                             \
     |/        2   \                                                |
   x ||-1 + cot (x)|                           3*cot(x)             |
-10 *||------------|   *log(10) + ----------------------------------|
     ||       2    |                    ______________              |
     |\1 + cot (x) /                   /         2                  |
     |                                /  -1 + cot (x)  /       2   \|
     |                               /   ------------ *\1 + cot (x)/|
     |                            4 /           2                   |
     \                            \/     1 + cot (x)                /
−10x((cot⁡2(x)−1cot⁡2(x)+1)34log⁡(10)+3cot⁡(x)cot⁡2(x)−1cot⁡2(x)+14(cot⁡2(x)+1))- 10^{x} \left(\left(\frac{\cot^{2}{\left(x \right)} - 1}{\cot^{2}{\left(x \right)} + 1}\right)^{\frac{3}{4}} \log{\left(10 \right)} + \frac{3 \cot{\left(x \right)}}{\sqrt[4]{\frac{\cot^{2}{\left(x \right)} - 1}{\cot^{2}{\left(x \right)} + 1}} \left(\cot^{2}{\left(x \right)} + 1\right)}\right) 
                                x         
    x    3/4                3*10 *sin(2*x)
- 10 *cos   (2*x)*log(10) - --------------
                              4 __________
                            2*\/ cos(2*x)
−3⋅10xsin⁡(2x)2cos⁡(2x)4−10xlog⁡(10)cos⁡34(2x)- \frac{3 \cdot 10^{x} \sin{\left(2 x \right)}}{2 \sqrt[4]{\cos{\left(2 x \right)}}} - 10^{x} \log{\left(10 \right)} \cos^{\frac{3}{4}}{\left(2 x \right)} 
                     3/4                            x              
    x /      1      \                           3*10               
- 10 *|-------------|   *log(10) - --------------------------------
      |   /pi      \|                      _______________         
      |csc|-- - 2*x||                     /       1                
      \   \2       //              2*    /  ------------- *csc(2*x)
                                        /      /pi      \          
                                     4 /    csc|-- - 2*x|          
                                     \/        \2       /
−10x(1csc⁡(−2x+π2))34log⁡(10)−3⋅10x21csc⁡(−2x+π2)4csc⁡(2x)- 10^{x} \left(\frac{1}{\csc{\left(- 2 x + \frac{\pi}{2} \right)}}\right)^{\frac{3}{4}} \log{\left(10 \right)} - \frac{3 \cdot 10^{x}}{2 \sqrt[4]{\frac{1}{\csc{\left(- 2 x + \frac{\pi}{2} \right)}}} \csc{\left(2 x \right)}} 
                    3/4                                             
      /        2   \                             x                  
    x |-1 + cot (x)|                         3*10 *cot(x)           
- 10 *|------------|   *log(10) - ----------------------------------
      |       2    |                    ______________              
      \1 + cot (x) /                   /         2                  
                                      /  -1 + cot (x)  /       2   \
                                     /   ------------ *\1 + cot (x)/
                                  4 /           2                   
                                  \/     1 + cot (x)
−10x(cot⁡2(x)−1cot⁡2(x)+1)34log⁡(10)−3⋅10xcot⁡(x)cot⁡2(x)−1cot⁡2(x)+14(cot⁡2(x)+1)- 10^{x} \left(\frac{\cot^{2}{\left(x \right)} - 1}{\cot^{2}{\left(x \right)} + 1}\right)^{\frac{3}{4}} \log{\left(10 \right)} - \frac{3 \cdot 10^{x} \cot{\left(x \right)}}{\sqrt[4]{\frac{\cot^{2}{\left(x \right)} - 1}{\cot^{2}{\left(x \right)} + 1}} \left(\cot^{2}{\left(x \right)} + 1\right)} 
-10^x*((-1 + cot(x)^2)/(1 + cot(x)^2))^(3/4)*log(10) - 3*10^x*cot(x)/(((-1 + cot(x)^2)/(1 + cot(x)^2))^(1/4)*(1 + cot(x)^2))
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