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Simplificación de expresiones/ Descomposición en fracciones simples/ acos(5*x)^4*(-2-2*tan(2*x)^2)/tan(2*x)^2-20*acos(5*x)^3/(sqrt(1-25*x^2)*tan(2*x))

¿Cómo vas a descomponer esta acos(5*x)^4*(-2-2*tan(2*x)^2)/tan(2*x)^2-20*acos(5*x)^3/(sqrt(1-25*x^2)*tan(2*x)) expresión en fracciones?

Expresión a simplificar:

Solución

Ha introducido [src] 
    4      /          2     \               3          
acos (5*x)*\-2 - 2*tan (2*x)/        20*acos (5*x)     
----------------------------- - -----------------------
             2                     ___________         
          tan (2*x)               /         2          
                                \/  1 - 25*x  *tan(2*x)
(−2tan⁡2(2x)−2)acos⁡4(5x)tan⁡2(2x)−20acos⁡3(5x)1−25x2tan⁡(2x)\frac{\left(- 2 \tan^{2}{\left(2 x \right)} - 2\right) \operatorname{acos}^{4}{\left(5 x \right)}}{\tan^{2}{\left(2 x \right)}} - \frac{20 \operatorname{acos}^{3}{\left(5 x \right)}}{\sqrt{1 - 25 x^{2}} \tan{\left(2 x \right)}} 
(acos(5*x)^4*(-2 - 2*tan(2*x)^2))/tan(2*x)^2 - 20*acos(5*x)^3/(sqrt(1 - 25*x^2)*tan(2*x))
Simplificación general [src] 
           /                              ___________          \
           |                             /         2           |
    3      |     20                  4*\/  1 - 25*x  *acos(5*x)|
acos (5*x)*|- -------- + 20*tan(x) - --------------------------|
           \  sin(2*x)                      1 - cos(4*x)       /
----------------------------------------------------------------
                            ___________                         
                           /         2                          
                         \/  1 - 25*x
(−41−25x2acos⁡(5x)1−cos⁡(4x)+20tan⁡(x)−20sin⁡(2x))acos⁡3(5x)1−25x2\frac{\left(- \frac{4 \sqrt{1 - 25 x^{2}} \operatorname{acos}{\left(5 x \right)}}{1 - \cos{\left(4 x \right)}} + 20 \tan{\left(x \right)} - \frac{20}{\sin{\left(2 x \right)}}\right) \operatorname{acos}^{3}{\left(5 x \right)}}{\sqrt{1 - 25 x^{2}}} 
acos(5*x)^3*(-20/sin(2*x) + 20*tan(x) - 4*sqrt(1 - 25*x^2)*acos(5*x)/(1 - cos(4*x)))/sqrt(1 - 25*x^2)
Denominador racional [src] 
                                                                                                                ___________                     
      4         3              4                     2     4         3            2     4                      /         2      3         2     
2*acos (5*x)*tan (2*x) + 2*acos (5*x)*tan(2*x) - 50*x *acos (5*x)*tan (2*x) - 50*x *acos (5*x)*tan(2*x) + 20*\/  1 - 25*x  *acos (5*x)*tan (2*x)
------------------------------------------------------------------------------------------------------------------------------------------------
                                                             /         2\    3                                                                  
                                                             \-1 + 25*x /*tan (2*x)
−50x2tan⁡3(2x)acos⁡4(5x)−50x2tan⁡(2x)acos⁡4(5x)+201−25x2tan⁡2(2x)acos⁡3(5x)+2tan⁡3(2x)acos⁡4(5x)+2tan⁡(2x)acos⁡4(5x)(25x2−1)tan⁡3(2x)\frac{- 50 x^{2} \tan^{3}{\left(2 x \right)} \operatorname{acos}^{4}{\left(5 x \right)} - 50 x^{2} \tan{\left(2 x \right)} \operatorname{acos}^{4}{\left(5 x \right)} + 20 \sqrt{1 - 25 x^{2}} \tan^{2}{\left(2 x \right)} \operatorname{acos}^{3}{\left(5 x \right)} + 2 \tan^{3}{\left(2 x \right)} \operatorname{acos}^{4}{\left(5 x \right)} + 2 \tan{\left(2 x \right)} \operatorname{acos}^{4}{\left(5 x \right)}}{\left(25 x^{2} - 1\right) \tan^{3}{\left(2 x \right)}} 
(2*acos(5*x)^4*tan(2*x)^3 + 2*acos(5*x)^4*tan(2*x) - 50*x^2*acos(5*x)^4*tan(2*x)^3 - 50*x^2*acos(5*x)^4*tan(2*x) + 20*sqrt(1 - 25*x^2)*acos(5*x)^3*tan(2*x)^2)/((-1 + 25*x^2)*tan(2*x)^3)
Combinatoria [src] 
              /                 ___________                ___________                    \
       3      |                /         2                /         2     2               |
-2*acos (5*x)*\10*tan(2*x) + \/  1 - 25*x  *acos(5*x) + \/  1 - 25*x  *tan (2*x)*acos(5*x)/
-------------------------------------------------------------------------------------------
                              _______________________    2                                 
                            \/ -(1 + 5*x)*(-1 + 5*x) *tan (2*x)
−2(1−25x2tan⁡2(2x)acos⁡(5x)+1−25x2acos⁡(5x)+10tan⁡(2x))acos⁡3(5x)−(5x−1)(5x+1)tan⁡2(2x)- \frac{2 \left(\sqrt{1 - 25 x^{2}} \tan^{2}{\left(2 x \right)} \operatorname{acos}{\left(5 x \right)} + \sqrt{1 - 25 x^{2}} \operatorname{acos}{\left(5 x \right)} + 10 \tan{\left(2 x \right)}\right) \operatorname{acos}^{3}{\left(5 x \right)}}{\sqrt{- \left(5 x - 1\right) \left(5 x + 1\right)} \tan^{2}{\left(2 x \right)}} 
-2*acos(5*x)^3*(10*tan(2*x) + sqrt(1 - 25*x^2)*acos(5*x) + sqrt(1 - 25*x^2)*tan(2*x)^2*acos(5*x))/(sqrt(-(1 + 5*x)*(-1 + 5*x))*tan(2*x)^2)
Potencias [src] 
                                 /                           2\                                      
                    2            |       /   2*I*x    -2*I*x\ |                                      
  / -2*I*x    2*I*x\      4      |     2*\- e      + e      / |                                      
  \e       + e     / *acos (5*x)*|-2 + -----------------------|                                      
                                 |                         2  |                                      
                                 |       / -2*I*x    2*I*x\   |             3      / -2*I*x    2*I*x\
                                 \       \e       + e     /   /    20*I*acos (5*x)*\e       + e     /
- ------------------------------------------------------------- + -----------------------------------
                                          2                          ___________                     
                      /   2*I*x    -2*I*x\                          /         2  /   2*I*x    -2*I*x\
                      \- e      + e      /                        \/  1 - 25*x  *\- e      + e      /
−(2(−e2ix+e−2ix)2(e2ix+e−2ix)2−2)(e2ix+e−2ix)2acos⁡4(5x)(−e2ix+e−2ix)2+20i(e2ix+e−2ix)acos⁡3(5x)1−25x2(−e2ix+e−2ix)- \frac{\left(\frac{2 \left(- e^{2 i x} + e^{- 2 i x}\right)^{2}}{\left(e^{2 i x} + e^{- 2 i x}\right)^{2}} - 2\right) \left(e^{2 i x} + e^{- 2 i x}\right)^{2} \operatorname{acos}^{4}{\left(5 x \right)}}{\left(- e^{2 i x} + e^{- 2 i x}\right)^{2}} + \frac{20 i \left(e^{2 i x} + e^{- 2 i x}\right) \operatorname{acos}^{3}{\left(5 x \right)}}{\sqrt{1 - 25 x^{2}} \left(- e^{2 i x} + e^{- 2 i x}\right)} 
-(exp(-2*i*x) + exp(2*i*x))^2*acos(5*x)^4*(-2 + 2*(-exp(2*i*x) + exp(-2*i*x))^2/(exp(-2*i*x) + exp(2*i*x))^2)/(-exp(2*i*x) + exp(-2*i*x))^2 + 20*i*acos(5*x)^3*(exp(-2*i*x) + exp(2*i*x))/(sqrt(1 - 25*x^2)*(-exp(2*i*x) + exp(-2*i*x)))
Unión de expresiones racionales [src] 
             /                  ___________                           \
      3      |                 /         2  /        2     \          |
2*acos (5*x)*\-10*tan(2*x) + \/  1 - 25*x  *\-1 - tan (2*x)/*acos(5*x)/
-----------------------------------------------------------------------
                           ___________                                 
                          /         2     2                            
                        \/  1 - 25*x  *tan (2*x)
2(1−25x2(−tan⁡2(2x)−1)acos⁡(5x)−10tan⁡(2x))acos⁡3(5x)1−25x2tan⁡2(2x)\frac{2 \left(\sqrt{1 - 25 x^{2}} \left(- \tan^{2}{\left(2 x \right)} - 1\right) \operatorname{acos}{\left(5 x \right)} - 10 \tan{\left(2 x \right)}\right) \operatorname{acos}^{3}{\left(5 x \right)}}{\sqrt{1 - 25 x^{2}} \tan^{2}{\left(2 x \right)}} 
2*acos(5*x)^3*(-10*tan(2*x) + sqrt(1 - 25*x^2)*(-1 - tan(2*x)^2)*acos(5*x))/(sqrt(1 - 25*x^2)*tan(2*x)^2)
Respuesta numérica [src] 
acos(5*x)^4*(-2.0 - 2.0*tan(2*x)^2)/tan(2*x)^2 - 4.0*(0.04 - x^2)^(-0.5)*acos(5*x)^3/tan(2*x)
acos(5*x)^4*(-2.0 - 2.0*tan(2*x)^2)/tan(2*x)^2 - 4.0*(0.04 - x^2)^(-0.5)*acos(5*x)^3/tan(2*x)
Parte trigonométrica [src] 
                                       3         /      pi\
                                20*acos (5*x)*sec|2*x - --|
        4         2/      pi\                    \      2 /
- 2*acos (5*x)*sec |2*x - --| - ---------------------------
                   \      2 /        ___________           
                                    /         2            
                                  \/  1 - 25*x  *sec(2*x)
−2acos⁡4(5x)sec⁡2(2x−π2)−20acos⁡3(5x)sec⁡(2x−π2)1−25x2sec⁡(2x)- 2 \operatorname{acos}^{4}{\left(5 x \right)} \sec^{2}{\left(2 x - \frac{\pi}{2} \right)} - \frac{20 \operatorname{acos}^{3}{\left(5 x \right)} \sec{\left(2 x - \frac{\pi}{2} \right)}}{\sqrt{1 - 25 x^{2}} \sec{\left(2 x \right)}} 
                          /           2       \                              
    4         2/      pi\ |      2*sec (2*x)  |                              
acos (5*x)*sec |2*x - --|*|-2 - --------------|                              
               \      2 / |        2/      pi\|          3         /      pi\
                          |     sec |2*x - --||   20*acos (5*x)*sec|2*x - --|
                          \         \      2 //                    \      2 /
----------------------------------------------- - ---------------------------
                      2                                ___________           
                   sec (2*x)                          /         2            
                                                    \/  1 - 25*x  *sec(2*x)
(−2sec⁡2(2x)sec⁡2(2x−π2)−2)acos⁡4(5x)sec⁡2(2x−π2)sec⁡2(2x)−20acos⁡3(5x)sec⁡(2x−π2)1−25x2sec⁡(2x)\frac{\left(- \frac{2 \sec^{2}{\left(2 x \right)}}{\sec^{2}{\left(2 x - \frac{\pi}{2} \right)}} - 2\right) \operatorname{acos}^{4}{\left(5 x \right)} \sec^{2}{\left(2 x - \frac{\pi}{2} \right)}}{\sec^{2}{\left(2 x \right)}} - \frac{20 \operatorname{acos}^{3}{\left(5 x \right)} \sec{\left(2 x - \frac{\pi}{2} \right)}}{\sqrt{1 - 25 x^{2}} \sec{\left(2 x \right)}} 
                                        2           
         3                 /       2   \      4     
  20*acos (5*x)*cot(2*x)   \1 + cot (x)/ *acos (5*x)
- ---------------------- - -------------------------
         ___________                    2           
        /         2                2*cot (x)        
      \/  1 - 25*x
−(cot⁡2(x)+1)2acos⁡4(5x)2cot⁡2(x)−20cot⁡(2x)acos⁡3(5x)1−25x2- \frac{\left(\cot^{2}{\left(x \right)} + 1\right)^{2} \operatorname{acos}^{4}{\left(5 x \right)}}{2 \cot^{2}{\left(x \right)}} - \frac{20 \cot{\left(2 x \right)} \operatorname{acos}^{3}{\left(5 x \right)}}{\sqrt{1 - 25 x^{2}}} 
                                                4     
         3                 1              4*acos (5*x)
- 20*acos (5*x)*----------------------- - ------------
                   ___________            1 - cos(4*x)
                  /         2                         
                \/  1 - 25*x  *tan(2*x)
−2011−25x2tan⁡(2x)acos⁡3(5x)−4acos⁡4(5x)1−cos⁡(4x)- 20 \frac{1}{\sqrt{1 - 25 x^{2}} \tan{\left(2 x \right)}} \operatorname{acos}^{3}{\left(5 x \right)} - \frac{4 \operatorname{acos}^{4}{\left(5 x \right)}}{1 - \cos{\left(4 x \right)}} 
                     /          2/pi      \\                               
                     |     2*csc |-- - 2*x||                               
    4         2      |           \2       /|                               
acos (5*x)*csc (2*x)*|-2 - ----------------|                               
                     |           2         |             3                 
                     \        csc (2*x)    /      20*acos (5*x)*csc(2*x)   
-------------------------------------------- - ----------------------------
                  2/pi      \                     ___________              
               csc |-- - 2*x|                    /         2     /pi      \
                   \2       /                  \/  1 - 25*x  *csc|-- - 2*x|
                                                                 \2       /
(−2−2csc⁡2(−2x+π2)csc⁡2(2x))acos⁡4(5x)csc⁡2(2x)csc⁡2(−2x+π2)−20acos⁡3(5x)csc⁡(2x)1−25x2csc⁡(−2x+π2)\frac{\left(-2 - \frac{2 \csc^{2}{\left(- 2 x + \frac{\pi}{2} \right)}}{\csc^{2}{\left(2 x \right)}}\right) \operatorname{acos}^{4}{\left(5 x \right)} \csc^{2}{\left(2 x \right)}}{\csc^{2}{\left(- 2 x + \frac{\pi}{2} \right)}} - \frac{20 \operatorname{acos}^{3}{\left(5 x \right)} \csc{\left(2 x \right)}}{\sqrt{1 - 25 x^{2}} \csc{\left(- 2 x + \frac{\pi}{2} \right)}} 
                                               3              
    4         2      /         2    \   20*acos (5*x)*cot(2*x)
acos (5*x)*cot (2*x)*|-2 - ---------| - ----------------------
                     |        2     |          ___________    
                     \     cot (2*x)/         /         2     
                                            \/  1 - 25*x
(−2−2cot⁡2(2x))cot⁡2(2x)acos⁡4(5x)−20cot⁡(2x)acos⁡3(5x)1−25x2\left(-2 - \frac{2}{\cot^{2}{\left(2 x \right)}}\right) \cot^{2}{\left(2 x \right)} \operatorname{acos}^{4}{\left(5 x \right)} - \frac{20 \cot{\left(2 x \right)} \operatorname{acos}^{3}{\left(5 x \right)}}{\sqrt{1 - 25 x^{2}}} 
                                                  /          4     \
                                 4         2      |     8*sin (2*x)|
                             acos (5*x)*sin (4*x)*|-2 - -----------|
          3                                       |         2      |
   10*acos (5*x)*sin(4*x)                         \      sin (4*x) /
- ------------------------ + ---------------------------------------
     ___________                                4                   
    /         2     2                      4*sin (2*x)              
  \/  1 - 25*x  *sin (2*x)
(−8sin⁡4(2x)sin⁡2(4x)−2)sin⁡2(4x)acos⁡4(5x)4sin⁡4(2x)−10sin⁡(4x)acos⁡3(5x)1−25x2sin⁡2(2x)\frac{\left(- \frac{8 \sin^{4}{\left(2 x \right)}}{\sin^{2}{\left(4 x \right)}} - 2\right) \sin^{2}{\left(4 x \right)} \operatorname{acos}^{4}{\left(5 x \right)}}{4 \sin^{4}{\left(2 x \right)}} - \frac{10 \sin{\left(4 x \right)} \operatorname{acos}^{3}{\left(5 x \right)}}{\sqrt{1 - 25 x^{2}} \sin^{2}{\left(2 x \right)}} 
        4                    3          
  2*acos (5*x)        20*acos (5*x)     
- ------------ - -----------------------
      2             ___________         
   sin (2*x)       /         2          
                 \/  1 - 25*x  *tan(2*x)
−2acos⁡4(5x)sin⁡2(2x)−20acos⁡3(5x)1−25x2tan⁡(2x)- \frac{2 \operatorname{acos}^{4}{\left(5 x \right)}}{\sin^{2}{\left(2 x \right)}} - \frac{20 \operatorname{acos}^{3}{\left(5 x \right)}}{\sqrt{1 - 25 x^{2}} \tan{\left(2 x \right)}} 
                                     3                 
        4         2           20*acos (5*x)*csc(2*x)   
- 2*acos (5*x)*csc (2*x) - ----------------------------
                              ___________              
                             /         2     /pi      \
                           \/  1 - 25*x  *csc|-- - 2*x|
                                             \2       /
−2acos⁡4(5x)csc⁡2(2x)−20acos⁡3(5x)csc⁡(2x)1−25x2csc⁡(−2x+π2)- 2 \operatorname{acos}^{4}{\left(5 x \right)} \csc^{2}{\left(2 x \right)} - \frac{20 \operatorname{acos}^{3}{\left(5 x \right)} \csc{\left(2 x \right)}}{\sqrt{1 - 25 x^{2}} \csc{\left(- 2 x + \frac{\pi}{2} \right)}} 
        4                  3                 
  4*acos (5*x)      20*acos (5*x)*cos(2*x)   
- ------------ - ----------------------------
  1 - cos(4*x)      ___________              
                   /         2     /      pi\
                 \/  1 - 25*x  *cos|2*x - --|
                                   \      2 /
−4acos⁡4(5x)1−cos⁡(4x)−20cos⁡(2x)acos⁡3(5x)1−25x2cos⁡(2x−π2)- \frac{4 \operatorname{acos}^{4}{\left(5 x \right)}}{1 - \cos{\left(4 x \right)}} - \frac{20 \cos{\left(2 x \right)} \operatorname{acos}^{3}{\left(5 x \right)}}{\sqrt{1 - 25 x^{2}} \cos{\left(2 x - \frac{\pi}{2} \right)}} 
                     /          2/      pi\\                               
                     |     2*cos |2*x - --||                               
    4         2      |           \      2 /|                               
acos (5*x)*cos (2*x)*|-2 - ----------------|                               
                     |           2         |             3                 
                     \        cos (2*x)    /      20*acos (5*x)*cos(2*x)   
-------------------------------------------- - ----------------------------
                  2/      pi\                     ___________              
               cos |2*x - --|                    /         2     /      pi\
                   \      2 /                  \/  1 - 25*x  *cos|2*x - --|
                                                                 \      2 /
(−2−2cos⁡2(2x−π2)cos⁡2(2x))cos⁡2(2x)acos⁡4(5x)cos⁡2(2x−π2)−20cos⁡(2x)acos⁡3(5x)1−25x2cos⁡(2x−π2)\frac{\left(-2 - \frac{2 \cos^{2}{\left(2 x - \frac{\pi}{2} \right)}}{\cos^{2}{\left(2 x \right)}}\right) \cos^{2}{\left(2 x \right)} \operatorname{acos}^{4}{\left(5 x \right)}}{\cos^{2}{\left(2 x - \frac{\pi}{2} \right)}} - \frac{20 \cos{\left(2 x \right)} \operatorname{acos}^{3}{\left(5 x \right)}}{\sqrt{1 - 25 x^{2}} \cos{\left(2 x - \frac{\pi}{2} \right)}} 
                     /          2     \                          
    4         2      |     2*sin (2*x)|                          
acos (5*x)*cos (2*x)*|-2 - -----------|                          
                     |         2      |           3              
                     \      cos (2*x) /    20*acos (5*x)*cos(2*x)
--------------------------------------- - -----------------------
                  2                          ___________         
               sin (2*x)                    /         2          
                                          \/  1 - 25*x  *sin(2*x)
(−2sin⁡2(2x)cos⁡2(2x)−2)cos⁡2(2x)acos⁡4(5x)sin⁡2(2x)−20cos⁡(2x)acos⁡3(5x)1−25x2sin⁡(2x)\frac{\left(- \frac{2 \sin^{2}{\left(2 x \right)}}{\cos^{2}{\left(2 x \right)}} - 2\right) \cos^{2}{\left(2 x \right)} \operatorname{acos}^{4}{\left(5 x \right)}}{\sin^{2}{\left(2 x \right)}} - \frac{20 \cos{\left(2 x \right)} \operatorname{acos}^{3}{\left(5 x \right)}}{\sqrt{1 - 25 x^{2}} \sin{\left(2 x \right)}} 
           4                  3              
     4*acos (5*x)      20*acos (5*x)*cot(2*x)
- ------------------ - ----------------------
              2               ___________    
      -1 + cot (2*x)         /         2     
  1 - --------------       \/  1 - 25*x      
             2                               
      1 + cot (2*x)
−4acos⁡4(5x)−cot⁡2(2x)−1cot⁡2(2x)+1+1−20cot⁡(2x)acos⁡3(5x)1−25x2- \frac{4 \operatorname{acos}^{4}{\left(5 x \right)}}{- \frac{\cot^{2}{\left(2 x \right)} - 1}{\cot^{2}{\left(2 x \right)} + 1} + 1} - \frac{20 \cot{\left(2 x \right)} \operatorname{acos}^{3}{\left(5 x \right)}}{\sqrt{1 - 25 x^{2}}} 
           4                  3               
     4*acos (5*x)      10*acos (5*x)*sin(4*x) 
- ----------------- - ------------------------
         /pi      \      ___________          
  1 - sin|-- + 4*x|     /         2     2     
         \2       /   \/  1 - 25*x  *sin (2*x)
−4acos⁡4(5x)1−sin⁡(4x+π2)−10sin⁡(4x)acos⁡3(5x)1−25x2sin⁡2(2x)- \frac{4 \operatorname{acos}^{4}{\left(5 x \right)}}{1 - \sin{\left(4 x + \frac{\pi}{2} \right)}} - \frac{10 \sin{\left(4 x \right)} \operatorname{acos}^{3}{\left(5 x \right)}}{\sqrt{1 - 25 x^{2}} \sin^{2}{\left(2 x \right)}} 
        4                    3          
  4*acos (5*x)        20*acos (5*x)     
- ------------ - -----------------------
  1 - cos(4*x)      ___________         
                   /         2          
                 \/  1 - 25*x  *tan(2*x)
−4acos⁡4(5x)1−cos⁡(4x)−20acos⁡3(5x)1−25x2tan⁡(2x)- \frac{4 \operatorname{acos}^{4}{\left(5 x \right)}}{1 - \cos{\left(4 x \right)}} - \frac{20 \operatorname{acos}^{3}{\left(5 x \right)}}{\sqrt{1 - 25 x^{2}} \tan{\left(2 x \right)}} 
         4                   3                 
   2*acos (5*x)       20*acos (5*x)*cos(2*x)   
- -------------- - ----------------------------
     2/      pi\      ___________              
  cos |2*x - --|     /         2     /      pi\
      \      2 /   \/  1 - 25*x  *cos|2*x - --|
                                     \      2 /
−2acos⁡4(5x)cos⁡2(2x−π2)−20cos⁡(2x)acos⁡3(5x)1−25x2cos⁡(2x−π2)- \frac{2 \operatorname{acos}^{4}{\left(5 x \right)}}{\cos^{2}{\left(2 x - \frac{\pi}{2} \right)}} - \frac{20 \cos{\left(2 x \right)} \operatorname{acos}^{3}{\left(5 x \right)}}{\sqrt{1 - 25 x^{2}} \cos{\left(2 x - \frac{\pi}{2} \right)}} 
                                       3          
        4         2             20*acos (5*x)     
- 2*acos (5*x)*csc (2*x) - -----------------------
                              ___________         
                             /         2          
                           \/  1 - 25*x  *tan(2*x)
−2acos⁡4(5x)csc⁡2(2x)−20acos⁡3(5x)1−25x2tan⁡(2x)- 2 \operatorname{acos}^{4}{\left(5 x \right)} \csc^{2}{\left(2 x \right)} - \frac{20 \operatorname{acos}^{3}{\left(5 x \right)}}{\sqrt{1 - 25 x^{2}} \tan{\left(2 x \right)}} 
        4               3              
  4*acos (5*x)   20*acos (5*x)*cot(2*x)
- ------------ - ----------------------
  1 - cos(4*x)          ___________    
                       /         2     
                     \/  1 - 25*x
−4acos⁡4(5x)1−cos⁡(4x)−20cot⁡(2x)acos⁡3(5x)1−25x2- \frac{4 \operatorname{acos}^{4}{\left(5 x \right)}}{1 - \cos{\left(4 x \right)}} - \frac{20 \cot{\left(2 x \right)} \operatorname{acos}^{3}{\left(5 x \right)}}{\sqrt{1 - 25 x^{2}}} 
           4                    3                 
     4*acos (5*x)        20*acos (5*x)*csc(2*x)   
- ----------------- - ----------------------------
            1            ___________              
  1 - -------------     /         2     /pi      \
         /pi      \   \/  1 - 25*x  *csc|-- - 2*x|
      csc|-- - 4*x|                     \2       /
         \2       /
−4acos⁡4(5x)1−1csc⁡(−4x+π2)−20acos⁡3(5x)csc⁡(2x)1−25x2csc⁡(−2x+π2)- \frac{4 \operatorname{acos}^{4}{\left(5 x \right)}}{1 - \frac{1}{\csc{\left(- 4 x + \frac{\pi}{2} \right)}}} - \frac{20 \operatorname{acos}^{3}{\left(5 x \right)} \csc{\left(2 x \right)}}{\sqrt{1 - 25 x^{2}} \csc{\left(- 2 x + \frac{\pi}{2} \right)}} 
           4                      3          
     4*acos (5*x)          20*acos (5*x)     
- ----------------- - -----------------------
             2           ___________         
      1 - tan (2*x)     /         2          
  1 - -------------   \/  1 - 25*x  *tan(2*x)
             2                               
      1 + tan (2*x)
−4acos⁡4(5x)−1−tan⁡2(2x)tan⁡2(2x)+1+1−20acos⁡3(5x)1−25x2tan⁡(2x)- \frac{4 \operatorname{acos}^{4}{\left(5 x \right)}}{- \frac{1 - \tan^{2}{\left(2 x \right)}}{\tan^{2}{\left(2 x \right)} + 1} + 1} - \frac{20 \operatorname{acos}^{3}{\left(5 x \right)}}{\sqrt{1 - 25 x^{2}} \tan{\left(2 x \right)}} 
                        3         /      pi\
        4        20*acos (5*x)*sec|2*x - --|
  4*acos (5*x)                    \      2 /
- ------------ - ---------------------------
         1            ___________           
  1 - --------       /         2            
      sec(4*x)     \/  1 - 25*x  *sec(2*x)
−4acos⁡4(5x)1−1sec⁡(4x)−20acos⁡3(5x)sec⁡(2x−π2)1−25x2sec⁡(2x)- \frac{4 \operatorname{acos}^{4}{\left(5 x \right)}}{1 - \frac{1}{\sec{\left(4 x \right)}}} - \frac{20 \operatorname{acos}^{3}{\left(5 x \right)} \sec{\left(2 x - \frac{\pi}{2} \right)}}{\sqrt{1 - 25 x^{2}} \sec{\left(2 x \right)}} 
                                         2           
              3             /       2   \      4     
       20*acos (5*x)        \1 + tan (x)/ *acos (5*x)
- ----------------------- - -------------------------
     ___________                         2           
    /         2                     2*tan (x)        
  \/  1 - 25*x  *tan(2*x)
−(tan⁡2(x)+1)2acos⁡4(5x)2tan⁡2(x)−20acos⁡3(5x)1−25x2tan⁡(2x)- \frac{\left(\tan^{2}{\left(x \right)} + 1\right)^{2} \operatorname{acos}^{4}{\left(5 x \right)}}{2 \tan^{2}{\left(x \right)}} - \frac{20 \operatorname{acos}^{3}{\left(5 x \right)}}{\sqrt{1 - 25 x^{2}} \tan{\left(2 x \right)}} 
                     /          2     \                          
    4         2      |     2*sec (2*x)|                          
acos (5*x)*csc (2*x)*|-2 - -----------|                          
                     |         2      |           3              
                     \      csc (2*x) /    20*acos (5*x)*csc(2*x)
--------------------------------------- - -----------------------
                  2                          ___________         
               sec (2*x)                    /         2          
                                          \/  1 - 25*x  *sec(2*x)
(−2−2sec⁡2(2x)csc⁡2(2x))acos⁡4(5x)csc⁡2(2x)sec⁡2(2x)−20acos⁡3(5x)csc⁡(2x)1−25x2sec⁡(2x)\frac{\left(-2 - \frac{2 \sec^{2}{\left(2 x \right)}}{\csc^{2}{\left(2 x \right)}}\right) \operatorname{acos}^{4}{\left(5 x \right)} \csc^{2}{\left(2 x \right)}}{\sec^{2}{\left(2 x \right)}} - \frac{20 \operatorname{acos}^{3}{\left(5 x \right)} \csc{\left(2 x \right)}}{\sqrt{1 - 25 x^{2}} \sec{\left(2 x \right)}} 
                                       3         /      pi\
                                20*acos (5*x)*sec|2*x - --|
        4         2/pi      \                    \      2 /
- 2*acos (5*x)*sec |-- - 2*x| - ---------------------------
                   \2       /        ___________           
                                    /         2            
                                  \/  1 - 25*x  *sec(2*x)
−2acos⁡4(5x)sec⁡2(−2x+π2)−20acos⁡3(5x)sec⁡(2x−π2)1−25x2sec⁡(2x)- 2 \operatorname{acos}^{4}{\left(5 x \right)} \sec^{2}{\left(- 2 x + \frac{\pi}{2} \right)} - \frac{20 \operatorname{acos}^{3}{\left(5 x \right)} \sec{\left(2 x - \frac{\pi}{2} \right)}}{\sqrt{1 - 25 x^{2}} \sec{\left(2 x \right)}} 
        4                3               
  2*acos (5*x)    10*acos (5*x)*sin(4*x) 
- ------------ - ------------------------
      2             ___________          
   sin (2*x)       /         2     2     
                 \/  1 - 25*x  *sin (2*x)
−2acos⁡4(5x)sin⁡2(2x)−10sin⁡(4x)acos⁡3(5x)1−25x2sin⁡2(2x)- \frac{2 \operatorname{acos}^{4}{\left(5 x \right)}}{\sin^{2}{\left(2 x \right)}} - \frac{10 \sin{\left(4 x \right)} \operatorname{acos}^{3}{\left(5 x \right)}}{\sqrt{1 - 25 x^{2}} \sin^{2}{\left(2 x \right)}} 
-2*acos(5*x)^4/sin(2*x)^2 - 10*acos(5*x)^3*sin(4*x)/(sqrt(1 - 25*x^2)*sin(2*x)^2)
Abrimos la expresión [src] 
                   4            4         2                 3                   3            
      4        acos (5*x)   acos (5*x)*tan (x)       10*acos (5*x)       10*acos (5*x)*tan(x)
- acos (5*x) - ---------- - ------------------ - --------------------- + --------------------
                    2               2               ___________                ___________   
               2*tan (x)                           /         2                /         2    
                                                 \/  1 - 25*x  *tan(x)      \/  1 - 25*x
−tan⁡2(x)acos⁡4(5x)2−acos⁡4(5x)−acos⁡4(5x)2tan⁡2(x)+10tan⁡(x)acos⁡3(5x)1−25x2−10acos⁡3(5x)1−25x2tan⁡(x)- \frac{\tan^{2}{\left(x \right)} \operatorname{acos}^{4}{\left(5 x \right)}}{2} - \operatorname{acos}^{4}{\left(5 x \right)} - \frac{\operatorname{acos}^{4}{\left(5 x \right)}}{2 \tan^{2}{\left(x \right)}} + \frac{10 \tan{\left(x \right)} \operatorname{acos}^{3}{\left(5 x \right)}}{\sqrt{1 - 25 x^{2}}} - \frac{10 \operatorname{acos}^{3}{\left(5 x \right)}}{\sqrt{1 - 25 x^{2}} \tan{\left(x \right)}} 
-acos(5*x)^4 - acos(5*x)^4/(2*tan(x)^2) - acos(5*x)^4*tan(x)^2/2 - 10*acos(5*x)^3/(sqrt(1 - 25*x^2)*tan(x)) + 10*acos(5*x)^3*tan(x)/sqrt(1 - 25*x^2)
Denominador común [src] 
                      ___________                                    
                     /         2      4               3              
        4        2*\/  1 - 25*x  *acos (5*x) + 20*acos (5*x)*tan(2*x)
- 2*acos (5*x) - ----------------------------------------------------
                                  ___________                        
                                 /         2     2                   
                               \/  1 - 25*x  *tan (2*x)
−2acos⁡4(5x)−21−25x2acos⁡4(5x)+20tan⁡(2x)acos⁡3(5x)1−25x2tan⁡2(2x)- 2 \operatorname{acos}^{4}{\left(5 x \right)} - \frac{2 \sqrt{1 - 25 x^{2}} \operatorname{acos}^{4}{\left(5 x \right)} + 20 \tan{\left(2 x \right)} \operatorname{acos}^{3}{\left(5 x \right)}}{\sqrt{1 - 25 x^{2}} \tan^{2}{\left(2 x \right)}} 
-2*acos(5*x)^4 - (2*sqrt(1 - 25*x^2)*acos(5*x)^4 + 20*acos(5*x)^3*tan(2*x))/(sqrt(1 - 25*x^2)*tan(2*x)^2)
    © Sr Examen – Калькулятор