Sr Examen
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?
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)
$$\frac{\left(- 2 \tan^{2}{\left(2 x \right)} - 2\right) \operatorname{acos}^{4}{\left(5 x \right)}}{\tan^{2}{\left(2 x \right)}} - \frac{20 \operatorname{acos}^{3}{\left(5 x \right)}}{\sqrt{1 - 25 x^{2}} \tan{\left(2 x \right)}}$$
(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
$$\frac{\left(- \frac{4 \sqrt{1 - 25 x^{2}} \operatorname{acos}{\left(5 x \right)}}{1 - \cos{\left(4 x \right)}} + 20 \tan{\left(x \right)} - \frac{20}{\sin{\left(2 x \right)}}\right) \operatorname{acos}^{3}{\left(5 x \right)}}{\sqrt{1 - 25 x^{2}}}$$
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)
$$\frac{- 50 x^{2} \tan^{3}{\left(2 x \right)} \operatorname{acos}^{4}{\left(5 x \right)} - 50 x^{2} \tan{\left(2 x \right)} \operatorname{acos}^{4}{\left(5 x \right)} + 20 \sqrt{1 - 25 x^{2}} \tan^{2}{\left(2 x \right)} \operatorname{acos}^{3}{\left(5 x \right)} + 2 \tan^{3}{\left(2 x \right)} \operatorname{acos}^{4}{\left(5 x \right)} + 2 \tan{\left(2 x \right)} \operatorname{acos}^{4}{\left(5 x \right)}}{\left(25 x^{2} - 1\right) \tan^{3}{\left(2 x \right)}}$$
(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)
$$- \frac{2 \left(\sqrt{1 - 25 x^{2}} \tan^{2}{\left(2 x \right)} \operatorname{acos}{\left(5 x \right)} + \sqrt{1 - 25 x^{2}} \operatorname{acos}{\left(5 x \right)} + 10 \tan{\left(2 x \right)}\right) \operatorname{acos}^{3}{\left(5 x \right)}}{\sqrt{- \left(5 x - 1\right) \left(5 x + 1\right)} \tan^{2}{\left(2 x \right)}}$$
-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 /
$$- \frac{\left(\frac{2 \left(- e^{2 i x} + e^{- 2 i x}\right)^{2}}{\left(e^{2 i x} + e^{- 2 i x}\right)^{2}} - 2\right) \left(e^{2 i x} + e^{- 2 i x}\right)^{2} \operatorname{acos}^{4}{\left(5 x \right)}}{\left(- e^{2 i x} + e^{- 2 i x}\right)^{2}} + \frac{20 i \left(e^{2 i x} + e^{- 2 i x}\right) \operatorname{acos}^{3}{\left(5 x \right)}}{\sqrt{1 - 25 x^{2}} \left(- e^{2 i x} + e^{- 2 i x}\right)}$$
-(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)
$$\frac{2 \left(\sqrt{1 - 25 x^{2}} \left(- \tan^{2}{\left(2 x \right)} - 1\right) \operatorname{acos}{\left(5 x \right)} - 10 \tan{\left(2 x \right)}\right) \operatorname{acos}^{3}{\left(5 x \right)}}{\sqrt{1 - 25 x^{2}} \tan^{2}{\left(2 x \right)}}$$
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)
$$- 2 \operatorname{acos}^{4}{\left(5 x \right)} \sec^{2}{\left(2 x - \frac{\pi}{2} \right)} - \frac{20 \operatorname{acos}^{3}{\left(5 x \right)} \sec{\left(2 x - \frac{\pi}{2} \right)}}{\sqrt{1 - 25 x^{2}} \sec{\left(2 x \right)}}$$
/ 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)
$$\frac{\left(- \frac{2 \sec^{2}{\left(2 x \right)}}{\sec^{2}{\left(2 x - \frac{\pi}{2} \right)}} - 2\right) \operatorname{acos}^{4}{\left(5 x \right)} \sec^{2}{\left(2 x - \frac{\pi}{2} \right)}}{\sec^{2}{\left(2 x \right)}} - \frac{20 \operatorname{acos}^{3}{\left(5 x \right)} \sec{\left(2 x - \frac{\pi}{2} \right)}}{\sqrt{1 - 25 x^{2}} \sec{\left(2 x \right)}}$$
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
$$- \frac{\left(\cot^{2}{\left(x \right)} + 1\right)^{2} \operatorname{acos}^{4}{\left(5 x \right)}}{2 \cot^{2}{\left(x \right)}} - \frac{20 \cot{\left(2 x \right)} \operatorname{acos}^{3}{\left(5 x \right)}}{\sqrt{1 - 25 x^{2}}}$$
4
3 1 4*acos (5*x)
- 20*acos (5*x)*----------------------- - ------------
___________ 1 - cos(4*x)
/ 2
\/ 1 - 25*x *tan(2*x)
$$- 20 \frac{1}{\sqrt{1 - 25 x^{2}} \tan{\left(2 x \right)}} \operatorname{acos}^{3}{\left(5 x \right)} - \frac{4 \operatorname{acos}^{4}{\left(5 x \right)}}{1 - \cos{\left(4 x \right)}}$$
/ 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 /
$$\frac{\left(-2 - \frac{2 \csc^{2}{\left(- 2 x + \frac{\pi}{2} \right)}}{\csc^{2}{\left(2 x \right)}}\right) \operatorname{acos}^{4}{\left(5 x \right)} \csc^{2}{\left(2 x \right)}}{\csc^{2}{\left(- 2 x + \frac{\pi}{2} \right)}} - \frac{20 \operatorname{acos}^{3}{\left(5 x \right)} \csc{\left(2 x \right)}}{\sqrt{1 - 25 x^{2}} \csc{\left(- 2 x + \frac{\pi}{2} \right)}}$$
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
$$\left(-2 - \frac{2}{\cot^{2}{\left(2 x \right)}}\right) \cot^{2}{\left(2 x \right)} \operatorname{acos}^{4}{\left(5 x \right)} - \frac{20 \cot{\left(2 x \right)} \operatorname{acos}^{3}{\left(5 x \right)}}{\sqrt{1 - 25 x^{2}}}$$
/ 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)
$$\frac{\left(- \frac{8 \sin^{4}{\left(2 x \right)}}{\sin^{2}{\left(4 x \right)}} - 2\right) \sin^{2}{\left(4 x \right)} \operatorname{acos}^{4}{\left(5 x \right)}}{4 \sin^{4}{\left(2 x \right)}} - \frac{10 \sin{\left(4 x \right)} \operatorname{acos}^{3}{\left(5 x \right)}}{\sqrt{1 - 25 x^{2}} \sin^{2}{\left(2 x \right)}}$$
4 3
2*acos (5*x) 20*acos (5*x)
- ------------ - -----------------------
2 ___________
sin (2*x) / 2
\/ 1 - 25*x *tan(2*x)
$$- \frac{2 \operatorname{acos}^{4}{\left(5 x \right)}}{\sin^{2}{\left(2 x \right)}} - \frac{20 \operatorname{acos}^{3}{\left(5 x \right)}}{\sqrt{1 - 25 x^{2}} \tan{\left(2 x \right)}}$$
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 /
$$- 2 \operatorname{acos}^{4}{\left(5 x \right)} \csc^{2}{\left(2 x \right)} - \frac{20 \operatorname{acos}^{3}{\left(5 x \right)} \csc{\left(2 x \right)}}{\sqrt{1 - 25 x^{2}} \csc{\left(- 2 x + \frac{\pi}{2} \right)}}$$
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 /
$$- \frac{4 \operatorname{acos}^{4}{\left(5 x \right)}}{1 - \cos{\left(4 x \right)}} - \frac{20 \cos{\left(2 x \right)} \operatorname{acos}^{3}{\left(5 x \right)}}{\sqrt{1 - 25 x^{2}} \cos{\left(2 x - \frac{\pi}{2} \right)}}$$
/ 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 /
$$\frac{\left(-2 - \frac{2 \cos^{2}{\left(2 x - \frac{\pi}{2} \right)}}{\cos^{2}{\left(2 x \right)}}\right) \cos^{2}{\left(2 x \right)} \operatorname{acos}^{4}{\left(5 x \right)}}{\cos^{2}{\left(2 x - \frac{\pi}{2} \right)}} - \frac{20 \cos{\left(2 x \right)} \operatorname{acos}^{3}{\left(5 x \right)}}{\sqrt{1 - 25 x^{2}} \cos{\left(2 x - \frac{\pi}{2} \right)}}$$
/ 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)
$$\frac{\left(- \frac{2 \sin^{2}{\left(2 x \right)}}{\cos^{2}{\left(2 x \right)}} - 2\right) \cos^{2}{\left(2 x \right)} \operatorname{acos}^{4}{\left(5 x \right)}}{\sin^{2}{\left(2 x \right)}} - \frac{20 \cos{\left(2 x \right)} \operatorname{acos}^{3}{\left(5 x \right)}}{\sqrt{1 - 25 x^{2}} \sin{\left(2 x \right)}}$$
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)
$$- \frac{4 \operatorname{acos}^{4}{\left(5 x \right)}}{- \frac{\cot^{2}{\left(2 x \right)} - 1}{\cot^{2}{\left(2 x \right)} + 1} + 1} - \frac{20 \cot{\left(2 x \right)} \operatorname{acos}^{3}{\left(5 x \right)}}{\sqrt{1 - 25 x^{2}}}$$
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)
$$- \frac{4 \operatorname{acos}^{4}{\left(5 x \right)}}{1 - \sin{\left(4 x + \frac{\pi}{2} \right)}} - \frac{10 \sin{\left(4 x \right)} \operatorname{acos}^{3}{\left(5 x \right)}}{\sqrt{1 - 25 x^{2}} \sin^{2}{\left(2 x \right)}}$$
4 3
4*acos (5*x) 20*acos (5*x)
- ------------ - -----------------------
1 - cos(4*x) ___________
/ 2
\/ 1 - 25*x *tan(2*x)
$$- \frac{4 \operatorname{acos}^{4}{\left(5 x \right)}}{1 - \cos{\left(4 x \right)}} - \frac{20 \operatorname{acos}^{3}{\left(5 x \right)}}{\sqrt{1 - 25 x^{2}} \tan{\left(2 x \right)}}$$
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 /
$$- \frac{2 \operatorname{acos}^{4}{\left(5 x \right)}}{\cos^{2}{\left(2 x - \frac{\pi}{2} \right)}} - \frac{20 \cos{\left(2 x \right)} \operatorname{acos}^{3}{\left(5 x \right)}}{\sqrt{1 - 25 x^{2}} \cos{\left(2 x - \frac{\pi}{2} \right)}}$$
3
4 2 20*acos (5*x)
- 2*acos (5*x)*csc (2*x) - -----------------------
___________
/ 2
\/ 1 - 25*x *tan(2*x)
$$- 2 \operatorname{acos}^{4}{\left(5 x \right)} \csc^{2}{\left(2 x \right)} - \frac{20 \operatorname{acos}^{3}{\left(5 x \right)}}{\sqrt{1 - 25 x^{2}} \tan{\left(2 x \right)}}$$
4 3
4*acos (5*x) 20*acos (5*x)*cot(2*x)
- ------------ - ----------------------
1 - cos(4*x) ___________
/ 2
\/ 1 - 25*x
$$- \frac{4 \operatorname{acos}^{4}{\left(5 x \right)}}{1 - \cos{\left(4 x \right)}} - \frac{20 \cot{\left(2 x \right)} \operatorname{acos}^{3}{\left(5 x \right)}}{\sqrt{1 - 25 x^{2}}}$$
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 /
$$- \frac{4 \operatorname{acos}^{4}{\left(5 x \right)}}{1 - \frac{1}{\csc{\left(- 4 x + \frac{\pi}{2} \right)}}} - \frac{20 \operatorname{acos}^{3}{\left(5 x \right)} \csc{\left(2 x \right)}}{\sqrt{1 - 25 x^{2}} \csc{\left(- 2 x + \frac{\pi}{2} \right)}}$$
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)
$$- \frac{4 \operatorname{acos}^{4}{\left(5 x \right)}}{- \frac{1 - \tan^{2}{\left(2 x \right)}}{\tan^{2}{\left(2 x \right)} + 1} + 1} - \frac{20 \operatorname{acos}^{3}{\left(5 x \right)}}{\sqrt{1 - 25 x^{2}} \tan{\left(2 x \right)}}$$
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)
$$- \frac{4 \operatorname{acos}^{4}{\left(5 x \right)}}{1 - \frac{1}{\sec{\left(4 x \right)}}} - \frac{20 \operatorname{acos}^{3}{\left(5 x \right)} \sec{\left(2 x - \frac{\pi}{2} \right)}}{\sqrt{1 - 25 x^{2}} \sec{\left(2 x \right)}}$$
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)
$$- \frac{\left(\tan^{2}{\left(x \right)} + 1\right)^{2} \operatorname{acos}^{4}{\left(5 x \right)}}{2 \tan^{2}{\left(x \right)}} - \frac{20 \operatorname{acos}^{3}{\left(5 x \right)}}{\sqrt{1 - 25 x^{2}} \tan{\left(2 x \right)}}$$
/ 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)
$$\frac{\left(-2 - \frac{2 \sec^{2}{\left(2 x \right)}}{\csc^{2}{\left(2 x \right)}}\right) \operatorname{acos}^{4}{\left(5 x \right)} \csc^{2}{\left(2 x \right)}}{\sec^{2}{\left(2 x \right)}} - \frac{20 \operatorname{acos}^{3}{\left(5 x \right)} \csc{\left(2 x \right)}}{\sqrt{1 - 25 x^{2}} \sec{\left(2 x \right)}}$$
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)
$$- 2 \operatorname{acos}^{4}{\left(5 x \right)} \sec^{2}{\left(- 2 x + \frac{\pi}{2} \right)} - \frac{20 \operatorname{acos}^{3}{\left(5 x \right)} \sec{\left(2 x - \frac{\pi}{2} \right)}}{\sqrt{1 - 25 x^{2}} \sec{\left(2 x \right)}}$$
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)
$$- \frac{2 \operatorname{acos}^{4}{\left(5 x \right)}}{\sin^{2}{\left(2 x \right)}} - \frac{10 \sin{\left(4 x \right)} \operatorname{acos}^{3}{\left(5 x \right)}}{\sqrt{1 - 25 x^{2}} \sin^{2}{\left(2 x \right)}}$$
-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)
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)
$$- 2 \operatorname{acos}^{4}{\left(5 x \right)} - \frac{2 \sqrt{1 - 25 x^{2}} \operatorname{acos}^{4}{\left(5 x \right)} + 20 \tan{\left(2 x \right)} \operatorname{acos}^{3}{\left(5 x \right)}}{\sqrt{1 - 25 x^{2}} \tan^{2}{\left(2 x \right)}}$$
-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)