Sr Examen
Simplificación de expresiones/
Descomposición en fracciones simples/
cot(5*x)^2*(-15-15*cot(5*x)^2)*asin(sqrt(x))+cot(5*x)^3/(2*sqrt(x)*sqrt(1-x))
¿Cómo vas a descomponer esta cot(5*x)^2*(-15-15*cot(5*x)^2)*asin(sqrt(x))+cot(5*x)^3/(2*sqrt(x)*sqrt(1-x)) expresión en fracciones?
Solución
Ha introducido
[src]
3
2 / 2 \ / ___\ cot (5*x)
cot (5*x)*\-15 - 15*cot (5*x)/*asin\\/ x / + -----------------
___ _______
2*\/ x *\/ 1 - x
$$\left(- 15 \cot^{2}{\left(5 x \right)} - 15\right) \cot^{2}{\left(5 x \right)} \operatorname{asin}{\left(\sqrt{x} \right)} + \frac{\cot^{3}{\left(5 x \right)}}{2 \sqrt{x} \sqrt{1 - x}}$$
(cot(5*x)^2*(-15 - 15*cot(5*x)^2))*asin(sqrt(x)) + cot(5*x)^3/(((2*sqrt(x))*sqrt(1 - x)))
Simplificación general
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3 2 / ___\
cot (5*x) 15*cot (5*x)*asin\\/ x /
----------------- - ------------------------
___ _______ 2
2*\/ x *\/ 1 - x sin (5*x)
$$- \frac{15 \cot^{2}{\left(5 x \right)} \operatorname{asin}{\left(\sqrt{x} \right)}}{\sin^{2}{\left(5 x \right)}} + \frac{\cot^{3}{\left(5 x \right)}}{2 \sqrt{x} \sqrt{1 - x}}$$
cot(5*x)^3/(2*sqrt(x)*sqrt(1 - x)) - 15*cot(5*x)^2*asin(sqrt(x))/sin(5*x)^2
Respuesta numérica
[src]
cot(5*x)^2*(-15.0 - 15.0*cot(5*x)^2)*asin(sqrt(x)) + 0.5*x^(-0.5)*(1.0 - x)^(-0.5)*cot(5*x)^3
cot(5*x)^2*(-15.0 - 15.0*cot(5*x)^2)*asin(sqrt(x)) + 0.5*x^(-0.5)*(1.0 - x)^(-0.5)*cot(5*x)^3
Denominador racional
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_______ 3 3/2 2 / ___\ 3/2 4 / ___\ ___ 2 / ___\ ___ 4 / ___\
- \/ 1 - x *cot (5*x) - 30*x *cot (5*x)*asin\\/ x / - 30*x *cot (5*x)*asin\\/ x / + 30*\/ x *cot (5*x)*asin\\/ x / + 30*\/ x *cot (5*x)*asin\\/ x /
-------------------------------------------------------------------------------------------------------------------------------------------------------
___
2*\/ x *(-1 + x)
$$\frac{- 30 x^{\frac{3}{2}} \cot^{4}{\left(5 x \right)} \operatorname{asin}{\left(\sqrt{x} \right)} - 30 x^{\frac{3}{2}} \cot^{2}{\left(5 x \right)} \operatorname{asin}{\left(\sqrt{x} \right)} + 30 \sqrt{x} \cot^{4}{\left(5 x \right)} \operatorname{asin}{\left(\sqrt{x} \right)} + 30 \sqrt{x} \cot^{2}{\left(5 x \right)} \operatorname{asin}{\left(\sqrt{x} \right)} - \sqrt{1 - x} \cot^{3}{\left(5 x \right)}}{2 \sqrt{x} \left(x - 1\right)}$$
(-sqrt(1 - x)*cot(5*x)^3 - 30*x^(3/2)*cot(5*x)^2*asin(sqrt(x)) - 30*x^(3/2)*cot(5*x)^4*asin(sqrt(x)) + 30*sqrt(x)*cot(5*x)^2*asin(sqrt(x)) + 30*sqrt(x)*cot(5*x)^4*asin(sqrt(x)))/(2*sqrt(x)*(-1 + x))
Unión de expresiones racionales
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2 / ___ _______ / 2 \ / ___\ \
cot (5*x)*\30*\/ x *\/ 1 - x *\-1 - cot (5*x)/*asin\\/ x / + cot(5*x)/
----------------------------------------------------------------------
___ _______
2*\/ x *\/ 1 - x
$$\frac{\left(30 \sqrt{x} \sqrt{1 - x} \left(- \cot^{2}{\left(5 x \right)} - 1\right) \operatorname{asin}{\left(\sqrt{x} \right)} + \cot{\left(5 x \right)}\right) \cot^{2}{\left(5 x \right)}}{2 \sqrt{x} \sqrt{1 - x}}$$
cot(5*x)^2*(30*sqrt(x)*sqrt(1 - x)*(-1 - cot(5*x)^2)*asin(sqrt(x)) + cot(5*x))/(2*sqrt(x)*sqrt(1 - x))
Combinatoria
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2 / ___ _______ / ___\ ___ _______ 2 / ___\\
-cot (5*x)*\-cot(5*x) + 30*\/ x *\/ 1 - x *asin\\/ x / + 30*\/ x *\/ 1 - x *cot (5*x)*asin\\/ x //
---------------------------------------------------------------------------------------------------
___ _______
2*\/ x *\/ 1 - x
$$- \frac{\left(30 \sqrt{x} \sqrt{1 - x} \cot^{2}{\left(5 x \right)} \operatorname{asin}{\left(\sqrt{x} \right)} + 30 \sqrt{x} \sqrt{1 - x} \operatorname{asin}{\left(\sqrt{x} \right)} - \cot{\left(5 x \right)}\right) \cot^{2}{\left(5 x \right)}}{2 \sqrt{x} \sqrt{1 - x}}$$
-cot(5*x)^2*(-cot(5*x) + 30*sqrt(x)*sqrt(1 - x)*asin(sqrt(x)) + 30*sqrt(x)*sqrt(1 - x)*cot(5*x)^2*asin(sqrt(x)))/(2*sqrt(x)*sqrt(1 - x))
Potencias
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3
cot (5*x) 2 / 2 \ / ___\
--------------- + cot (5*x)*\-15 - 15*cot (5*x)/*asin\\/ x /
___________
2*\/ x*(1 - x)
$$\left(- 15 \cot^{2}{\left(5 x \right)} - 15\right) \cot^{2}{\left(5 x \right)} \operatorname{asin}{\left(\sqrt{x} \right)} + \frac{\cot^{3}{\left(5 x \right)}}{2 \sqrt{x \left(1 - x\right)}}$$
cot(5*x)^3/(2*sqrt(x*(1 - x))) + cot(5*x)^2*(-15 - 15*cot(5*x)^2)*asin(sqrt(x))
Denominador común
[src]
3
2 / ___\ 4 / ___\ cot (5*x)
- 15*cot (5*x)*asin\\/ x / - 15*cot (5*x)*asin\\/ x / + -----------------
___ _______
2*\/ x *\/ 1 - x
$$- 15 \cot^{4}{\left(5 x \right)} \operatorname{asin}{\left(\sqrt{x} \right)} - 15 \cot^{2}{\left(5 x \right)} \operatorname{asin}{\left(\sqrt{x} \right)} + \frac{\cot^{3}{\left(5 x \right)}}{2 \sqrt{x} \sqrt{1 - x}}$$
-15*cot(5*x)^2*asin(sqrt(x)) - 15*cot(5*x)^4*asin(sqrt(x)) + cot(5*x)^3/(2*sqrt(x)*sqrt(1 - x))
Parte trigonométrica
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2
/ 2/5*x\\ / ___\
15*|1 + tan |---|| *asin\\/ x /
1 \ \ 2 //
--------------------------- - -------------------------------
___ _______ 3 2 2/5*x\
2*\/ x *\/ 1 - x *tan (5*x) 4*tan (5*x)*tan |---|
\ 2 /
$$- \frac{15 \left(\tan^{2}{\left(\frac{5 x}{2} \right)} + 1\right)^{2} \operatorname{asin}{\left(\sqrt{x} \right)}}{4 \tan^{2}{\left(\frac{5 x}{2} \right)} \tan^{2}{\left(5 x \right)}} + \frac{1}{2 \sqrt{x} \sqrt{1 - x} \tan^{3}{\left(5 x \right)}}$$
/ 2 \
2 | 15*csc (5*x) | / ___\
csc (5*x)*|-15 - --------------|*asin\\/ x /
| 2/pi \|
| csc |-- - 5*x|| 3
\ \2 // csc (5*x)
-------------------------------------------- + --------------------------------
2/pi \ ___ _______ 3/pi \
csc |-- - 5*x| 2*\/ x *\/ 1 - x *csc |-- - 5*x|
\2 / \2 /
$$\frac{\left(- \frac{15 \csc^{2}{\left(5 x \right)}}{\csc^{2}{\left(- 5 x + \frac{\pi}{2} \right)}} - 15\right) \operatorname{asin}{\left(\sqrt{x} \right)} \csc^{2}{\left(5 x \right)}}{\csc^{2}{\left(- 5 x + \frac{\pi}{2} \right)}} + \frac{\csc^{3}{\left(5 x \right)}}{2 \sqrt{x} \sqrt{1 - x} \csc^{3}{\left(- 5 x + \frac{\pi}{2} \right)}}$$
4 / ___\ 3
15*csc (5*x)*asin\\/ x / csc (5*x)
- ------------------------ + --------------------------------
2/pi \ ___ _______ 3/pi \
csc |-- - 5*x| 2*\/ x *\/ 1 - x *csc |-- - 5*x|
\2 / \2 /
$$- \frac{15 \operatorname{asin}{\left(\sqrt{x} \right)} \csc^{4}{\left(5 x \right)}}{\csc^{2}{\left(- 5 x + \frac{\pi}{2} \right)}} + \frac{\csc^{3}{\left(5 x \right)}}{2 \sqrt{x} \sqrt{1 - x} \csc^{3}{\left(- 5 x + \frac{\pi}{2} \right)}}$$
3 / ___\
cot (5*x) 15*(1 - cos(20*x))*asin\\/ x /
----------------- - ---------------------------------
___ _______ 3 3
2*\/ x *\/ 1 - x 8*(1 - cos(5*x)) *(1 + cos(5*x))
$$- \frac{15 \left(1 - \cos{\left(20 x \right)}\right) \operatorname{asin}{\left(\sqrt{x} \right)}}{8 \left(1 - \cos{\left(5 x \right)}\right)^{3} \left(\cos{\left(5 x \right)} + 1\right)^{3}} + \frac{\cot^{3}{\left(5 x \right)}}{2 \sqrt{x} \sqrt{1 - x}}$$
2
/ 2/5*x\\ / ___\
15*|1 - tan |---|| *asin\\/ x /
1 \ \ 2 //
--------------------------- - -------------------------------
___ _______ 3 4/5*x\ 4/5*x\
2*\/ x *\/ 1 - x *tan (5*x) 16*cos |---|*tan |---|
\ 2 / \ 2 /
$$- \frac{15 \left(1 - \tan^{2}{\left(\frac{5 x}{2} \right)}\right)^{2} \operatorname{asin}{\left(\sqrt{x} \right)}}{16 \cos^{4}{\left(\frac{5 x}{2} \right)} \tan^{4}{\left(\frac{5 x}{2} \right)}} + \frac{1}{2 \sqrt{x} \sqrt{1 - x} \tan^{3}{\left(5 x \right)}}$$
6 / ___\ 3
15*csc (5*x)*asin\\/ x / csc (5*x)
- ------------------------ + --------------------------------
2 ___ _______ 3/pi \
4*csc (10*x) 2*\/ x *\/ 1 - x *csc |-- - 5*x|
\2 /
$$- \frac{15 \operatorname{asin}{\left(\sqrt{x} \right)} \csc^{6}{\left(5 x \right)}}{4 \csc^{2}{\left(10 x \right)}} + \frac{\csc^{3}{\left(5 x \right)}}{2 \sqrt{x} \sqrt{1 - x} \csc^{3}{\left(- 5 x + \frac{\pi}{2} \right)}}$$
6 / ___\
1 15*csc (5*x)*asin\\/ x /
--------------------------- - ------------------------
___ _______ 3 2
2*\/ x *\/ 1 - x *tan (5*x) 4*csc (10*x)
$$- \frac{15 \operatorname{asin}{\left(\sqrt{x} \right)} \csc^{6}{\left(5 x \right)}}{4 \csc^{2}{\left(10 x \right)}} + \frac{1}{2 \sqrt{x} \sqrt{1 - x} \tan^{3}{\left(5 x \right)}}$$
4/ pi\ / ___\ 3/ pi\
15*sec |5*x - --|*asin\\/ x / sec |5*x - --|
\ 2 / \ 2 /
- ----------------------------- + ---------------------------
2 ___ _______ 3
sec (5*x) 2*\/ x *\/ 1 - x *sec (5*x)
$$- \frac{15 \operatorname{asin}{\left(\sqrt{x} \right)} \sec^{4}{\left(5 x - \frac{\pi}{2} \right)}}{\sec^{2}{\left(5 x \right)}} + \frac{\sec^{3}{\left(5 x - \frac{\pi}{2} \right)}}{2 \sqrt{x} \sqrt{1 - x} \sec^{3}{\left(5 x \right)}}$$
2/pi \ / ___\
15*sin |-- + 5*x|*asin\\/ x / 3
\2 / sin (10*x)
- ----------------------------- + ----------------------------
4 ___ _______ 6
sin (5*x) 16*\/ x *\/ 1 - x *sin (5*x)
$$- \frac{15 \sin^{2}{\left(5 x + \frac{\pi}{2} \right)} \operatorname{asin}{\left(\sqrt{x} \right)}}{\sin^{4}{\left(5 x \right)}} + \frac{\sin^{3}{\left(10 x \right)}}{16 \sqrt{x} \sqrt{1 - x} \sin^{6}{\left(5 x \right)}}$$
1 2 4 / ___\
--------------------------- - 15*cos (5*x)*csc (5*x)*asin\\/ x /
___ _______ 3
2*\/ x *\/ 1 - x *tan (5*x)
$$- 15 \cos^{2}{\left(5 x \right)} \operatorname{asin}{\left(\sqrt{x} \right)} \csc^{4}{\left(5 x \right)} + \frac{1}{2 \sqrt{x} \sqrt{1 - x} \tan^{3}{\left(5 x \right)}}$$
2 / ___\
1 15*cos (5*x)*asin\\/ x /
--------------------------- - ------------------------
___ _______ 3 4
2*\/ x *\/ 1 - x *tan (5*x) sin (5*x)
$$- \frac{15 \cos^{2}{\left(5 x \right)} \operatorname{asin}{\left(\sqrt{x} \right)}}{\sin^{4}{\left(5 x \right)}} + \frac{1}{2 \sqrt{x} \sqrt{1 - x} \tan^{3}{\left(5 x \right)}}$$
/ 2 \
2 | 15*sin (10*x)| / ___\
sin (10*x)*|-15 - -------------|*asin\\/ x /
| 4 | 3
\ 4*sin (5*x) / sin (10*x)
-------------------------------------------- + ----------------------------
4 ___ _______ 6
4*sin (5*x) 16*\/ x *\/ 1 - x *sin (5*x)
$$\frac{\left(-15 - \frac{15 \sin^{2}{\left(10 x \right)}}{4 \sin^{4}{\left(5 x \right)}}\right) \sin^{2}{\left(10 x \right)} \operatorname{asin}{\left(\sqrt{x} \right)}}{4 \sin^{4}{\left(5 x \right)}} + \frac{\sin^{3}{\left(10 x \right)}}{16 \sqrt{x} \sqrt{1 - x} \sin^{6}{\left(5 x \right)}}$$
2 / ___\
3 1 15*cot (5*x)*asin\\/ x /
cot (5*x)*----------------- - ------------------------
___ _______ 2
2*\/ x *\/ 1 - x sin (5*x)
$$\frac{1}{2 \sqrt{x} \sqrt{1 - x}} \cot^{3}{\left(5 x \right)} - \frac{15 \cot^{2}{\left(5 x \right)} \operatorname{asin}{\left(\sqrt{x} \right)}}{\sin^{2}{\left(5 x \right)}}$$
/ 15 \ / ___\
|-15 - ---------|*asin\\/ x /
| 2 |
\ tan (5*x)/ 1
----------------------------- + ---------------------------
2 ___ _______ 3
tan (5*x) 2*\/ x *\/ 1 - x *tan (5*x)
$$\frac{\left(-15 - \frac{15}{\tan^{2}{\left(5 x \right)}}\right) \operatorname{asin}{\left(\sqrt{x} \right)}}{\tan^{2}{\left(5 x \right)}} + \frac{1}{2 \sqrt{x} \sqrt{1 - x} \tan^{3}{\left(5 x \right)}}$$
/ 2 \
2 | 15*csc (5*x)| / ___\
csc (5*x)*|-15 - ------------|*asin\\/ x /
| 2 | 3
\ sec (5*x) / csc (5*x)
------------------------------------------ + ---------------------------
2 ___ _______ 3
sec (5*x) 2*\/ x *\/ 1 - x *sec (5*x)
$$\frac{\left(- \frac{15 \csc^{2}{\left(5 x \right)}}{\sec^{2}{\left(5 x \right)}} - 15\right) \operatorname{asin}{\left(\sqrt{x} \right)} \csc^{2}{\left(5 x \right)}}{\sec^{2}{\left(5 x \right)}} + \frac{\csc^{3}{\left(5 x \right)}}{2 \sqrt{x} \sqrt{1 - x} \sec^{3}{\left(5 x \right)}}$$
/ 2 \
2 | 15*cos (5*x)| / ___\
cos (5*x)*|-15 - ------------|*asin\\/ x /
| 2 | 3
\ sin (5*x) / cos (5*x)
------------------------------------------ + ---------------------------
2 ___ _______ 3
sin (5*x) 2*\/ x *\/ 1 - x *sin (5*x)
$$\frac{\left(-15 - \frac{15 \cos^{2}{\left(5 x \right)}}{\sin^{2}{\left(5 x \right)}}\right) \cos^{2}{\left(5 x \right)} \operatorname{asin}{\left(\sqrt{x} \right)}}{\sin^{2}{\left(5 x \right)}} + \frac{\cos^{3}{\left(5 x \right)}}{2 \sqrt{x} \sqrt{1 - x} \sin^{3}{\left(5 x \right)}}$$
2 / ___\ 3
15*sin (10*x)*asin\\/ x / sin (10*x)
- ------------------------- + ----------------------------
6 ___ _______ 6
4*sin (5*x) 16*\/ x *\/ 1 - x *sin (5*x)
$$- \frac{15 \sin^{2}{\left(10 x \right)} \operatorname{asin}{\left(\sqrt{x} \right)}}{4 \sin^{6}{\left(5 x \right)}} + \frac{\sin^{3}{\left(10 x \right)}}{16 \sqrt{x} \sqrt{1 - x} \sin^{6}{\left(5 x \right)}}$$
6
/ 2/5*x\\ 2 / ___\
3 15*|1 + cot |---|| *cot (5*x)*asin\\/ x /
cot (5*x) \ \ 2 //
----------------- - -----------------------------------------
___ _______ 2
2*\/ x *\/ 1 - x / 2 \ 6/5*x\
64*\1 + cot (5*x)/ *cot |---|
\ 2 /
$$- \frac{15 \left(\cot^{2}{\left(\frac{5 x}{2} \right)} + 1\right)^{6} \cot^{2}{\left(5 x \right)} \operatorname{asin}{\left(\sqrt{x} \right)}}{64 \left(\cot^{2}{\left(5 x \right)} + 1\right)^{2} \cot^{6}{\left(\frac{5 x}{2} \right)}} + \frac{\cot^{3}{\left(5 x \right)}}{2 \sqrt{x} \sqrt{1 - x}}$$
3 2 / ___\
cot (5*x) 15*cot (5*x)*asin\\/ x /
----------------- - ------------------------
___ _______ 2
2*\/ x *\/ 1 - x sin (5*x)
$$- \frac{15 \cot^{2}{\left(5 x \right)} \operatorname{asin}{\left(\sqrt{x} \right)}}{\sin^{2}{\left(5 x \right)}} + \frac{\cot^{3}{\left(5 x \right)}}{2 \sqrt{x} \sqrt{1 - x}}$$
3 / ___\
cot (5*x) 30*asin\\/ x /
----------------- - -------------------------
___ _______ 2
2*\/ x *\/ 1 - x (1 - cos(10*x))*tan (5*x)
$$- \frac{30 \operatorname{asin}{\left(\sqrt{x} \right)}}{\left(1 - \cos{\left(10 x \right)}\right) \tan^{2}{\left(5 x \right)}} + \frac{\cot^{3}{\left(5 x \right)}}{2 \sqrt{x} \sqrt{1 - x}}$$
2/ pi\ / ___\
15*cos |10*x - --|*asin\\/ x / 3
\ 2 / cos (5*x)
- ------------------------------ + --------------------------------
6/ pi\ ___ _______ 3/ pi\
4*cos |5*x - --| 2*\/ x *\/ 1 - x *cos |5*x - --|
\ 2 / \ 2 /
$$- \frac{15 \cos^{2}{\left(10 x - \frac{\pi}{2} \right)} \operatorname{asin}{\left(\sqrt{x} \right)}}{4 \cos^{6}{\left(5 x - \frac{\pi}{2} \right)}} + \frac{\cos^{3}{\left(5 x \right)}}{2 \sqrt{x} \sqrt{1 - x} \cos^{3}{\left(5 x - \frac{\pi}{2} \right)}}$$
6
/ 2/5*x\\ 2 / ___\
15*|1 + tan |---|| *tan (5*x)*asin\\/ x /
1 \ \ 2 //
--------------------------- - -----------------------------------------
___ _______ 3 2
2*\/ x *\/ 1 - x *tan (5*x) / 2 \ 6/5*x\
64*\1 + tan (5*x)/ *tan |---|
\ 2 /
$$- \frac{15 \left(\tan^{2}{\left(\frac{5 x}{2} \right)} + 1\right)^{6} \tan^{2}{\left(5 x \right)} \operatorname{asin}{\left(\sqrt{x} \right)}}{64 \left(\tan^{2}{\left(5 x \right)} + 1\right)^{2} \tan^{6}{\left(\frac{5 x}{2} \right)}} + \frac{1}{2 \sqrt{x} \sqrt{1 - x} \tan^{3}{\left(5 x \right)}}$$
6/ pi\ / ___\ 3/ pi\
15*sec |5*x - --|*asin\\/ x / sec |5*x - --|
\ 2 / \ 2 /
- ----------------------------- + ---------------------------
2/ pi\ ___ _______ 3
4*sec |10*x - --| 2*\/ x *\/ 1 - x *sec (5*x)
\ 2 /
$$- \frac{15 \operatorname{asin}{\left(\sqrt{x} \right)} \sec^{6}{\left(5 x - \frac{\pi}{2} \right)}}{4 \sec^{2}{\left(10 x - \frac{\pi}{2} \right)}} + \frac{\sec^{3}{\left(5 x - \frac{\pi}{2} \right)}}{2 \sqrt{x} \sqrt{1 - x} \sec^{3}{\left(5 x \right)}}$$
2
/ 2/5*x\\ 4/5*x\ / ___\
3 15*|-1 + cot |---|| *tan |---|*asin\\/ x /
cot (5*x) \ \ 2 // \ 2 /
----------------- - ------------------------------------------
___ _______ 4/5*x\
2*\/ x *\/ 1 - x 16*sin |---|
\ 2 /
$$- \frac{15 \left(\cot^{2}{\left(\frac{5 x}{2} \right)} - 1\right)^{2} \tan^{4}{\left(\frac{5 x}{2} \right)} \operatorname{asin}{\left(\sqrt{x} \right)}}{16 \sin^{4}{\left(\frac{5 x}{2} \right)}} + \frac{\cot^{3}{\left(5 x \right)}}{2 \sqrt{x} \sqrt{1 - x}}$$
2 / ___\ 3
15*cos (5*x)*asin\\/ x / cos (5*x)
- ------------------------ + --------------------------------
4/ pi\ ___ _______ 3/ pi\
cos |5*x - --| 2*\/ x *\/ 1 - x *cos |5*x - --|
\ 2 / \ 2 /
$$- \frac{15 \cos^{2}{\left(5 x \right)} \operatorname{asin}{\left(\sqrt{x} \right)}}{\cos^{4}{\left(5 x - \frac{\pi}{2} \right)}} + \frac{\cos^{3}{\left(5 x \right)}}{2 \sqrt{x} \sqrt{1 - x} \cos^{3}{\left(5 x - \frac{\pi}{2} \right)}}$$
/ 2 \
2 | 15*cos (5*x) | / ___\
cos (5*x)*|-15 - --------------|*asin\\/ x /
| 2/ pi\|
| cos |5*x - --|| 3
\ \ 2 // cos (5*x)
-------------------------------------------- + --------------------------------
2/ pi\ ___ _______ 3/ pi\
cos |5*x - --| 2*\/ x *\/ 1 - x *cos |5*x - --|
\ 2 / \ 2 /
$$\frac{\left(- \frac{15 \cos^{2}{\left(5 x \right)}}{\cos^{2}{\left(5 x - \frac{\pi}{2} \right)}} - 15\right) \cos^{2}{\left(5 x \right)} \operatorname{asin}{\left(\sqrt{x} \right)}}{\cos^{2}{\left(5 x - \frac{\pi}{2} \right)}} + \frac{\cos^{3}{\left(5 x \right)}}{2 \sqrt{x} \sqrt{1 - x} \cos^{3}{\left(5 x - \frac{\pi}{2} \right)}}$$
2 2
/ 2/5*x\\ / 2/5*x\\ / ___\
15*|1 + tan |---|| *|1 - tan |---|| *asin\\/ x /
1 \ \ 2 // \ \ 2 //
--------------------------- - ------------------------------------------------
___ _______ 3 4/5*x\
2*\/ x *\/ 1 - x *tan (5*x) 16*tan |---|
\ 2 /
$$- \frac{15 \left(1 - \tan^{2}{\left(\frac{5 x}{2} \right)}\right)^{2} \left(\tan^{2}{\left(\frac{5 x}{2} \right)} + 1\right)^{2} \operatorname{asin}{\left(\sqrt{x} \right)}}{16 \tan^{4}{\left(\frac{5 x}{2} \right)}} + \frac{1}{2 \sqrt{x} \sqrt{1 - x} \tan^{3}{\left(5 x \right)}}$$
/ ___\
1 15*(1 - cos(20*x))*asin\\/ x /
--------------------------- - ---------------------------------
___ _______ 3 3 3
2*\/ x *\/ 1 - x *tan (5*x) 8*(1 - cos(5*x)) *(1 + cos(5*x))
$$- \frac{15 \left(1 - \cos{\left(20 x \right)}\right) \operatorname{asin}{\left(\sqrt{x} \right)}}{8 \left(1 - \cos{\left(5 x \right)}\right)^{3} \left(\cos{\left(5 x \right)} + 1\right)^{3}} + \frac{1}{2 \sqrt{x} \sqrt{1 - x} \tan^{3}{\left(5 x \right)}}$$
/ 2/ pi\\
| 15*sec |5*x - --||
2/ pi\ | \ 2 /| / ___\
sec |5*x - --|*|-15 - -----------------|*asin\\/ x / 3/ pi\
\ 2 / | 2 | sec |5*x - --|
\ sec (5*x) / \ 2 /
---------------------------------------------------- + ---------------------------
2 ___ _______ 3
sec (5*x) 2*\/ x *\/ 1 - x *sec (5*x)
$$\frac{\left(-15 - \frac{15 \sec^{2}{\left(5 x - \frac{\pi}{2} \right)}}{\sec^{2}{\left(5 x \right)}}\right) \operatorname{asin}{\left(\sqrt{x} \right)} \sec^{2}{\left(5 x - \frac{\pi}{2} \right)}}{\sec^{2}{\left(5 x \right)}} + \frac{\sec^{3}{\left(5 x - \frac{\pi}{2} \right)}}{2 \sqrt{x} \sqrt{1 - x} \sec^{3}{\left(5 x \right)}}$$
2 / ___\
1 15*sin (10*x)*asin\\/ x /
--------------------------- - -------------------------
___ _______ 3 6
2*\/ x *\/ 1 - x *tan (5*x) 4*sin (5*x)
$$- \frac{15 \sin^{2}{\left(10 x \right)} \operatorname{asin}{\left(\sqrt{x} \right)}}{4 \sin^{6}{\left(5 x \right)}} + \frac{1}{2 \sqrt{x} \sqrt{1 - x} \tan^{3}{\left(5 x \right)}}$$
2
/ 2/5*x\\ 2 / ___\
3 15*|1 + cot |---|| *cot (5*x)*asin\\/ x /
cot (5*x) \ \ 2 //
----------------- - -----------------------------------------
___ _______ 2/5*x\
2*\/ x *\/ 1 - x 4*cot |---|
\ 2 /
$$- \frac{15 \left(\cot^{2}{\left(\frac{5 x}{2} \right)} + 1\right)^{2} \cot^{2}{\left(5 x \right)} \operatorname{asin}{\left(\sqrt{x} \right)}}{4 \cot^{2}{\left(\frac{5 x}{2} \right)}} + \frac{\cot^{3}{\left(5 x \right)}}{2 \sqrt{x} \sqrt{1 - x}}$$
2 2
/ 2/5*x\\ / 2/5*x\\ / ___\
3 15*|1 + cot |---|| *|-1 + cot |---|| *asin\\/ x /
cot (5*x) \ \ 2 // \ \ 2 //
----------------- - -------------------------------------------------
___ _______ 4/5*x\
2*\/ x *\/ 1 - x 16*cot |---|
\ 2 /
$$- \frac{15 \left(\cot^{2}{\left(\frac{5 x}{2} \right)} - 1\right)^{2} \left(\cot^{2}{\left(\frac{5 x}{2} \right)} + 1\right)^{2} \operatorname{asin}{\left(\sqrt{x} \right)}}{16 \cot^{4}{\left(\frac{5 x}{2} \right)}} + \frac{\cot^{3}{\left(5 x \right)}}{2 \sqrt{x} \sqrt{1 - x}}$$
cot(5*x)^3/(2*sqrt(x)*sqrt(1 - x)) - 15*(1 + cot(5*x/2)^2)^2*(-1 + cot(5*x/2)^2)^2*asin(sqrt(x))/(16*cot(5*x/2)^4)