Sr Examen
Simplificación de expresiones/
Descomposición en fracciones simples/
asin(x)^(sin(x)/x)*((cos(x)/x-sin(x)/x^2)*log(asin(x))+sin(x)/(x*sqrt(1-x^2)*asin(x)))
¿Cómo vas a descomponer esta asin(x)^(sin(x)/x)*((cos(x)/x-sin(x)/x^2)*log(asin(x))+sin(x)/(x*sqrt(1-x^2)*asin(x))) expresión en fracciones?
Solución
Ha introducido
[src]
sin(x)
------
x //cos(x) sin(x)\ sin(x) \
(asin(x)) *||------ - ------|*log(asin(x)) + ---------------------|
|| x 2 | ________ |
|\ x / / 2 |
\ x*\/ 1 - x *asin(x)/
$$\left(\left(- \frac{\sin{\left(x \right)}}{x^{2}} + \frac{\cos{\left(x \right)}}{x}\right) \log{\left(\operatorname{asin}{\left(x \right)} \right)} + \frac{\sin{\left(x \right)}}{x \sqrt{1 - x^{2}} \operatorname{asin}{\left(x \right)}}\right) \operatorname{asin}^{\frac{\sin{\left(x \right)}}{x}}{\left(x \right)}$$
asin(x)^(sin(x)/x)*((cos(x)/x - sin(x)/x^2)*log(asin(x)) + sin(x)/(((x*sqrt(1 - x^2))*asin(x))))
Simplificación general
[src]
sin(x)
-1 + ------ / ________ \
x | / 2 |
(asin(x)) *\x*sin(x) - \/ 1 - x *(-x*cos(x) + sin(x))*asin(x)*log(asin(x))/
---------------------------------------------------------------------------------------
________
2 / 2
x *\/ 1 - x
$$\frac{\left(x \sin{\left(x \right)} - \sqrt{1 - x^{2}} \left(- x \cos{\left(x \right)} + \sin{\left(x \right)}\right) \log{\left(\operatorname{asin}{\left(x \right)} \right)} \operatorname{asin}{\left(x \right)}\right) \operatorname{asin}^{-1 + \frac{\sin{\left(x \right)}}{x}}{\left(x \right)}}{x^{2} \sqrt{1 - x^{2}}}$$
asin(x)^(-1 + sin(x)/x)*(x*sin(x) - sqrt(1 - x^2)*(-x*cos(x) + sin(x))*asin(x)*log(asin(x)))/(x^2*sqrt(1 - x^2))
Respuesta numérica
[src]
asin(x)^(sin(x)/x)*((cos(x)/x - sin(x)/x^2)*log(asin(x)) + (1.0 - x^2)^(-0.5)*sin(x)/(x*asin(x)))
asin(x)^(sin(x)/x)*((cos(x)/x - sin(x)/x^2)*log(asin(x)) + (1.0 - x^2)^(-0.5)*sin(x)/(x*asin(x)))
Denominador racional
[src]
sin(x) sin(x) sin(x) sin(x) sin(x)
________ -1 + ------ -1 + ------ -1 + ------ -1 + ------ -1 + ------
3 / 2 x 2 x 5 x 3 x 4 x
- x *\/ 1 - x *(asin(x)) *sin(x) + x *(asin(x)) *asin(x)*log(asin(x))*sin(x) + x *(asin(x)) *asin(x)*cos(x)*log(asin(x)) - x *(asin(x)) *asin(x)*cos(x)*log(asin(x)) - x *(asin(x)) *asin(x)*log(asin(x))*sin(x)
--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
4 / 2\
x *\-1 + x /
$$\frac{x^{5} \log{\left(\operatorname{asin}{\left(x \right)} \right)} \cos{\left(x \right)} \operatorname{asin}{\left(x \right)} \operatorname{asin}^{-1 + \frac{\sin{\left(x \right)}}{x}}{\left(x \right)} - x^{4} \log{\left(\operatorname{asin}{\left(x \right)} \right)} \sin{\left(x \right)} \operatorname{asin}{\left(x \right)} \operatorname{asin}^{-1 + \frac{\sin{\left(x \right)}}{x}}{\left(x \right)} - x^{3} \sqrt{1 - x^{2}} \sin{\left(x \right)} \operatorname{asin}^{-1 + \frac{\sin{\left(x \right)}}{x}}{\left(x \right)} - x^{3} \log{\left(\operatorname{asin}{\left(x \right)} \right)} \cos{\left(x \right)} \operatorname{asin}{\left(x \right)} \operatorname{asin}^{-1 + \frac{\sin{\left(x \right)}}{x}}{\left(x \right)} + x^{2} \log{\left(\operatorname{asin}{\left(x \right)} \right)} \sin{\left(x \right)} \operatorname{asin}{\left(x \right)} \operatorname{asin}^{-1 + \frac{\sin{\left(x \right)}}{x}}{\left(x \right)}}{x^{4} \left(x^{2} - 1\right)}$$
(-x^3*sqrt(1 - x^2)*asin(x)^(-1 + sin(x)/x)*sin(x) + x^2*asin(x)^(-1 + sin(x)/x)*asin(x)*log(asin(x))*sin(x) + x^5*asin(x)^(-1 + sin(x)/x)*asin(x)*cos(x)*log(asin(x)) - x^3*asin(x)^(-1 + sin(x)/x)*asin(x)*cos(x)*log(asin(x)) - x^4*asin(x)^(-1 + sin(x)/x)*asin(x)*log(asin(x))*sin(x))/(x^4*(-1 + x^2))
Combinatoria
[src]
sin(x)
------ / ________ ________ \
x | / 2 / 2 |
(asin(x)) *\x*sin(x) - \/ 1 - x *asin(x)*log(asin(x))*sin(x) + x*\/ 1 - x *asin(x)*cos(x)*log(asin(x))/
----------------------------------------------------------------------------------------------------------------
2 ___________________
x *\/ -(1 + x)*(-1 + x) *asin(x)
$$\frac{\left(x \sqrt{1 - x^{2}} \log{\left(\operatorname{asin}{\left(x \right)} \right)} \cos{\left(x \right)} \operatorname{asin}{\left(x \right)} + x \sin{\left(x \right)} - \sqrt{1 - x^{2}} \log{\left(\operatorname{asin}{\left(x \right)} \right)} \sin{\left(x \right)} \operatorname{asin}{\left(x \right)}\right) \operatorname{asin}^{\frac{\sin{\left(x \right)}}{x}}{\left(x \right)}}{x^{2} \sqrt{- \left(x - 1\right) \left(x + 1\right)} \operatorname{asin}{\left(x \right)}}$$
asin(x)^(sin(x)/x)*(x*sin(x) - sqrt(1 - x^2)*asin(x)*log(asin(x))*sin(x) + x*sqrt(1 - x^2)*asin(x)*cos(x)*log(asin(x)))/(x^2*sqrt(-(1 + x)*(-1 + x))*asin(x))
Potencias
[src]
sin(x)
------
x //cos(x) sin(x)\ sin(x) \
(asin(x)) *||------ - ------|*log(asin(x)) + ---------------------|
|| x 2 | ________ |
|\ x / / 2 |
\ x*\/ 1 - x *asin(x)/
$$\left(\left(\frac{\cos{\left(x \right)}}{x} - \frac{\sin{\left(x \right)}}{x^{2}}\right) \log{\left(\operatorname{asin}{\left(x \right)} \right)} + \frac{\sin{\left(x \right)}}{x \sqrt{1 - x^{2}} \operatorname{asin}{\left(x \right)}}\right) \operatorname{asin}^{\frac{\sin{\left(x \right)}}{x}}{\left(x \right)}$$
/ -I*x I*x\ // I*x -I*x \ \
-I*\- e + e / ||e e | |
-------------------- ||---- + ----- / -I*x I*x\| / -I*x I*x\ |
2*x || 2 2 I*\- e + e /| I*\- e + e / |
(asin(x)) *||------------ + ------------------|*log(asin(x)) - -----------------------|
|| x 2 | ________ |
|\ 2*x / / 2 |
\ 2*x*\/ 1 - x *asin(x)/
$$\left(\left(\frac{\frac{e^{i x}}{2} + \frac{e^{- i x}}{2}}{x} + \frac{i \left(e^{i x} - e^{- i x}\right)}{2 x^{2}}\right) \log{\left(\operatorname{asin}{\left(x \right)} \right)} - \frac{i \left(e^{i x} - e^{- i x}\right)}{2 x \sqrt{1 - x^{2}} \operatorname{asin}{\left(x \right)}}\right) \operatorname{asin}^{- \frac{i \left(e^{i x} - e^{- i x}\right)}{2 x}}{\left(x \right)}$$
asin(x)^(-i*(-exp(-i*x) + exp(i*x))/(2*x))*(((exp(i*x)/2 + exp(-i*x)/2)/x + i*(-exp(-i*x) + exp(i*x))/(2*x^2))*log(asin(x)) - i*(-exp(-i*x) + exp(i*x))/(2*x*sqrt(1 - x^2)*asin(x)))
Unión de expresiones racionales
[src]
sin(x)
------ / ________ \
x | / 2 |
(asin(x)) *\x*sin(x) + \/ 1 - x *(-sin(x) + x*cos(x))*asin(x)*log(asin(x))/
----------------------------------------------------------------------------------
________
2 / 2
x *\/ 1 - x *asin(x)
$$\frac{\left(x \sin{\left(x \right)} + \sqrt{1 - x^{2}} \left(x \cos{\left(x \right)} - \sin{\left(x \right)}\right) \log{\left(\operatorname{asin}{\left(x \right)} \right)} \operatorname{asin}{\left(x \right)}\right) \operatorname{asin}^{\frac{\sin{\left(x \right)}}{x}}{\left(x \right)}}{x^{2} \sqrt{1 - x^{2}} \operatorname{asin}{\left(x \right)}}$$
asin(x)^(sin(x)/x)*(x*sin(x) + sqrt(1 - x^2)*(-sin(x) + x*cos(x))*asin(x)*log(asin(x)))/(x^2*sqrt(1 - x^2)*asin(x))
Compilar la expresión
[src]
sin(x)
------
x //cos(x) sin(x)\ sin(x) \
(asin(x)) *||------ - ------|*log(asin(x)) + ---------------------|
|| x 2 | ________ |
|\ x / / 2 |
\ x*\/ 1 - x *asin(x)/
$$\left(\left(\frac{\cos{\left(x \right)}}{x} - \frac{\sin{\left(x \right)}}{x^{2}}\right) \log{\left(\operatorname{asin}{\left(x \right)} \right)} + \frac{\sin{\left(x \right)}}{x \sqrt{1 - x^{2}} \operatorname{asin}{\left(x \right)}}\right) \operatorname{asin}^{\frac{\sin{\left(x \right)}}{x}}{\left(x \right)}$$
asin(x)^(sin(x)/x)*((cos(x)/x - sin(x)/x^2)*log(asin(x)) + sin(x)/(x*sqrt(1 - x^2)*asin(x)))
Denominador común
[src]
sin(x) sin(x) sin(x)
------ ________ ------ ________ ------
x / 2 x / 2 x
x*(asin(x)) *sin(x) - \/ 1 - x *(asin(x)) *asin(x)*log(asin(x))*sin(x) + x*\/ 1 - x *(asin(x)) *asin(x)*cos(x)*log(asin(x))
----------------------------------------------------------------------------------------------------------------------------------------------
________
2 / 2
x *\/ 1 - x *asin(x)
$$\frac{x \sqrt{1 - x^{2}} \log{\left(\operatorname{asin}{\left(x \right)} \right)} \cos{\left(x \right)} \operatorname{asin}{\left(x \right)} \operatorname{asin}^{\frac{\sin{\left(x \right)}}{x}}{\left(x \right)} + x \sin{\left(x \right)} \operatorname{asin}^{\frac{\sin{\left(x \right)}}{x}}{\left(x \right)} - \sqrt{1 - x^{2}} \log{\left(\operatorname{asin}{\left(x \right)} \right)} \sin{\left(x \right)} \operatorname{asin}{\left(x \right)} \operatorname{asin}^{\frac{\sin{\left(x \right)}}{x}}{\left(x \right)}}{x^{2} \sqrt{1 - x^{2}} \operatorname{asin}{\left(x \right)}}$$
(x*asin(x)^(sin(x)/x)*sin(x) - sqrt(1 - x^2)*asin(x)^(sin(x)/x)*asin(x)*log(asin(x))*sin(x) + x*sqrt(1 - x^2)*asin(x)^(sin(x)/x)*asin(x)*cos(x)*log(asin(x)))/(x^2*sqrt(1 - x^2)*asin(x))
Parte trigonométrica
[src]
1
--------
x*csc(x) // 1 1 \ 1 \
(asin(x)) *||------------- - ---------|*log(asin(x)) + ----------------------------|
|| /pi \ 2 | ________ |
||x*csc|-- - x| x *csc(x)| / 2 |
\\ \2 / / x*\/ 1 - x *asin(x)*csc(x)/
$$\left(\left(\frac{1}{x \csc{\left(- x + \frac{\pi}{2} \right)}} - \frac{1}{x^{2} \csc{\left(x \right)}}\right) \log{\left(\operatorname{asin}{\left(x \right)} \right)} + \frac{1}{x \sqrt{1 - x^{2}} \operatorname{asin}{\left(x \right)} \csc{\left(x \right)}}\right) \operatorname{asin}^{\frac{1}{x \csc{\left(x \right)}}}{\left(x \right)}$$
/x\
2*tan|-|
\2/
---------------
/ 2/x\\ // 2/x\ /x\ \ /x\ \
x*|1 + tan |-|| || 1 - tan |-| 2*tan|-| | 2*tan|-| |
\ \2// || \2/ \2/ | \2/ |
(asin(x)) *||--------------- - ----------------|*log(asin(x)) + -----------------------------------|
|| / 2/x\\ 2 / 2/x\\| ________ |
||x*|1 + tan |-|| x *|1 + tan |-||| / 2/x\\ / 2 |
|\ \ \2// \ \2/// x*|1 + tan |-||*\/ 1 - x *asin(x)|
\ \ \2// /
$$\left(\left(\frac{1 - \tan^{2}{\left(\frac{x}{2} \right)}}{x \left(\tan^{2}{\left(\frac{x}{2} \right)} + 1\right)} - \frac{2 \tan{\left(\frac{x}{2} \right)}}{x^{2} \left(\tan^{2}{\left(\frac{x}{2} \right)} + 1\right)}\right) \log{\left(\operatorname{asin}{\left(x \right)} \right)} + \frac{2 \tan{\left(\frac{x}{2} \right)}}{x \sqrt{1 - x^{2}} \left(\tan^{2}{\left(\frac{x}{2} \right)} + 1\right) \operatorname{asin}{\left(x \right)}}\right) \operatorname{asin}^{\frac{2 \tan{\left(\frac{x}{2} \right)}}{x \left(\tan^{2}{\left(\frac{x}{2} \right)} + 1\right)}}{\left(x \right)}$$
/x\ // 2/x\ /x\ \ \
2*tan|-| ||1 - tan |-| 2*tan|-| | |
\2/ || \2/ \2/ | |
--------------- ||----------- - ---------------|*log(asin(x)) |
/ 2/x\\ || 2/x\ / 2/x\\| /x\ |
x*|1 + tan |-|| ||1 + tan |-| x*|1 + tan |-||| 2*tan|-| |
\ \2// |\ \2/ \ \2/// \2/ |
(asin(x)) *|-------------------------------------------- + -----------------------------------|
| x ________ |
| / 2/x\\ / 2 |
| x*|1 + tan |-||*\/ 1 - x *asin(x)|
\ \ \2// /
$$\left(\frac{\left(\frac{1 - \tan^{2}{\left(\frac{x}{2} \right)}}{\tan^{2}{\left(\frac{x}{2} \right)} + 1} - \frac{2 \tan{\left(\frac{x}{2} \right)}}{x \left(\tan^{2}{\left(\frac{x}{2} \right)} + 1\right)}\right) \log{\left(\operatorname{asin}{\left(x \right)} \right)}}{x} + \frac{2 \tan{\left(\frac{x}{2} \right)}}{x \sqrt{1 - x^{2}} \left(\tan^{2}{\left(\frac{x}{2} \right)} + 1\right) \operatorname{asin}{\left(x \right)}}\right) \operatorname{asin}^{\frac{2 \tan{\left(\frac{x}{2} \right)}}{x \left(\tan^{2}{\left(\frac{x}{2} \right)} + 1\right)}}{\left(x \right)}$$
sin(x) // sin(x) / pi\\ \
------ ||- ------ + sin|x + --||*log(asin(x)) |
x |\ x \ 2 // sin(x) |
(asin(x)) *|------------------------------------- + ---------------------|
| x ________ |
| / 2 |
\ x*\/ 1 - x *asin(x)/
$$\left(\frac{\left(\sin{\left(x + \frac{\pi}{2} \right)} - \frac{\sin{\left(x \right)}}{x}\right) \log{\left(\operatorname{asin}{\left(x \right)} \right)}}{x} + \frac{\sin{\left(x \right)}}{x \sqrt{1 - x^{2}} \operatorname{asin}{\left(x \right)}}\right) \operatorname{asin}^{\frac{\sin{\left(x \right)}}{x}}{\left(x \right)}$$
/ pi\
cos|x - --|
\ 2 / // / pi\\ / pi\ \
----------- || cos|x - --|| cos|x - --| |
x ||cos(x) \ 2 /| \ 2 / |
(asin(x)) *||------ - -----------|*log(asin(x)) + ---------------------|
|| x 2 | ________ |
|\ x / / 2 |
\ x*\/ 1 - x *asin(x)/
$$\left(\left(\frac{\cos{\left(x \right)}}{x} - \frac{\cos{\left(x - \frac{\pi}{2} \right)}}{x^{2}}\right) \log{\left(\operatorname{asin}{\left(x \right)} \right)} + \frac{\cos{\left(x - \frac{\pi}{2} \right)}}{x \sqrt{1 - x^{2}} \operatorname{asin}{\left(x \right)}}\right) \operatorname{asin}^{\frac{\cos{\left(x - \frac{\pi}{2} \right)}}{x}}{\left(x \right)}$$
sin(x)
------
x //cos(x) sin(x)\ sin(x) \
(asin(x)) *||------ - ------|*log(asin(x)) + ---------------------|
|| x 2 | ________ |
|\ x / / 2 |
\ x*\/ 1 - x *asin(x)/
$$\left(\left(\frac{\cos{\left(x \right)}}{x} - \frac{\sin{\left(x \right)}}{x^{2}}\right) \log{\left(\operatorname{asin}{\left(x \right)} \right)} + \frac{\sin{\left(x \right)}}{x \sqrt{1 - x^{2}} \operatorname{asin}{\left(x \right)}}\right) \operatorname{asin}^{\frac{\sin{\left(x \right)}}{x}}{\left(x \right)}$$
sin(x) // / pi\ \ \
------ ||sin|x + --| | |
x || \ 2 / sin(x)| sin(x) |
(asin(x)) *||----------- - ------|*log(asin(x)) + ---------------------|
|| x 2 | ________ |
|\ x / / 2 |
\ x*\/ 1 - x *asin(x)/
$$\left(\left(\frac{\sin{\left(x + \frac{\pi}{2} \right)}}{x} - \frac{\sin{\left(x \right)}}{x^{2}}\right) \log{\left(\operatorname{asin}{\left(x \right)} \right)} + \frac{\sin{\left(x \right)}}{x \sqrt{1 - x^{2}} \operatorname{asin}{\left(x \right)}}\right) \operatorname{asin}^{\frac{\sin{\left(x \right)}}{x}}{\left(x \right)}$$
sin(x) / / sin(x) \ \
------ | |- ------ + cos(x)|*log(asin(x))|
x | 1 \ x / |
(asin(x)) *|---------------------*sin(x) + --------------------------------|
| ________ x |
| / 2 |
\x*\/ 1 - x *asin(x) /
$$\left(\frac{1}{x \sqrt{1 - x^{2}} \operatorname{asin}{\left(x \right)}} \sin{\left(x \right)} + \frac{\left(\cos{\left(x \right)} - \frac{\sin{\left(x \right)}}{x}\right) \log{\left(\operatorname{asin}{\left(x \right)} \right)}}{x}\right) \operatorname{asin}^{\frac{\sin{\left(x \right)}}{x}}{\left(x \right)}$$
1
--------
x*csc(x) // 1 1 \ 1 \
(asin(x)) *||-------- - ---------|*log(asin(x)) + ----------------------------|
||x*sec(x) 2 | ________ |
|\ x *csc(x)/ / 2 |
\ x*\/ 1 - x *asin(x)*csc(x)/
$$\left(\left(\frac{1}{x \sec{\left(x \right)}} - \frac{1}{x^{2} \csc{\left(x \right)}}\right) \log{\left(\operatorname{asin}{\left(x \right)} \right)} + \frac{1}{x \sqrt{1 - x^{2}} \operatorname{asin}{\left(x \right)} \csc{\left(x \right)}}\right) \operatorname{asin}^{\frac{1}{x \csc{\left(x \right)}}}{\left(x \right)}$$
/x\ // 2/x\ /x\ \ \
2*cot|-| ||-1 + cot |-| 2*cot|-| | |
\2/ || \2/ \2/ | |
--------------- ||------------ - ---------------|*log(asin(x)) |
/ 2/x\\ || 2/x\ / 2/x\\| /x\ |
x*|1 + cot |-|| ||1 + cot |-| x*|1 + cot |-||| 2*cot|-| |
\ \2// |\ \2/ \ \2/// \2/ |
(asin(x)) *|--------------------------------------------- + -----------------------------------|
| x ________ |
| / 2/x\\ / 2 |
| x*|1 + cot |-||*\/ 1 - x *asin(x)|
\ \ \2// /
$$\left(\frac{\left(\frac{\cot^{2}{\left(\frac{x}{2} \right)} - 1}{\cot^{2}{\left(\frac{x}{2} \right)} + 1} - \frac{2 \cot{\left(\frac{x}{2} \right)}}{x \left(\cot^{2}{\left(\frac{x}{2} \right)} + 1\right)}\right) \log{\left(\operatorname{asin}{\left(x \right)} \right)}}{x} + \frac{2 \cot{\left(\frac{x}{2} \right)}}{x \sqrt{1 - x^{2}} \left(\cot^{2}{\left(\frac{x}{2} \right)} + 1\right) \operatorname{asin}{\left(x \right)}}\right) \operatorname{asin}^{\frac{2 \cot{\left(\frac{x}{2} \right)}}{x \left(\cot^{2}{\left(\frac{x}{2} \right)} + 1\right)}}{\left(x \right)}$$
sin(x) // sin(x) \ \
------ ||- ------ + cos(x)|*log(asin(x)) |
x |\ x / sin(x) |
(asin(x)) *|-------------------------------- + ---------------------|
| x ________ |
| / 2 |
\ x*\/ 1 - x *asin(x)/
$$\left(\frac{\left(\cos{\left(x \right)} - \frac{\sin{\left(x \right)}}{x}\right) \log{\left(\operatorname{asin}{\left(x \right)} \right)}}{x} + \frac{\sin{\left(x \right)}}{x \sqrt{1 - x^{2}} \operatorname{asin}{\left(x \right)}}\right) \operatorname{asin}^{\frac{\sin{\left(x \right)}}{x}}{\left(x \right)}$$
// 1 1 \ \
||----------- - --------|*log(asin(x)) |
1 || /pi \ x*csc(x)| |
-------- ||csc|-- - x| | |
x*csc(x) |\ \2 / / 1 |
(asin(x)) *|------------------------------------- + ----------------------------|
| x ________ |
| / 2 |
\ x*\/ 1 - x *asin(x)*csc(x)/
$$\left(\frac{\left(\frac{1}{\csc{\left(- x + \frac{\pi}{2} \right)}} - \frac{1}{x \csc{\left(x \right)}}\right) \log{\left(\operatorname{asin}{\left(x \right)} \right)}}{x} + \frac{1}{x \sqrt{1 - x^{2}} \operatorname{asin}{\left(x \right)} \csc{\left(x \right)}}\right) \operatorname{asin}^{\frac{1}{x \csc{\left(x \right)}}}{\left(x \right)}$$
1 // 1 1 \ \
------------- ||------ - -------------|*log(asin(x)) |
/ pi\ ||sec(x) / pi\| |
x*sec|x - --| || x*sec|x - --|| |
\ 2 / |\ \ 2 // 1 |
(asin(x)) *|------------------------------------- + ---------------------------------|
| x ________ |
| / 2 / pi\|
| x*\/ 1 - x *asin(x)*sec|x - --||
\ \ 2 //
$$\left(\frac{\left(\frac{1}{\sec{\left(x \right)}} - \frac{1}{x \sec{\left(x - \frac{\pi}{2} \right)}}\right) \log{\left(\operatorname{asin}{\left(x \right)} \right)}}{x} + \frac{1}{x \sqrt{1 - x^{2}} \operatorname{asin}{\left(x \right)} \sec{\left(x - \frac{\pi}{2} \right)}}\right) \operatorname{asin}^{\frac{1}{x \sec{\left(x - \frac{\pi}{2} \right)}}}{\left(x \right)}$$
1
-------------
/ pi\
x*sec|x - --|
\ 2 / // 1 1 \ 1 \
(asin(x)) *||-------- - --------------|*log(asin(x)) + ---------------------------------|
||x*sec(x) 2 / pi\| ________ |
|| x *sec|x - --|| / 2 / pi\|
|\ \ 2 // x*\/ 1 - x *asin(x)*sec|x - --||
\ \ 2 //
$$\left(\left(\frac{1}{x \sec{\left(x \right)}} - \frac{1}{x^{2} \sec{\left(x - \frac{\pi}{2} \right)}}\right) \log{\left(\operatorname{asin}{\left(x \right)} \right)} + \frac{1}{x \sqrt{1 - x^{2}} \operatorname{asin}{\left(x \right)} \sec{\left(x - \frac{\pi}{2} \right)}}\right) \operatorname{asin}^{\frac{1}{x \sec{\left(x - \frac{\pi}{2} \right)}}}{\left(x \right)}$$
/x\
2*cot|-|
\2/
---------------
/ 2/x\\ // 2/x\ /x\ \ /x\ \
x*|1 + cot |-|| || -1 + cot |-| 2*cot|-| | 2*cot|-| |
\ \2// || \2/ \2/ | \2/ |
(asin(x)) *||--------------- - ----------------|*log(asin(x)) + -----------------------------------|
|| / 2/x\\ 2 / 2/x\\| ________ |
||x*|1 + cot |-|| x *|1 + cot |-||| / 2/x\\ / 2 |
|\ \ \2// \ \2/// x*|1 + cot |-||*\/ 1 - x *asin(x)|
\ \ \2// /
$$\left(\left(\frac{\cot^{2}{\left(\frac{x}{2} \right)} - 1}{x \left(\cot^{2}{\left(\frac{x}{2} \right)} + 1\right)} - \frac{2 \cot{\left(\frac{x}{2} \right)}}{x^{2} \left(\cot^{2}{\left(\frac{x}{2} \right)} + 1\right)}\right) \log{\left(\operatorname{asin}{\left(x \right)} \right)} + \frac{2 \cot{\left(\frac{x}{2} \right)}}{x \sqrt{1 - x^{2}} \left(\cot^{2}{\left(\frac{x}{2} \right)} + 1\right) \operatorname{asin}{\left(x \right)}}\right) \operatorname{asin}^{\frac{2 \cot{\left(\frac{x}{2} \right)}}{x \left(\cot^{2}{\left(\frac{x}{2} \right)} + 1\right)}}{\left(x \right)}$$
/ pi\ // / pi\ \ \
cos|x - --| || cos|x - --| | |
\ 2 / || \ 2 / | / pi\ |
----------- ||- ----------- + cos(x)|*log(asin(x)) cos|x - --| |
x |\ x / \ 2 / |
(asin(x)) *|------------------------------------- + ---------------------|
| x ________ |
| / 2 |
\ x*\/ 1 - x *asin(x)/
$$\left(\frac{\left(\cos{\left(x \right)} - \frac{\cos{\left(x - \frac{\pi}{2} \right)}}{x}\right) \log{\left(\operatorname{asin}{\left(x \right)} \right)}}{x} + \frac{\cos{\left(x - \frac{\pi}{2} \right)}}{x \sqrt{1 - x^{2}} \operatorname{asin}{\left(x \right)}}\right) \operatorname{asin}^{\frac{\cos{\left(x - \frac{\pi}{2} \right)}}{x}}{\left(x \right)}$$
asin(x)^(cos(x - pi/2)/x)*((-cos(x - pi/2)/x + cos(x))*log(asin(x))/x + cos(x - pi/2)/(x*sqrt(1 - x^2)*asin(x)))