Sr Examen
Simplificación de expresiones/
Descomposición en fracciones simples/
tan(x)^(2*(1-x)^(2/3))*(-4*log(tan(x))/(3*(1-x)^(1/3))+2*(1-x)^(2/3)*(1+tan(x)^2)/tan(x))
¿Cómo vas a descomponer esta tan(x)^(2*(1-x)^(2/3))*(-4*log(tan(x))/(3*(1-x)^(1/3))+2*(1-x)^(2/3)*(1+tan(x)^2)/tan(x)) expresión en fracciones?
Solución
Ha introducido
[src]
2/3 / 2/3 / 2 \\
2*(1 - x) |-4*log(tan(x)) 2*(1 - x) *\1 + tan (x)/|
(tan(x)) *|-------------- + --------------------------|
| 3 _______ tan(x) |
\ 3*\/ 1 - x /
$$\left(\frac{2 \left(1 - x\right)^{\frac{2}{3}} \left(\tan^{2}{\left(x \right)} + 1\right)}{\tan{\left(x \right)}} + \frac{\left(-1\right) 4 \log{\left(\tan{\left(x \right)} \right)}}{3 \sqrt[3]{1 - x}}\right) \tan^{2 \left(1 - x\right)^{\frac{2}{3}}}{\left(x \right)}$$
tan(x)^(2*(1 - x)^(2/3))*((-4*log(tan(x)))/((3*(1 - x)^(1/3))) + ((2*(1 - x)^(2/3))*(1 + tan(x)^2))/tan(x))
Simplificación general
[src]
2/3
-1 + 2*(1 - x) /3 - 3*x \
2*(tan(x)) *|------- - 2*log(tan(x))*tan(x)|
| 2 |
\cos (x) /
------------------------------------------------------------
3 _______
3*\/ 1 - x
$$\frac{2 \left(\frac{3 - 3 x}{\cos^{2}{\left(x \right)}} - 2 \log{\left(\tan{\left(x \right)} \right)} \tan{\left(x \right)}\right) \tan^{2 \left(1 - x\right)^{\frac{2}{3}} - 1}{\left(x \right)}}{3 \sqrt[3]{1 - x}}$$
2*tan(x)^(-1 + 2*(1 - x)^(2/3))*((3 - 3*x)/cos(x)^2 - 2*log(tan(x))*tan(x))/(3*(1 - x)^(1/3))
Respuesta numérica
[src]
tan(x)^(2.0*(1.0 - x)^0.666666666666667)*(-1.33333333333333*(1.0 - x)^(-0.333333333333333)*log(tan(x)) + 2.0*(1.0 - x)^0.666666666666667*(1.0 + tan(x)^2)/tan(x))
tan(x)^(2.0*(1.0 - x)^0.666666666666667)*(-1.33333333333333*(1.0 - x)^(-0.333333333333333)*log(tan(x)) + 2.0*(1.0 - x)^0.666666666666667*(1.0 + tan(x)^2)/tan(x))
Unión de expresiones racionales
[src]
2/3
2*(1 - x) / / 2 \ \
2*(tan(x)) *\-2*log(tan(x))*tan(x) + 3*\1 + tan (x)/*(1 - x)/
------------------------------------------------------------------------
3 _______
3*\/ 1 - x *tan(x)
$$\frac{2 \left(3 \left(1 - x\right) \left(\tan^{2}{\left(x \right)} + 1\right) - 2 \log{\left(\tan{\left(x \right)} \right)} \tan{\left(x \right)}\right) \tan^{2 \left(1 - x\right)^{\frac{2}{3}}}{\left(x \right)}}{3 \sqrt[3]{1 - x} \tan{\left(x \right)}}$$
2*tan(x)^(2*(1 - x)^(2/3))*(-2*log(tan(x))*tan(x) + 3*(1 + tan(x)^2)*(1 - x))/(3*(1 - x)^(1/3)*tan(x))
Potencias
[src]
2/3 / 2/3 / 2 \\
2*(1 - x) | 4*log(tan(x)) 2*(1 - x) *\1 + tan (x)/|
(tan(x)) *|- ------------- + --------------------------|
| 3 _______ tan(x) |
\ 3*\/ 1 - x /
$$\left(\frac{2 \left(1 - x\right)^{\frac{2}{3}} \left(\tan^{2}{\left(x \right)} + 1\right)}{\tan{\left(x \right)}} - \frac{4 \log{\left(\tan{\left(x \right)} \right)}}{3 \sqrt[3]{1 - x}}\right) \tan^{2 \left(1 - x\right)^{\frac{2}{3}}}{\left(x \right)}$$
/ 2/3\
\(1 - x) / / 2/3 / 2 \\
2 | 4*log(tan(x)) (1 - x) *\2 + 2*tan (x)/|
tan (x) *|- ------------- + --------------------------|
| 3 _______ tan(x) |
\ 3*\/ 1 - x /
$$\left(\frac{\left(1 - x\right)^{\frac{2}{3}} \left(2 \tan^{2}{\left(x \right)} + 2\right)}{\tan{\left(x \right)}} - \frac{4 \log{\left(\tan{\left(x \right)} \right)}}{3 \sqrt[3]{1 - x}}\right) \left(\tan^{2}{\left(x \right)}\right)^{\left(1 - x\right)^{\frac{2}{3}}}$$
/ / 2\ \
| | / I*x -I*x\ | |
| / / I*x -I*x\\ 2/3 | \- e + e / | / I*x -I*x\|
2/3 | |I*\- e + e /| 2*I*(1 - x) *|1 - -----------------|*\e + e /|
2*(1 - x) | 4*log|------------------| | 2 | |
/ / I*x -I*x\\ | | I*x -I*x | | / I*x -I*x\ | |
|I*\- e + e /| | \ e + e / \ \e + e / / |
|------------------| *|- ------------------------- - -----------------------------------------------------|
| I*x -I*x | | 3 _______ I*x -I*x |
\ e + e / \ 3*\/ 1 - x - e + e /
$$\left(\frac{i \left(- e^{i x} + e^{- i x}\right)}{e^{i x} + e^{- i x}}\right)^{2 \left(1 - x\right)^{\frac{2}{3}}} \left(- \frac{2 i \left(1 - x\right)^{\frac{2}{3}} \left(- \frac{\left(- e^{i x} + e^{- i x}\right)^{2}}{\left(e^{i x} + e^{- i x}\right)^{2}} + 1\right) \left(e^{i x} + e^{- i x}\right)}{- e^{i x} + e^{- i x}} - \frac{4 \log{\left(\frac{i \left(- e^{i x} + e^{- i x}\right)}{e^{i x} + e^{- i x}} \right)}}{3 \sqrt[3]{1 - x}}\right)$$
2/3 / 2/3 / 2 \\
2*(1 - x) | 4*log(tan(x)) (1 - x) *\2 + 2*tan (x)/|
(tan(x)) *|- ------------- + --------------------------|
| 3 _______ tan(x) |
\ 3*\/ 1 - x /
$$\left(\frac{\left(1 - x\right)^{\frac{2}{3}} \left(2 \tan^{2}{\left(x \right)} + 2\right)}{\tan{\left(x \right)}} - \frac{4 \log{\left(\tan{\left(x \right)} \right)}}{3 \sqrt[3]{1 - x}}\right) \tan^{2 \left(1 - x\right)^{\frac{2}{3}}}{\left(x \right)}$$
tan(x)^(2*(1 - x)^(2/3))*(-4*log(tan(x))/(3*(1 - x)^(1/3)) + (1 - x)^(2/3)*(2 + 2*tan(x)^2)/tan(x))
Denominador común
[src]
/ 2/3 2/3 2/3 2/3 2/3\
| 2*(1 - x) 2 2*(1 - x) 2*(1 - x) 2*(1 - x) 2 2*(1 - x) |
-\- 6*(tan(x)) - 6*tan (x)*(tan(x)) + 6*x*(tan(x)) + 4*(tan(x)) *log(tan(x))*tan(x) + 6*x*tan (x)*(tan(x)) /
-----------------------------------------------------------------------------------------------------------------------------------------------------------------------
3 _______
3*\/ 1 - x *tan(x)
$$- \frac{6 x \tan^{2}{\left(x \right)} \tan^{2 \left(1 - x\right)^{\frac{2}{3}}}{\left(x \right)} + 6 x \tan^{2 \left(1 - x\right)^{\frac{2}{3}}}{\left(x \right)} + 4 \log{\left(\tan{\left(x \right)} \right)} \tan{\left(x \right)} \tan^{2 \left(1 - x\right)^{\frac{2}{3}}}{\left(x \right)} - 6 \tan^{2}{\left(x \right)} \tan^{2 \left(1 - x\right)^{\frac{2}{3}}}{\left(x \right)} - 6 \tan^{2 \left(1 - x\right)^{\frac{2}{3}}}{\left(x \right)}}{3 \sqrt[3]{1 - x} \tan{\left(x \right)}}$$
-(-6*tan(x)^(2*(1 - x)^(2/3)) - 6*tan(x)^2*tan(x)^(2*(1 - x)^(2/3)) + 6*x*tan(x)^(2*(1 - x)^(2/3)) + 4*tan(x)^(2*(1 - x)^(2/3))*log(tan(x))*tan(x) + 6*x*tan(x)^2*tan(x)^(2*(1 - x)^(2/3)))/(3*(1 - x)^(1/3)*tan(x))
Compilar la expresión
[src]
2/3 / 2/3 / 2 \\
2*(1 - x) | 4*log(tan(x)) 2*(1 - x) *\1 + tan (x)/|
(tan(x)) *|- ------------- + --------------------------|
| 3 _______ tan(x) |
\ 3*\/ 1 - x /
$$\left(\frac{2 \left(1 - x\right)^{\frac{2}{3}} \left(\tan^{2}{\left(x \right)} + 1\right)}{\tan{\left(x \right)}} - \frac{4 \log{\left(\tan{\left(x \right)} \right)}}{3 \sqrt[3]{1 - x}}\right) \tan^{2 \left(1 - x\right)^{\frac{2}{3}}}{\left(x \right)}$$
tan(x)^(2*(1 - x)^(2/3))*(-4*log(tan(x))/(3*(1 - x)^(1/3)) + 2*(1 - x)^(2/3)*(1 + tan(x)^2)/tan(x))
Denominador racional
[src]
2/3
2*(1 - x) / / 2 \ \
(tan(x)) *\-4*log(tan(x))*tan(x) + 6*\1 + tan (x)/*(1 - x)/
----------------------------------------------------------------------
3 _______
3*\/ 1 - x *tan(x)
$$\frac{\left(6 \left(1 - x\right) \left(\tan^{2}{\left(x \right)} + 1\right) - 4 \log{\left(\tan{\left(x \right)} \right)} \tan{\left(x \right)}\right) \tan^{2 \left(1 - x\right)^{\frac{2}{3}}}{\left(x \right)}}{3 \sqrt[3]{1 - x} \tan{\left(x \right)}}$$
tan(x)^(2*(1 - x)^(2/3))*(-4*log(tan(x))*tan(x) + 6*(1 + tan(x)^2)*(1 - x))/(3*(1 - x)^(1/3)*tan(x))
Combinatoria
[src]
2/3
2*(1 - x) / 2 2 \
-2*(tan(x)) *\-3 - 3*tan (x) + 3*x + 2*log(tan(x))*tan(x) + 3*x*tan (x)/
-----------------------------------------------------------------------------------
3 _______
3*\/ 1 - x *tan(x)
$$- \frac{2 \left(3 x \tan^{2}{\left(x \right)} + 3 x + 2 \log{\left(\tan{\left(x \right)} \right)} \tan{\left(x \right)} - 3 \tan^{2}{\left(x \right)} - 3\right) \tan^{2 \left(1 - x\right)^{\frac{2}{3}}}{\left(x \right)}}{3 \sqrt[3]{1 - x} \tan{\left(x \right)}}$$
-2*tan(x)^(2*(1 - x)^(2/3))*(-3 - 3*tan(x)^2 + 3*x + 2*log(tan(x))*tan(x) + 3*x*tan(x)^2)/(3*(1 - x)^(1/3)*tan(x))
Parte trigonométrica
[src]
/ / 2/pi \\ \
2/3 | / /pi \\ | csc |-- - x|| |
2*(1 - x) | |csc|-- - x|| 2/3 | \2 /| |
/ /pi \\ | | \2 /| 2*(1 - x) *|1 + ------------|*csc(x)|
|csc|-- - x|| | 4*log|-----------| | 2 | |
| \2 /| | \ csc(x) / \ csc (x) / |
|-----------| *|- ------------------ + --------------------------------------|
\ csc(x) / | 3 _______ /pi \ |
| 3*\/ 1 - x csc|-- - x| |
\ \2 / /
$$\left(\frac{\csc{\left(- x + \frac{\pi}{2} \right)}}{\csc{\left(x \right)}}\right)^{2 \left(1 - x\right)^{\frac{2}{3}}} \left(\frac{2 \left(1 - x\right)^{\frac{2}{3}} \left(1 + \frac{\csc^{2}{\left(- x + \frac{\pi}{2} \right)}}{\csc^{2}{\left(x \right)}}\right) \csc{\left(x \right)}}{\csc{\left(- x + \frac{\pi}{2} \right)}} - \frac{4 \log{\left(\frac{\csc{\left(- x + \frac{\pi}{2} \right)}}{\csc{\left(x \right)}} \right)}}{3 \sqrt[3]{1 - x}}\right)$$
/ / 2 \ \
| 2/3 | sin (x)| |
2/3 | /sin(x)\ 2*(1 - x) *|1 + -------|*cos(x)|
2*(1 - x) | 4*log|------| | 2 | |
/sin(x)\ | \cos(x)/ \ cos (x)/ |
|------| *|- ------------- + ---------------------------------|
\cos(x)/ | 3 _______ sin(x) |
\ 3*\/ 1 - x /
$$\left(\frac{\sin{\left(x \right)}}{\cos{\left(x \right)}}\right)^{2 \left(1 - x\right)^{\frac{2}{3}}} \left(\frac{2 \left(1 - x\right)^{\frac{2}{3}} \left(\frac{\sin^{2}{\left(x \right)}}{\cos^{2}{\left(x \right)}} + 1\right) \cos{\left(x \right)}}{\sin{\left(x \right)}} - \frac{4 \log{\left(\frac{\sin{\left(x \right)}}{\cos{\left(x \right)}} \right)}}{3 \sqrt[3]{1 - x}}\right)$$
2/3 / / 1 \ \
2*(1 - x) | 4*log|------| 2/3 / 2 \|
/ 1 \ | \cot(x)/ 2*(1 - x) *\1 + cot (x)/|
|------| *|- ------------- + --------------------------|
\cot(x)/ | 3 _______ cot(x) |
\ 3*\/ 1 - x /
$$\left(\frac{2 \left(1 - x\right)^{\frac{2}{3}} \left(\cot^{2}{\left(x \right)} + 1\right)}{\cot{\left(x \right)}} - \frac{4 \log{\left(\frac{1}{\cot{\left(x \right)}} \right)}}{3 \sqrt[3]{1 - x}}\right) \left(\frac{1}{\cot{\left(x \right)}}\right)^{2 \left(1 - x\right)^{\frac{2}{3}}}$$
2/3 / / /pi \\\
2*(1 - x) | |csc|-- - x|||
/ /pi \\ | | \2 /||
|csc|-- - x|| | 4*log|-----------||
| \2 /| | 2/3 \ csc(x) /|
|-----------| *|4*(1 - x) *csc(2*x) - ------------------|
\ csc(x) / | 3 _______ |
\ 3*\/ 1 - x /
$$\left(\frac{\csc{\left(- x + \frac{\pi}{2} \right)}}{\csc{\left(x \right)}}\right)^{2 \left(1 - x\right)^{\frac{2}{3}}} \left(4 \left(1 - x\right)^{\frac{2}{3}} \csc{\left(2 x \right)} - \frac{4 \log{\left(\frac{\csc{\left(- x + \frac{\pi}{2} \right)}}{\csc{\left(x \right)}} \right)}}{3 \sqrt[3]{1 - x}}\right)$$
/ / 4 \ \
2/3 | / 2 \ 2/3 | 4*sin (x)| |
2*(1 - x) | |2*sin (x)| (1 - x) *|1 + ---------|*sin(2*x)|
/ 2 \ | 4*log|---------| | 2 | |
|2*sin (x)| | \ sin(2*x)/ \ sin (2*x)/ |
|---------| *|- ---------------- + -----------------------------------|
\ sin(2*x)/ | 3 _______ 2 |
\ 3*\/ 1 - x sin (x) /
$$\left(\frac{2 \sin^{2}{\left(x \right)}}{\sin{\left(2 x \right)}}\right)^{2 \left(1 - x\right)^{\frac{2}{3}}} \left(\frac{\left(1 - x\right)^{\frac{2}{3}} \left(\frac{4 \sin^{4}{\left(x \right)}}{\sin^{2}{\left(2 x \right)}} + 1\right) \sin{\left(2 x \right)}}{\sin^{2}{\left(x \right)}} - \frac{4 \log{\left(\frac{2 \sin^{2}{\left(x \right)}}{\sin{\left(2 x \right)}} \right)}}{3 \sqrt[3]{1 - x}}\right)$$
2/3 / / / pi\\\
2*(1 - x) | |cos|x - --|||
/ / pi\\ | | \ 2 /||
|cos|x - --|| | 2/3 4*log|-----------||
| \ 2 /| | 4*(1 - x) \ cos(x) /|
|-----------| *|------------- - ------------------|
\ cos(x) / | / pi\ 3 _______ |
|cos|2*x - --| 3*\/ 1 - x |
\ \ 2 / /
$$\left(\frac{\cos{\left(x - \frac{\pi}{2} \right)}}{\cos{\left(x \right)}}\right)^{2 \left(1 - x\right)^{\frac{2}{3}}} \left(\frac{4 \left(1 - x\right)^{\frac{2}{3}}}{\cos{\left(2 x - \frac{\pi}{2} \right)}} - \frac{4 \log{\left(\frac{\cos{\left(x - \frac{\pi}{2} \right)}}{\cos{\left(x \right)}} \right)}}{3 \sqrt[3]{1 - x}}\right)$$
2/3
2*(1 - x) / 2/3 4*log(tan(x))\
(tan(x)) *|4*(1 - x) *csc(2*x) - -------------|
| 3 _______ |
\ 3*\/ 1 - x /
$$\left(4 \left(1 - x\right)^{\frac{2}{3}} \csc{\left(2 x \right)} - \frac{4 \log{\left(\tan{\left(x \right)} \right)}}{3 \sqrt[3]{1 - x}}\right) \tan^{2 \left(1 - x\right)^{\frac{2}{3}}}{\left(x \right)}$$
/ / 2/ pi\\ \
2/3 | / / pi\\ | cos |x - --|| |
2*(1 - x) | |cos|x - --|| 2/3 | \ 2 /| |
/ / pi\\ | | \ 2 /| 2*(1 - x) *|1 + ------------|*cos(x)|
|cos|x - --|| | 4*log|-----------| | 2 | |
| \ 2 /| | \ cos(x) / \ cos (x) / |
|-----------| *|- ------------------ + --------------------------------------|
\ cos(x) / | 3 _______ / pi\ |
| 3*\/ 1 - x cos|x - --| |
\ \ 2 / /
$$\left(\frac{\cos{\left(x - \frac{\pi}{2} \right)}}{\cos{\left(x \right)}}\right)^{2 \left(1 - x\right)^{\frac{2}{3}}} \left(\frac{2 \left(1 - x\right)^{\frac{2}{3}} \left(1 + \frac{\cos^{2}{\left(x - \frac{\pi}{2} \right)}}{\cos^{2}{\left(x \right)}}\right) \cos{\left(x \right)}}{\cos{\left(x - \frac{\pi}{2} \right)}} - \frac{4 \log{\left(\frac{\cos{\left(x - \frac{\pi}{2} \right)}}{\cos{\left(x \right)}} \right)}}{3 \sqrt[3]{1 - x}}\right)$$
2/3 / / 1 \ \
2*(1 - x) | 4*log|------| |
/ 1 \ | \cot(x)/ 2/3 / 1 \ |
|------| *|- ------------- + 2*(1 - x) *|1 + -------|*cot(x)|
\cot(x)/ | 3 _______ | 2 | |
\ 3*\/ 1 - x \ cot (x)/ /
$$\left(2 \left(1 - x\right)^{\frac{2}{3}} \left(1 + \frac{1}{\cot^{2}{\left(x \right)}}\right) \cot{\left(x \right)} - \frac{4 \log{\left(\frac{1}{\cot{\left(x \right)}} \right)}}{3 \sqrt[3]{1 - x}}\right) \left(\frac{1}{\cot{\left(x \right)}}\right)^{2 \left(1 - x\right)^{\frac{2}{3}}}$$
2/3 / 2/3\
2*(1 - x) | 1 4*(1 - x) |
(tan(x)) *|- 4*-----------*log(tan(x)) + ------------|
| 3 _______ sin(2*x) |
\ 3*\/ 1 - x /
$$\left(- 4 \frac{1}{3 \sqrt[3]{1 - x}} \log{\left(\tan{\left(x \right)} \right)} + \frac{4 \left(1 - x\right)^{\frac{2}{3}}}{\sin{\left(2 x \right)}}\right) \tan^{2 \left(1 - x\right)^{\frac{2}{3}}}{\left(x \right)}$$
2/3 / 2/3 / 2 \\
2*(1 - x) | 4*log(tan(x)) 2*(1 - x) *\1 + tan (x)/|
(tan(x)) *|- ------------- + --------------------------|
| 3 _______ tan(x) |
\ 3*\/ 1 - x /
$$\left(\frac{2 \left(1 - x\right)^{\frac{2}{3}} \left(\tan^{2}{\left(x \right)} + 1\right)}{\tan{\left(x \right)}} - \frac{4 \log{\left(\tan{\left(x \right)} \right)}}{3 \sqrt[3]{1 - x}}\right) \tan^{2 \left(1 - x\right)^{\frac{2}{3}}}{\left(x \right)}$$
/ / sec(x) \\
| 4*log|-----------||
2/3 | | / pi\||
2*(1 - x) | |sec|x - --|||
/ sec(x) \ | 2/3 / pi\ \ \ 2 //|
|-----------| *|4*(1 - x) *sec|2*x - --| - ------------------|
| / pi\| | \ 2 / 3 _______ |
|sec|x - --|| \ 3*\/ 1 - x /
\ \ 2 //
$$\left(\frac{\sec{\left(x \right)}}{\sec{\left(x - \frac{\pi}{2} \right)}}\right)^{2 \left(1 - x\right)^{\frac{2}{3}}} \left(4 \left(1 - x\right)^{\frac{2}{3}} \sec{\left(2 x - \frac{\pi}{2} \right)} - \frac{4 \log{\left(\frac{\sec{\left(x \right)}}{\sec{\left(x - \frac{\pi}{2} \right)}} \right)}}{3 \sqrt[3]{1 - x}}\right)$$
/ / 2 \ \
| 2/3 | sec (x)| |
2/3 | /sec(x)\ 2*(1 - x) *|1 + -------|*csc(x)|
2*(1 - x) | 4*log|------| | 2 | |
/sec(x)\ | \csc(x)/ \ csc (x)/ |
|------| *|- ------------- + ---------------------------------|
\csc(x)/ | 3 _______ sec(x) |
\ 3*\/ 1 - x /
$$\left(\frac{\sec{\left(x \right)}}{\csc{\left(x \right)}}\right)^{2 \left(1 - x\right)^{\frac{2}{3}}} \left(\frac{2 \left(1 - x\right)^{\frac{2}{3}} \left(1 + \frac{\sec^{2}{\left(x \right)}}{\csc^{2}{\left(x \right)}}\right) \csc{\left(x \right)}}{\sec{\left(x \right)}} - \frac{4 \log{\left(\frac{\sec{\left(x \right)}}{\csc{\left(x \right)}} \right)}}{3 \sqrt[3]{1 - x}}\right)$$
/ / 2 \ \
| / sec(x) \ 2/3 | sec (x) | / pi\|
| 4*log|-----------| 2*(1 - x) *|1 + ------------|*sec|x - --||
2/3 | | / pi\| | 2/ pi\| \ 2 /|
2*(1 - x) | |sec|x - --|| | sec |x - --|| |
/ sec(x) \ | \ \ 2 // \ \ 2 // |
|-----------| *|- ------------------ + -------------------------------------------|
| / pi\| | 3 _______ sec(x) |
|sec|x - --|| \ 3*\/ 1 - x /
\ \ 2 //
$$\left(\frac{\sec{\left(x \right)}}{\sec{\left(x - \frac{\pi}{2} \right)}}\right)^{2 \left(1 - x\right)^{\frac{2}{3}}} \left(\frac{2 \left(1 - x\right)^{\frac{2}{3}} \left(\frac{\sec^{2}{\left(x \right)}}{\sec^{2}{\left(x - \frac{\pi}{2} \right)}} + 1\right) \sec{\left(x - \frac{\pi}{2} \right)}}{\sec{\left(x \right)}} - \frac{4 \log{\left(\frac{\sec{\left(x \right)}}{\sec{\left(x - \frac{\pi}{2} \right)}} \right)}}{3 \sqrt[3]{1 - x}}\right)$$
2/3 / / 2 \\
2*(1 - x) | |2*sin (x)||
/ 2 \ | 2/3 4*log|---------||
|2*sin (x)| |4*(1 - x) \ sin(2*x)/|
|---------| *|------------ - ----------------|
\ sin(2*x)/ | sin(2*x) 3 _______ |
\ 3*\/ 1 - x /
$$\left(\frac{2 \sin^{2}{\left(x \right)}}{\sin{\left(2 x \right)}}\right)^{2 \left(1 - x\right)^{\frac{2}{3}}} \left(\frac{4 \left(1 - x\right)^{\frac{2}{3}}}{\sin{\left(2 x \right)}} - \frac{4 \log{\left(\frac{2 \sin^{2}{\left(x \right)}}{\sin{\left(2 x \right)}} \right)}}{3 \sqrt[3]{1 - x}}\right)$$
2/3 / 2/3 \
2*(1 - x) |4*(1 - x) 4*log(tan(x))|
(tan(x)) *|------------ - -------------|
| sin(2*x) 3 _______ |
\ 3*\/ 1 - x /
$$\left(\frac{4 \left(1 - x\right)^{\frac{2}{3}}}{\sin{\left(2 x \right)}} - \frac{4 \log{\left(\tan{\left(x \right)} \right)}}{3 \sqrt[3]{1 - x}}\right) \tan^{2 \left(1 - x\right)^{\frac{2}{3}}}{\left(x \right)}$$
tan(x)^(2*(1 - x)^(2/3))*(4*(1 - x)^(2/3)/sin(2*x) - 4*log(tan(x))/(3*(1 - x)^(1/3)))