Parte trigonométrica
[src]
___ / 2/ pi\\ / pi\
\/ 2 *|1 + cot |x + --||*cot|2*x + --|
\ \ 8 // \ 4 /
----------------------------------------
/ 2/ pi\\ / 2/ pi\\
|1 + cot |2*x + --||*|-1 + cot |x + --||
\ \ 4 // \ \ 8 //
$$\frac{\sqrt{2} \left(\cot^{2}{\left(x + \frac{\pi}{8} \right)} + 1\right) \cot{\left(2 x + \frac{\pi}{4} \right)}}{\left(\cot^{2}{\left(x + \frac{\pi}{8} \right)} - 1\right) \left(\cot^{2}{\left(2 x + \frac{\pi}{4} \right)} + 1\right)}$$
___
\/ 2 *cos(4*x)
-----------------
/ 3*pi\
2*sin|2*x + ----|
\ 4 /
$$\frac{\sqrt{2} \cos{\left(4 x \right)}}{2 \sin{\left(2 x + \frac{3 \pi}{4} \right)}}$$
___
\/ 2
-------------
/ pi\
sec|2*x - --|
\ 4 /
$$\frac{\sqrt{2}}{\sec{\left(2 x - \frac{\pi}{4} \right)}}$$
___ 2/ pi\ / pi\
2*\/ 2 *sin |x + --|*cot|x + --|
\ 8 / \ 8 /
$$2 \sqrt{2} \sin^{2}{\left(x + \frac{\pi}{8} \right)} \cot{\left(x + \frac{\pi}{8} \right)}$$
___ / pi\
\/ 2 *csc|-2*x + --|
\ 4 /
--------------------
2*sec(4*x)
$$\frac{\sqrt{2} \csc{\left(- 2 x + \frac{\pi}{4} \right)}}{2 \sec{\left(4 x \right)}}$$
___ /pi \
\/ 2 *sin|-- + 4*x|
\2 /
-------------------
/ 3*pi\
2*sin|2*x + ----|
\ 4 /
$$\frac{\sqrt{2} \sin{\left(4 x + \frac{\pi}{2} \right)}}{2 \sin{\left(2 x + \frac{3 \pi}{4} \right)}}$$
1
----------------------------------------
/ 1 1 \ /pi \
|------------- - --------|*csc|-- - 4*x|
| /pi \ csc(2*x)| \2 /
|csc|-- - 2*x| |
\ \2 / /
$$\frac{1}{\left(\frac{1}{\csc{\left(- 2 x + \frac{\pi}{2} \right)}} - \frac{1}{\csc{\left(2 x \right)}}\right) \csc{\left(- 4 x + \frac{\pi}{2} \right)}}$$
___ / pi\
\/ 2 *sec|2*x + --|
\ 4 /
-------------------
2*sec(4*x)
$$\frac{\sqrt{2} \sec{\left(2 x + \frac{\pi}{4} \right)}}{2 \sec{\left(4 x \right)}}$$
___
-\/ 2 *cos(4*x)
---------------------------------------------------------
___________ ___________
___ / ___ / ___
- \/ 2 *cos(2*x) + \/ 2 + \/ 2 *\/ 2 - \/ 2 *sin(2*x)
$$- \frac{\sqrt{2} \cos{\left(4 x \right)}}{\sqrt{2 - \sqrt{2}} \sqrt{\sqrt{2} + 2} \sin{\left(2 x \right)} - \sqrt{2} \cos{\left(2 x \right)}}$$
cos(4*x)
--------------------------
/ pi\
- cos|2*x - --| + cos(2*x)
\ 2 /
$$\frac{\cos{\left(4 x \right)}}{\cos{\left(2 x \right)} - \cos{\left(2 x - \frac{\pi}{2} \right)}}$$
___ / pi\
\/ 2 *cos|2*x - --|
\ 4 /
$$\sqrt{2} \cos{\left(2 x - \frac{\pi}{4} \right)}$$
/pi \
sin|-- + 4*x|
\2 /
-------------------------
/pi \
-sin(2*x) + sin|-- + 2*x|
\2 /
$$\frac{\sin{\left(4 x + \frac{\pi}{2} \right)}}{- \sin{\left(2 x \right)} + \sin{\left(2 x + \frac{\pi}{2} \right)}}$$
___
\/ 2
-----------------------------
/ pi\ /pi \
2*cos|2*x + --|*csc|-- - 4*x|
\ 4 / \2 /
$$\frac{\sqrt{2}}{2 \cos{\left(2 x + \frac{\pi}{4} \right)} \csc{\left(- 4 x + \frac{\pi}{2} \right)}}$$
1
------------------------------
/ 1 1 \
|-------- - --------|*sec(4*x)
\sec(2*x) csc(2*x)/
$$\frac{1}{\left(\frac{1}{\sec{\left(2 x \right)}} - \frac{1}{\csc{\left(2 x \right)}}\right) \sec{\left(4 x \right)}}$$
___ / pi\
\/ 2 *tan|2*x + --|
\ 4 /
-----------------------------------------------------
/ 2/ pi\\ / 2/ pi\\ 2/ pi\
|1 + tan |2*x + --||*|-1 + cot |x + --||*sin |x + --|
\ \ 4 // \ \ 8 // \ 8 /
$$\frac{\sqrt{2} \tan{\left(2 x + \frac{\pi}{4} \right)}}{\left(\tan^{2}{\left(2 x + \frac{\pi}{4} \right)} + 1\right) \left(\cot^{2}{\left(x + \frac{\pi}{8} \right)} - 1\right) \sin^{2}{\left(x + \frac{\pi}{8} \right)}}$$
___ / 2/ pi\\ / 2 \
\/ 2 *|1 + cot |x + --||*\-1 + cot (2*x)/
\ \ 8 //
-----------------------------------------
/ 2 \ / 2/ pi\\
2*\1 + cot (2*x)/*|-1 + cot |x + --||
\ \ 8 //
$$\frac{\sqrt{2} \left(\cot^{2}{\left(2 x \right)} - 1\right) \left(\cot^{2}{\left(x + \frac{\pi}{8} \right)} + 1\right)}{2 \left(\cot^{2}{\left(2 x \right)} + 1\right) \left(\cot^{2}{\left(x + \frac{\pi}{8} \right)} - 1\right)}$$
___ / pi\
2*\/ 2 *cot|x + --|
\ 8 /
-------------------
2/ pi\
1 + cot |x + --|
\ 8 /
$$\frac{2 \sqrt{2} \cot{\left(x + \frac{\pi}{8} \right)}}{\cot^{2}{\left(x + \frac{\pi}{8} \right)} + 1}$$
___ / pi\
2*\/ 2 *tan|x + --|
\ 8 /
-------------------
2/ pi\
1 + tan |x + --|
\ 8 /
$$\frac{2 \sqrt{2} \tan{\left(x + \frac{\pi}{8} \right)}}{\tan^{2}{\left(x + \frac{\pi}{8} \right)} + 1}$$
2
1 - tan (2*x)
-------------------------------------------
/ 2 \
/ 2 \ |1 - tan (x) 2*tan(x) |
\1 + tan (2*x)/*|----------- - -----------|
| 2 2 |
\1 + tan (x) 1 + tan (x)/
$$\frac{1 - \tan^{2}{\left(2 x \right)}}{\left(\frac{1 - \tan^{2}{\left(x \right)}}{\tan^{2}{\left(x \right)} + 1} - \frac{2 \tan{\left(x \right)}}{\tan^{2}{\left(x \right)} + 1}\right) \left(\tan^{2}{\left(2 x \right)} + 1\right)}$$
___ / pi\
\/ 2 *csc|-2*x + --|
\ 4 /
--------------------
/pi \
2*csc|-- - 4*x|
\2 /
$$\frac{\sqrt{2} \csc{\left(- 2 x + \frac{\pi}{4} \right)}}{2 \csc{\left(- 4 x + \frac{\pi}{2} \right)}}$$
___
\/ 2
-------------
/ pi\
csc|2*x + --|
\ 4 /
$$\frac{\sqrt{2}}{\csc{\left(2 x + \frac{\pi}{4} \right)}}$$
___ 2 / 2/ pi\\ / 2 \
\/ 2 *cos (2*x)*|1 + tan |x + --||*\1 - tan (2*x)/
\ \ 8 //
--------------------------------------------------
/ 2/ pi\\
2*|1 - tan |x + --||
\ \ 8 //
$$\frac{\sqrt{2} \left(1 - \tan^{2}{\left(2 x \right)}\right) \left(\tan^{2}{\left(x + \frac{\pi}{8} \right)} + 1\right) \cos^{2}{\left(2 x \right)}}{2 \left(1 - \tan^{2}{\left(x + \frac{\pi}{8} \right)}\right)}$$
___ /pi \
\/ 2 *sin|-- + 4*x|
\2 /
-------------------
/ pi\
2*cos|2*x + --|
\ 4 /
$$\frac{\sqrt{2} \sin{\left(4 x + \frac{\pi}{2} \right)}}{2 \cos{\left(2 x + \frac{\pi}{4} \right)}}$$
2
-1 + cot (2*x)
--------------------------------------------
/ 2 \
/ 2 \ |-1 + cot (x) 2*cot(x) |
\1 + cot (2*x)/*|------------ - -----------|
| 2 2 |
\1 + cot (x) 1 + cot (x)/
$$\frac{\cot^{2}{\left(2 x \right)} - 1}{\left(\frac{\cot^{2}{\left(x \right)} - 1}{\cot^{2}{\left(x \right)} + 1} - \frac{2 \cot{\left(x \right)}}{\cot^{2}{\left(x \right)} + 1}\right) \left(\cot^{2}{\left(2 x \right)} + 1\right)}$$
___
\/ 2
------------------------
/ pi\
2*cos|2*x + --|*sec(4*x)
\ 4 /
$$\frac{\sqrt{2}}{2 \cos{\left(2 x + \frac{\pi}{4} \right)} \sec{\left(4 x \right)}}$$
___ / pi\
\/ 2 *sin|2*x + --|
\ 4 /
$$\sqrt{2} \sin{\left(2 x + \frac{\pi}{4} \right)}$$
___ / 2/ pi\\ / pi\
\/ 2 *|1 + tan |x + --||*tan|2*x + --|
\ \ 8 // \ 4 /
---------------------------------------
/ 2/ pi\\ / 2/ pi\\
|1 + tan |2*x + --||*|1 - tan |x + --||
\ \ 4 // \ \ 8 //
$$\frac{\sqrt{2} \left(\tan^{2}{\left(x + \frac{\pi}{8} \right)} + 1\right) \tan{\left(2 x + \frac{\pi}{4} \right)}}{\left(1 - \tan^{2}{\left(x + \frac{\pi}{8} \right)}\right) \left(\tan^{2}{\left(2 x + \frac{\pi}{4} \right)} + 1\right)}$$
___ / 2/ pi\\ / 2 \
\/ 2 *|1 + tan |x + --||*\1 - tan (2*x)/
\ \ 8 //
----------------------------------------
/ 2 \ / 2/ pi\\
2*\1 + tan (2*x)/*|1 - tan |x + --||
\ \ 8 //
$$\frac{\sqrt{2} \left(1 - \tan^{2}{\left(2 x \right)}\right) \left(\tan^{2}{\left(x + \frac{\pi}{8} \right)} + 1\right)}{2 \left(1 - \tan^{2}{\left(x + \frac{\pi}{8} \right)}\right) \left(\tan^{2}{\left(2 x \right)} + 1\right)}$$
1
-----------------------------------
/ 1 1 \
|-------- - -------------|*sec(4*x)
|sec(2*x) / pi\|
| sec|2*x - --||
\ \ 2 //
$$\frac{1}{\left(- \frac{1}{\sec{\left(2 x - \frac{\pi}{2} \right)}} + \frac{1}{\sec{\left(2 x \right)}}\right) \sec{\left(4 x \right)}}$$
___
\/ 2 *cos(4*x)
---------------
/ pi\
2*cos|2*x + --|
\ 4 /
$$\frac{\sqrt{2} \cos{\left(4 x \right)}}{2 \cos{\left(2 x + \frac{\pi}{4} \right)}}$$
___ / 2/ pi\\ / pi\
\/ 2 *|1 + cot |x + --||*tan|2*x + --|
\ \ 8 // \ 4 /
----------------------------------------
/ 2/ pi\\ / 2/ pi\\
|1 + tan |2*x + --||*|-1 + cot |x + --||
\ \ 4 // \ \ 8 //
$$\frac{\sqrt{2} \left(\cot^{2}{\left(x + \frac{\pi}{8} \right)} + 1\right) \tan{\left(2 x + \frac{\pi}{4} \right)}}{\left(\tan^{2}{\left(2 x + \frac{\pi}{4} \right)} + 1\right) \left(\cot^{2}{\left(x + \frac{\pi}{8} \right)} - 1\right)}$$
sqrt(2)*(1 + cot(x + pi/8)^2)*tan(2*x + pi/4)/((1 + tan(2*x + pi/4)^2)*(-1 + cot(x + pi/8)^2))