$$- x + \frac{3 \pi}{2}$$
/ 2/x pi\\
| sec |- - --||
/ 1 \ | \2 4 /|
|1 + -----------|*|-1 + ------------|
| / pi\| | 2/x pi\|
| sec|x - --|| | sec |- + --||
1 3*pi \ \ 2 // \ \2 4 //
----------- - x + ---- + -------------------------------------
/ pi\ 2 2
sec|x - --|
\ 2 /
$$- x + \frac{\left(1 + \frac{1}{\sec{\left(x - \frac{\pi}{2} \right)}}\right) \left(\frac{\sec^{2}{\left(\frac{x}{2} - \frac{\pi}{4} \right)}}{\sec^{2}{\left(\frac{x}{2} + \frac{\pi}{4} \right)}} - 1\right)}{2} + \frac{3 \pi}{2} + \frac{1}{\sec{\left(x - \frac{\pi}{2} \right)}}$$
/ /x\ \
| 2*tan|-| |
| \2/ | / 1 \
|1 + -----------|*|-1 + ------------|
| 2/x\| | 2/x pi\| /x\
| 1 + tan |-|| | tan |- + --|| 2*tan|-|
3*pi \ \2// \ \2 4 // \2/
-x + ---- + ------------------------------------- + -----------
2 2 2/x\
1 + tan |-|
\2/
$$- x + \frac{\left(-1 + \frac{1}{\tan^{2}{\left(\frac{x}{2} + \frac{\pi}{4} \right)}}\right) \left(1 + \frac{2 \tan{\left(\frac{x}{2} \right)}}{\tan^{2}{\left(\frac{x}{2} \right)} + 1}\right)}{2} + \frac{3 \pi}{2} + \frac{2 \tan{\left(\frac{x}{2} \right)}}{\tan^{2}{\left(\frac{x}{2} \right)} + 1}$$
3*pi
-x + ---- + sin(x) + sin(pi + x)
2
$$- x + \sin{\left(x \right)} + \sin{\left(x + \pi \right)} + \frac{3 \pi}{2}$$
3*pi / 3*pi\
-x - sin(x) + ---- + cos|x + ----|
2 \ 2 /
$$- x - \sin{\left(x \right)} + \cos{\left(x + \frac{3 \pi}{2} \right)} + \frac{3 \pi}{2}$$
2/x pi\ /x\
-1 + cot |- + --| 2*cot|-|
3*pi \2 4 / \2/
-x + ---- + ----------------- + -----------
2 2/x pi\ 2/x\
1 + cot |- + --| 1 + cot |-|
\2 4 / \2/
$$- x + \frac{\cot^{2}{\left(\frac{x}{2} + \frac{\pi}{4} \right)} - 1}{\cot^{2}{\left(\frac{x}{2} + \frac{\pi}{4} \right)} + 1} + \frac{3 \pi}{2} + \frac{2 \cot{\left(\frac{x}{2} \right)}}{\cot^{2}{\left(\frac{x}{2} \right)} + 1}$$
/ 1 \
(1 + sin(x))*|-1 + ------------|
| 2/x pi\|
| tan |- + --||
3*pi \ \2 4 //
-x + ---- + -------------------------------- + sin(x)
2 2
$$- x + \frac{\left(-1 + \frac{1}{\tan^{2}{\left(\frac{x}{2} + \frac{\pi}{4} \right)}}\right) \left(\sin{\left(x \right)} + 1\right)}{2} + \sin{\left(x \right)} + \frac{3 \pi}{2}$$
2/x pi\ /x\
1 - tan |- + --| 2*tan|-|
3*pi \2 4 / \2/
-x + ---- + ---------------- + -----------
2 2/x pi\ 2/x\
1 + tan |- + --| 1 + tan |-|
\2 4 / \2/
$$- x + \frac{1 - \tan^{2}{\left(\frac{x}{2} + \frac{\pi}{4} \right)}}{\tan^{2}{\left(\frac{x}{2} + \frac{\pi}{4} \right)} + 1} + \frac{3 \pi}{2} + \frac{2 \tan{\left(\frac{x}{2} \right)}}{\tan^{2}{\left(\frac{x}{2} \right)} + 1}$$
/ 2/x pi\\
(1 + sin(x))*|-1 + cot |- + --||
3*pi \ \2 4 //
-x + ---- + -------------------------------- + sin(x)
2 2
$$- x + \frac{\left(\sin{\left(x \right)} + 1\right) \left(\cot^{2}{\left(\frac{x}{2} + \frac{\pi}{4} \right)} - 1\right)}{2} + \sin{\left(x \right)} + \frac{3 \pi}{2}$$
/ 2/x pi\ \
| csc |- + --| |
/ 1 \ | \2 4 / |
|1 + ------|*|-1 + --------------|
\ csc(x)/ | 2/ x pi\|
| csc |- - + --||
1 3*pi \ \ 2 4 //
------ - x + ---- + ----------------------------------
csc(x) 2 2
$$- x + \frac{\left(-1 + \frac{\csc^{2}{\left(\frac{x}{2} + \frac{\pi}{4} \right)}}{\csc^{2}{\left(- \frac{x}{2} + \frac{\pi}{4} \right)}}\right) \left(1 + \frac{1}{\csc{\left(x \right)}}\right)}{2} + \frac{3 \pi}{2} + \frac{1}{\csc{\left(x \right)}}$$
1 1 3*pi
------------- - x - ------ + ----
/ 3*pi\ csc(x) 2
sec|x + ----|
\ 2 /
$$- x + \frac{3 \pi}{2} + \frac{1}{\sec{\left(x + \frac{3 \pi}{2} \right)}} - \frac{1}{\csc{\left(x \right)}}$$
/ 2 \
| cos (x) |
(1 + sin(x))*|-1 + --------------|
| 4/x pi\|
| 4*sin |- + --||
3*pi \ \2 4 //
-x + ---- + ---------------------------------- + sin(x)
2 2
$$- x + \frac{\left(-1 + \frac{\cos^{2}{\left(x \right)}}{4 \sin^{4}{\left(\frac{x}{2} + \frac{\pi}{4} \right)}}\right) \left(\sin{\left(x \right)} + 1\right)}{2} + \sin{\left(x \right)} + \frac{3 \pi}{2}$$
1 1 3*pi
------ - x - ----------- + ----
csc(x) /pi \ 2
sec|-- - x|
\2 /
$$- x + \frac{3 \pi}{2} - \frac{1}{\sec{\left(- x + \frac{\pi}{2} \right)}} + \frac{1}{\csc{\left(x \right)}}$$
/ pi\ 3*pi
-x - cos|x - --| + ---- + sin(x)
\ 2 / 2
$$- x + \sin{\left(x \right)} - \cos{\left(x - \frac{\pi}{2} \right)} + \frac{3 \pi}{2}$$
/ /x\ \
| 2*cot|-| |
| \2/ | / 2/x pi\\
|1 + -----------|*|-1 + cot |- + --||
| 2/x\| \ \2 4 // /x\
| 1 + cot |-|| 2*cot|-|
3*pi \ \2// \2/
-x + ---- + ------------------------------------- + -----------
2 2 2/x\
1 + cot |-|
\2/
$$- x + \frac{\left(1 + \frac{2 \cot{\left(\frac{x}{2} \right)}}{\cot^{2}{\left(\frac{x}{2} \right)} + 1}\right) \left(\cot^{2}{\left(\frac{x}{2} + \frac{\pi}{4} \right)} - 1\right)}{2} + \frac{3 \pi}{2} + \frac{2 \cot{\left(\frac{x}{2} \right)}}{\cot^{2}{\left(\frac{x}{2} \right)} + 1}$$
/ 2/x pi\\
| cos |- + --||
/ / pi\\ | \2 4 /|
|1 + cos|x - --||*|-1 + ------------|
\ \ 2 // | 2/x pi\|
| cos |- - --||
3*pi \ \2 4 // / pi\
-x + ---- + ------------------------------------- + cos|x - --|
2 2 \ 2 /
$$- x + \frac{\left(-1 + \frac{\cos^{2}{\left(\frac{x}{2} + \frac{\pi}{4} \right)}}{\cos^{2}{\left(\frac{x}{2} - \frac{\pi}{4} \right)}}\right) \left(\cos{\left(x - \frac{\pi}{2} \right)} + 1\right)}{2} + \cos{\left(x - \frac{\pi}{2} \right)} + \frac{3 \pi}{2}$$
-x + 3*pi/2 + (1 + cos(x - pi/2))*(-1 + cos(x/2 + pi/4)^2/cos(x/2 - pi/4)^2)/2 + cos(x - pi/2)