Parte trigonométrica
[src]
/ 2/ pi \\ /x\
2*|1 - tan |---------||*cot|-|
1 \ \2*(2 + x)// \2/
- ----------------- + -----------------------------------
/ 3*pi\ / 2/x\\ / 2/ pi \\
tan(x)*tan|-----| |1 + cot |-||*|1 + tan |---------||
\2 + x/ \ \2// \ \2*(2 + x)//
$$\frac{2 \left(1 - \tan^{2}{\left(\frac{\pi}{2 \left(x + 2\right)} \right)}\right) \cot{\left(\frac{x}{2} \right)}}{\left(\tan^{2}{\left(\frac{\pi}{2 \left(x + 2\right)} \right)} + 1\right) \left(\cot^{2}{\left(\frac{x}{2} \right)} + 1\right)} - \frac{1}{\tan{\left(x \right)} \tan{\left(\frac{3 \pi}{x + 2} \right)}}$$
/ pi\ / pi 3*pi\
sec|x - --|*sec|- -- + -----|
1 \ 2 / \ 2 2 + x/
- ---------------------- - -----------------------------
/ pi \ / pi\ / 3*pi\
sec|-----|*sec|x + --| sec(x)*sec|-----|
\2 + x/ \ 2 / \2 + x/
$$- \frac{1}{\sec{\left(\frac{\pi}{x + 2} \right)} \sec{\left(x + \frac{\pi}{2} \right)}} - \frac{\sec{\left(- \frac{\pi}{2} + \frac{3 \pi}{x + 2} \right)} \sec{\left(x - \frac{\pi}{2} \right)}}{\sec{\left(x \right)} \sec{\left(\frac{3 \pi}{x + 2} \right)}}$$
/ 2/ pi \\ /x\
2*|-1 + cot |---------||*cot|-|
/ 3*pi\ \ \2*(2 + x)// \2/
- cot(x)*cot|-----| + -----------------------------------
\2 + x/ / 2/x\\ / 2/ pi \\
|1 + cot |-||*|1 + cot |---------||
\ \2// \ \2*(2 + x)//
$$- \cot{\left(x \right)} \cot{\left(\frac{3 \pi}{x + 2} \right)} + \frac{2 \left(\cot^{2}{\left(\frac{\pi}{2 \left(x + 2\right)} \right)} - 1\right) \cot{\left(\frac{x}{2} \right)}}{\left(\cot^{2}{\left(\frac{x}{2} \right)} + 1\right) \left(\cot^{2}{\left(\frac{\pi}{2 \left(x + 2\right)} \right)} + 1\right)}$$
/ 2/ pi \\ /x\
2*|1 - tan |---------||*tan|-|
1 \ \2*(2 + x)// \2/
- ----------------- + -----------------------------------
/ 3*pi\ / 2/x\\ / 2/ pi \\
tan(x)*tan|-----| |1 + tan |-||*|1 + tan |---------||
\2 + x/ \ \2// \ \2*(2 + x)//
$$\frac{2 \left(1 - \tan^{2}{\left(\frac{\pi}{2 \left(x + 2\right)} \right)}\right) \tan{\left(\frac{x}{2} \right)}}{\left(\tan^{2}{\left(\frac{x}{2} \right)} + 1\right) \left(\tan^{2}{\left(\frac{\pi}{2 \left(x + 2\right)} \right)} + 1\right)} - \frac{1}{\tan{\left(x \right)} \tan{\left(\frac{3 \pi}{x + 2} \right)}}$$
/ 2/ pi \\
2*|1 - tan |---------||
1 \ \2*(2 + x)//
- ----------------- + ------------------------------------------
/ 3*pi\ / 1 \ / 2/ pi \\ /x\
tan(x)*tan|-----| |1 + -------|*|1 + tan |---------||*tan|-|
\2 + x/ | 2/x\| \ \2*(2 + x)// \2/
| tan |-||
\ \2//
$$- \frac{1}{\tan{\left(x \right)} \tan{\left(\frac{3 \pi}{x + 2} \right)}} + \frac{2 \left(1 - \tan^{2}{\left(\frac{\pi}{2 \left(x + 2\right)} \right)}\right)}{\left(1 + \frac{1}{\tan^{2}{\left(\frac{x}{2} \right)}}\right) \left(\tan^{2}{\left(\frac{\pi}{2 \left(x + 2\right)} \right)} + 1\right) \tan{\left(\frac{x}{2} \right)}}$$
/ 2/ pi \\
2*|-1 + cot |---------||
/ 3*pi\ \ \2*(2 + x)//
- cot(x)*cot|-----| + ------------------------------------------
\2 + x/ / 1 \ / 2/ pi \\ /x\
|1 + -------|*|1 + cot |---------||*cot|-|
| 2/x\| \ \2*(2 + x)// \2/
| cot |-||
\ \2//
$$- \cot{\left(x \right)} \cot{\left(\frac{3 \pi}{x + 2} \right)} + \frac{2 \left(\cot^{2}{\left(\frac{\pi}{2 \left(x + 2\right)} \right)} - 1\right)}{\left(1 + \frac{1}{\cot^{2}{\left(\frac{x}{2} \right)}}\right) \left(\cot^{2}{\left(\frac{\pi}{2 \left(x + 2\right)} \right)} + 1\right) \cot{\left(\frac{x}{2} \right)}}$$
/ 6*pi\
sin(2*x)*sin|-----|
/pi pi \ \2 + x/
sin(x)*sin|-- + -----| - ---------------------
\2 2 + x/ 2 2/ 3*pi\
4*sin (x)*sin |-----|
\2 + x/
$$\sin{\left(x \right)} \sin{\left(\frac{\pi}{2} + \frac{\pi}{x + 2} \right)} - \frac{\sin{\left(2 x \right)} \sin{\left(\frac{6 \pi}{x + 2} \right)}}{4 \sin^{2}{\left(x \right)} \sin^{2}{\left(\frac{3 \pi}{x + 2} \right)}}$$
/ 2/ pi \\ /x\
2*|-1 + cot |---------||*tan|-|
/ 3*pi\ \ \2*(2 + x)// \2/
- cot(x)*cot|-----| + -----------------------------------
\2 + x/ / 2/ pi \\ / 2/x\\
|1 + cot |---------||*|1 + tan |-||
\ \2*(2 + x)// \ \2//
$$- \cot{\left(x \right)} \cot{\left(\frac{3 \pi}{x + 2} \right)} + \frac{2 \left(\cot^{2}{\left(\frac{\pi}{2 \left(x + 2\right)} \right)} - 1\right) \tan{\left(\frac{x}{2} \right)}}{\left(\tan^{2}{\left(\frac{x}{2} \right)} + 1\right) \left(\cot^{2}{\left(\frac{\pi}{2 \left(x + 2\right)} \right)} + 1\right)}$$
/ 3*pi\
csc(x)*csc|-----|
1 \2 + x/
---------------------- - ---------------------------
/pi pi \ /pi \ /pi 3*pi\
csc(x)*csc|-- - -----| csc|-- - x|*csc|-- - -----|
\2 2 + x/ \2 / \2 2 + x/
$$- \frac{\csc{\left(x \right)} \csc{\left(\frac{3 \pi}{x + 2} \right)}}{\csc{\left(\frac{\pi}{2} - \frac{3 \pi}{x + 2} \right)} \csc{\left(- x + \frac{\pi}{2} \right)}} + \frac{1}{\csc{\left(x \right)} \csc{\left(\frac{\pi}{2} - \frac{\pi}{x + 2} \right)}}$$
/ 3*pi\
cos(x)*cos|-----|
/ pi \ / pi\ \2 + x/
- cos|-----|*cos|x + --| - -----------------------------
\2 + x/ \ 2 / /pi \ / pi 3*pi\
cos|-- - x|*cos|- -- + -----|
\2 / \ 2 2 + x/
$$- \frac{\cos{\left(x \right)} \cos{\left(\frac{3 \pi}{x + 2} \right)}}{\cos{\left(- \frac{\pi}{2} + \frac{3 \pi}{x + 2} \right)} \cos{\left(- x + \frac{\pi}{2} \right)}} - \cos{\left(\frac{\pi}{x + 2} \right)} \cos{\left(x + \frac{\pi}{2} \right)}$$
/ 3*pi\
cos(x)*cos|-----|
/ pi \ / pi\ \2 + x/
cos|-----|*cos|x - --| - -----------------------------
\2 + x/ \ 2 / / pi\ / pi 3*pi\
cos|x - --|*cos|- -- + -----|
\ 2 / \ 2 2 + x/
$$- \frac{\cos{\left(x \right)} \cos{\left(\frac{3 \pi}{x + 2} \right)}}{\cos{\left(- \frac{\pi}{2} + \frac{3 \pi}{x + 2} \right)} \cos{\left(x - \frac{\pi}{2} \right)}} + \cos{\left(\frac{\pi}{x + 2} \right)} \cos{\left(x - \frac{\pi}{2} \right)}$$
/ pi\ / pi 3*pi\
sec|x - --|*sec|- -- + -----|
1 \ 2 / \ 2 2 + x/
---------------------- - -----------------------------
/ pi \ / pi\ / 3*pi\
sec|-----|*sec|x - --| sec(x)*sec|-----|
\2 + x/ \ 2 / \2 + x/
$$\frac{1}{\sec{\left(\frac{\pi}{x + 2} \right)} \sec{\left(x - \frac{\pi}{2} \right)}} - \frac{\sec{\left(- \frac{\pi}{2} + \frac{3 \pi}{x + 2} \right)} \sec{\left(x - \frac{\pi}{2} \right)}}{\sec{\left(x \right)} \sec{\left(\frac{3 \pi}{x + 2} \right)}}$$
/ pi \ / 3*pi\
cos|-----|*sin(x) + cot|-----|*cot(pi - x)
\2 + x/ \2 + x/
$$\sin{\left(x \right)} \cos{\left(\frac{\pi}{x + 2} \right)} + \cot{\left(\frac{3 \pi}{x + 2} \right)} \cot{\left(\pi - x \right)}$$
/ 6*pi\
sin(2*x)*sin|-----|
/ pi \ \2 + x/
cos|-----|*sin(x) - ---------------------
\2 + x/ 2 2/ 3*pi\
4*sin (x)*sin |-----|
\2 + x/
$$\sin{\left(x \right)} \cos{\left(\frac{\pi}{x + 2} \right)} - \frac{\sin{\left(2 x \right)} \sin{\left(\frac{6 \pi}{x + 2} \right)}}{4 \sin^{2}{\left(x \right)} \sin^{2}{\left(\frac{3 \pi}{x + 2} \right)}}$$
/ pi \ 1
cos|-----|*sin(x) - -----------------
\2 + x/ / 3*pi\
tan(x)*tan|-----|
\2 + x/
$$\sin{\left(x \right)} \cos{\left(\frac{\pi}{x + 2} \right)} - \frac{1}{\tan{\left(x \right)} \tan{\left(\frac{3 \pi}{x + 2} \right)}}$$
/ 3*pi\
cos(x)*cos|-----|
/ pi \ \2 + x/
cos|-----|*sin(x) - -----------------
\2 + x/ / 3*pi\
sin(x)*sin|-----|
\2 + x/
$$\sin{\left(x \right)} \cos{\left(\frac{\pi}{x + 2} \right)} - \frac{\cos{\left(x \right)} \cos{\left(\frac{3 \pi}{x + 2} \right)}}{\sin{\left(x \right)} \sin{\left(\frac{3 \pi}{x + 2} \right)}}$$
/ 3*pi\
csc(x)*csc|-----|
1 \2 + x/
----------------- - -----------------
/ pi \ / 3*pi\
csc(x)*sec|-----| sec(x)*sec|-----|
\2 + x/ \2 + x/
$$- \frac{\csc{\left(x \right)} \csc{\left(\frac{3 \pi}{x + 2} \right)}}{\sec{\left(x \right)} \sec{\left(\frac{3 \pi}{x + 2} \right)}} + \frac{1}{\csc{\left(x \right)} \sec{\left(\frac{\pi}{x + 2} \right)}}$$
1/(csc(x)*sec(pi/(2 + x))) - csc(x)*csc(3*pi/(2 + x))/(sec(x)*sec(3*pi/(2 + x)))