Parte trigonométrica
[src]
sin(2*x) ___ 2/x pi\ /x pi\
- -------- + 2*\/ 2 *sin |- + --|*cot|- + --|
4 \2 8 / \2 8 /
− sin ( 2 x ) 4 + 2 2 sin 2 ( x 2 + π 8 ) cot ( x 2 + π 8 ) - \frac{\sin{\left(2 x \right)}}{4} + 2 \sqrt{2} \sin^{2}{\left(\frac{x}{2} + \frac{\pi}{8} \right)} \cot{\left(\frac{x}{2} + \frac{\pi}{8} \right)} − 4 sin ( 2 x ) + 2 2 sin 2 ( 2 x + 8 π ) cot ( 2 x + 8 π )
___ /x pi\
2*\/ 2 *tan|- + --|
tan(x) \2 8 /
- --------------- + -------------------
/ 2 \ 2/x pi\
2*\1 + tan (x)/ 1 + tan |- + --|
\2 8 /
2 2 tan ( x 2 + π 8 ) tan 2 ( x 2 + π 8 ) + 1 − tan ( x ) 2 ( tan 2 ( x ) + 1 ) \frac{2 \sqrt{2} \tan{\left(\frac{x}{2} + \frac{\pi}{8} \right)}}{\tan^{2}{\left(\frac{x}{2} + \frac{\pi}{8} \right)} + 1} - \frac{\tan{\left(x \right)}}{2 \left(\tan^{2}{\left(x \right)} + 1\right)} tan 2 ( 2 x + 8 π ) + 1 2 2 tan ( 2 x + 8 π ) − 2 ( tan 2 ( x ) + 1 ) tan ( x )
___ / 2/x pi\\ / 2 \
\/ 2 *|1 + cot |- + --||*\-1 + cot (x)/
cot(x) \ \2 8 //
- --------------- + ---------------------------------------
/ 2 \ / 2 \ / 2/x pi\\
2*\1 + cot (x)/ 2*\1 + cot (x)/*|-1 + cot |- + --||
\ \2 8 //
2 ( cot 2 ( x ) − 1 ) ( cot 2 ( x 2 + π 8 ) + 1 ) 2 ( cot 2 ( x ) + 1 ) ( cot 2 ( x 2 + π 8 ) − 1 ) − cot ( x ) 2 ( cot 2 ( x ) + 1 ) \frac{\sqrt{2} \left(\cot^{2}{\left(x \right)} - 1\right) \left(\cot^{2}{\left(\frac{x}{2} + \frac{\pi}{8} \right)} + 1\right)}{2 \left(\cot^{2}{\left(x \right)} + 1\right) \left(\cot^{2}{\left(\frac{x}{2} + \frac{\pi}{8} \right)} - 1\right)} - \frac{\cot{\left(x \right)}}{2 \left(\cot^{2}{\left(x \right)} + 1\right)} 2 ( cot 2 ( x ) + 1 ) ( cot 2 ( 2 x + 8 π ) − 1 ) 2 ( cot 2 ( x ) − 1 ) ( cot 2 ( 2 x + 8 π ) + 1 ) − 2 ( cot 2 ( x ) + 1 ) cot ( x )
___ /x pi\
2*\/ 2 *tan|- + --|
sin(2*x) \2 8 /
- -------- + -------------------
4 2/x pi\
1 + tan |- + --|
\2 8 /
− sin ( 2 x ) 4 + 2 2 tan ( x 2 + π 8 ) tan 2 ( x 2 + π 8 ) + 1 - \frac{\sin{\left(2 x \right)}}{4} + \frac{2 \sqrt{2} \tan{\left(\frac{x}{2} + \frac{\pi}{8} \right)}}{\tan^{2}{\left(\frac{x}{2} + \frac{\pi}{8} \right)} + 1} − 4 sin ( 2 x ) + tan 2 ( 2 x + 8 π ) + 1 2 2 tan ( 2 x + 8 π )
___ / pi\
\/ 2 *cos(2*x)*sec|x + --|
sin(2*x) \ 4 /
- -------- + --------------------------
4 2
− sin ( 2 x ) 4 + 2 cos ( 2 x ) sec ( x + π 4 ) 2 - \frac{\sin{\left(2 x \right)}}{4} + \frac{\sqrt{2} \cos{\left(2 x \right)} \sec{\left(x + \frac{\pi}{4} \right)}}{2} − 4 sin ( 2 x ) + 2 2 cos ( 2 x ) sec ( x + 4 π )
___ / pi\
\/ 2 *csc|-x + --|
1 \ 4 /
- ---------- + ------------------
4*csc(2*x) /pi \
2*csc|-- - 2*x|
\2 /
2 csc ( − x + π 4 ) 2 csc ( − 2 x + π 2 ) − 1 4 csc ( 2 x ) \frac{\sqrt{2} \csc{\left(- x + \frac{\pi}{4} \right)}}{2 \csc{\left(- 2 x + \frac{\pi}{2} \right)}} - \frac{1}{4 \csc{\left(2 x \right)}} 2 csc ( − 2 x + 2 π ) 2 csc ( − x + 4 π ) − 4 csc ( 2 x ) 1
sin(2*x) ___ / pi\
- -------- + \/ 2 *cos|x - --|
4 \ 4 /
− sin ( 2 x ) 4 + 2 cos ( x − π 4 ) - \frac{\sin{\left(2 x \right)}}{4} + \sqrt{2} \cos{\left(x - \frac{\pi}{4} \right)} − 4 sin ( 2 x ) + 2 cos ( x − 4 π )
___ / 2/x pi\\ / 2 \
\/ 2 *|1 + tan |- + --||*\1 - tan (x)/
tan(x) \ \2 8 //
- --------------- + --------------------------------------
/ 2 \ / 2 \ / 2/x pi\\
2*\1 + tan (x)/ 2*\1 + tan (x)/*|1 - tan |- + --||
\ \2 8 //
2 ( 1 − tan 2 ( x ) ) ( tan 2 ( x 2 + π 8 ) + 1 ) 2 ( 1 − tan 2 ( x 2 + π 8 ) ) ( tan 2 ( x ) + 1 ) − tan ( x ) 2 ( tan 2 ( x ) + 1 ) \frac{\sqrt{2} \left(1 - \tan^{2}{\left(x \right)}\right) \left(\tan^{2}{\left(\frac{x}{2} + \frac{\pi}{8} \right)} + 1\right)}{2 \left(1 - \tan^{2}{\left(\frac{x}{2} + \frac{\pi}{8} \right)}\right) \left(\tan^{2}{\left(x \right)} + 1\right)} - \frac{\tan{\left(x \right)}}{2 \left(\tan^{2}{\left(x \right)} + 1\right)} 2 ( 1 − tan 2 ( 2 x + 8 π ) ) ( tan 2 ( x ) + 1 ) 2 ( 1 − tan 2 ( x ) ) ( tan 2 ( 2 x + 8 π ) + 1 ) − 2 ( tan 2 ( x ) + 1 ) tan ( x )
/ pi\
cos(x)*cos|x - --|
cos(2*x) \ 2 /
---------------------- - ------------------
/ pi\ 2
- cos|x - --| + cos(x)
\ 2 /
− cos ( x ) cos ( x − π 2 ) 2 + cos ( 2 x ) cos ( x ) − cos ( x − π 2 ) - \frac{\cos{\left(x \right)} \cos{\left(x - \frac{\pi}{2} \right)}}{2} + \frac{\cos{\left(2 x \right)}}{\cos{\left(x \right)} - \cos{\left(x - \frac{\pi}{2} \right)}} − 2 cos ( x ) cos ( x − 2 π ) + cos ( x ) − cos ( x − 2 π ) cos ( 2 x )
/ 2/x\\ /x\
2 |-1 + cot |-||*cot|-|
-1 + cot (x) \ \2// \2/
------------------------------------------ - ---------------------
/ 2/x\ /x\ \ 2
|-1 + cot |-| 2*cot|-| | / 2/x\\
/ 2 \ | \2/ \2/ | |1 + cot |-||
\1 + cot (x)/*|------------ - -----------| \ \2//
| 2/x\ 2/x\|
|1 + cot |-| 1 + cot |-||
\ \2/ \2//
− ( cot 2 ( x 2 ) − 1 ) cot ( x 2 ) ( cot 2 ( x 2 ) + 1 ) 2 + cot 2 ( x ) − 1 ( cot 2 ( x 2 ) − 1 cot 2 ( x 2 ) + 1 − 2 cot ( x 2 ) cot 2 ( x 2 ) + 1 ) ( cot 2 ( x ) + 1 ) - \frac{\left(\cot^{2}{\left(\frac{x}{2} \right)} - 1\right) \cot{\left(\frac{x}{2} \right)}}{\left(\cot^{2}{\left(\frac{x}{2} \right)} + 1\right)^{2}} + \frac{\cot^{2}{\left(x \right)} - 1}{\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)}}{\cot^{2}{\left(\frac{x}{2} \right)} + 1}\right) \left(\cot^{2}{\left(x \right)} + 1\right)} − ( cot 2 ( 2 x ) + 1 ) 2 ( cot 2 ( 2 x ) − 1 ) cot ( 2 x ) + ( c o t 2 ( 2 x ) + 1 c o t 2 ( 2 x ) − 1 − c o t 2 ( 2 x ) + 1 2 c o t ( 2 x ) ) ( cot 2 ( x ) + 1 ) cot 2 ( x ) − 1
/pi \ / pi\
sin|-- + 2*x| sin(x)*sin|x + --|
\2 / \ 2 /
--------------------- - ------------------
/ pi\ 2
-sin(x) + sin|x + --|
\ 2 /
− sin ( x ) sin ( x + π 2 ) 2 + sin ( 2 x + π 2 ) − sin ( x ) + sin ( x + π 2 ) - \frac{\sin{\left(x \right)} \sin{\left(x + \frac{\pi}{2} \right)}}{2} + \frac{\sin{\left(2 x + \frac{\pi}{2} \right)}}{- \sin{\left(x \right)} + \sin{\left(x + \frac{\pi}{2} \right)}} − 2 sin ( x ) sin ( x + 2 π ) + − sin ( x ) + sin ( x + 2 π ) sin ( 2 x + 2 π )
___ / pi\
\/ 2 *cos(2*x)*csc|-x + --|
sin(2*x) \ 4 /
- -------- + ---------------------------
4 2
− sin ( 2 x ) 4 + 2 cos ( 2 x ) csc ( − x + π 4 ) 2 - \frac{\sin{\left(2 x \right)}}{4} + \frac{\sqrt{2} \cos{\left(2 x \right)} \csc{\left(- x + \frac{\pi}{4} \right)}}{2} − 4 sin ( 2 x ) + 2 2 cos ( 2 x ) csc ( − x + 4 π )
___
1 \/ 2
- --------------- + -----------
/ pi\ / pi\
4*sec|2*x - --| sec|x - --|
\ 2 / \ 4 /
− 1 4 sec ( 2 x − π 2 ) + 2 sec ( x − π 4 ) - \frac{1}{4 \sec{\left(2 x - \frac{\pi}{2} \right)}} + \frac{\sqrt{2}}{\sec{\left(x - \frac{\pi}{4} \right)}} − 4 sec ( 2 x − 2 π ) 1 + sec ( x − 4 π ) 2
___ / pi\
\/ 2 *sec|x + --|
1 \ 4 /
- --------------- + -----------------
/ pi\ 2*sec(2*x)
4*sec|2*x - --|
\ 2 /
− 1 4 sec ( 2 x − π 2 ) + 2 sec ( x + π 4 ) 2 sec ( 2 x ) - \frac{1}{4 \sec{\left(2 x - \frac{\pi}{2} \right)}} + \frac{\sqrt{2} \sec{\left(x + \frac{\pi}{4} \right)}}{2 \sec{\left(2 x \right)}} − 4 sec ( 2 x − 2 π ) 1 + 2 sec ( 2 x ) 2 sec ( x + 4 π )
1 1
-------------------------- - ---------------
/ 1 1 \ 2*csc(x)*sec(x)
|------ - ------|*sec(2*x)
\sec(x) csc(x)/
− 1 2 csc ( x ) sec ( x ) + 1 ( 1 sec ( x ) − 1 csc ( x ) ) sec ( 2 x ) - \frac{1}{2 \csc{\left(x \right)} \sec{\left(x \right)}} + \frac{1}{\left(\frac{1}{\sec{\left(x \right)}} - \frac{1}{\csc{\left(x \right)}}\right) \sec{\left(2 x \right)}} − 2 csc ( x ) sec ( x ) 1 + ( s e c ( x ) 1 − c s c ( x ) 1 ) sec ( 2 x ) 1
___
sin(2*x) \/ 2 *cos(2*x)
- -------- + --------------
4 / pi\
2*cos|x + --|
\ 4 /
− sin ( 2 x ) 4 + 2 cos ( 2 x ) 2 cos ( x + π 4 ) - \frac{\sin{\left(2 x \right)}}{4} + \frac{\sqrt{2} \cos{\left(2 x \right)}}{2 \cos{\left(x + \frac{\pi}{4} \right)}} − 4 sin ( 2 x ) + 2 cos ( x + 4 π ) 2 cos ( 2 x )
1 1
------------------------------- - --------------------
/ 1 1 \ / pi\
|------ - -----------|*sec(2*x) 2*sec(x)*sec|x - --|
|sec(x) / pi\| \ 2 /
| sec|x - --||
\ \ 2 //
− 1 2 sec ( x ) sec ( x − π 2 ) + 1 ( − 1 sec ( x − π 2 ) + 1 sec ( x ) ) sec ( 2 x ) - \frac{1}{2 \sec{\left(x \right)} \sec{\left(x - \frac{\pi}{2} \right)}} + \frac{1}{\left(- \frac{1}{\sec{\left(x - \frac{\pi}{2} \right)}} + \frac{1}{\sec{\left(x \right)}}\right) \sec{\left(2 x \right)}} − 2 sec ( x ) sec ( x − 2 π ) 1 + ( − s e c ( x − 2 π ) 1 + s e c ( x ) 1 ) sec ( 2 x ) 1
sin(2*x) ___ / pi\
- -------- + \/ 2 *sin|x + --|
4 \ 4 /
− sin ( 2 x ) 4 + 2 sin ( x + π 4 ) - \frac{\sin{\left(2 x \right)}}{4} + \sqrt{2} \sin{\left(x + \frac{\pi}{4} \right)} − 4 sin ( 2 x ) + 2 sin ( x + 4 π )
___ /pi \
\/ 2 *sin|-- + 2*x|
sin(2*x) \2 /
- -------- + -------------------
4 / 3*pi\
2*sin|x + ----|
\ 4 /
− sin ( 2 x ) 4 + 2 sin ( 2 x + π 2 ) 2 sin ( x + 3 π 4 ) - \frac{\sin{\left(2 x \right)}}{4} + \frac{\sqrt{2} \sin{\left(2 x + \frac{\pi}{2} \right)}}{2 \sin{\left(x + \frac{3 \pi}{4} \right)}} − 4 sin ( 2 x ) + 2 sin ( x + 4 3 π ) 2 sin ( 2 x + 2 π )
___ 2 / 2/x pi\\ / 2 \
\/ 2 *cos (x)*|1 + tan |- + --||*\1 - tan (x)/
sin(2*x) \ \2 8 //
- -------- + ----------------------------------------------
4 / 2/x pi\\
2*|1 - tan |- + --||
\ \2 8 //
2 ( 1 − tan 2 ( x ) ) ( tan 2 ( x 2 + π 8 ) + 1 ) cos 2 ( x ) 2 ( 1 − tan 2 ( x 2 + π 8 ) ) − sin ( 2 x ) 4 \frac{\sqrt{2} \left(1 - \tan^{2}{\left(x \right)}\right) \left(\tan^{2}{\left(\frac{x}{2} + \frac{\pi}{8} \right)} + 1\right) \cos^{2}{\left(x \right)}}{2 \left(1 - \tan^{2}{\left(\frac{x}{2} + \frac{\pi}{8} \right)}\right)} - \frac{\sin{\left(2 x \right)}}{4} 2 ( 1 − tan 2 ( 2 x + 8 π ) ) 2 ( 1 − tan 2 ( x ) ) ( tan 2 ( 2 x + 8 π ) + 1 ) cos 2 ( x ) − 4 sin ( 2 x )
___
1 \/ 2
- ---------- + -----------
4*csc(2*x) / pi\
csc|x + --|
\ 4 /
2 csc ( x + π 4 ) − 1 4 csc ( 2 x ) \frac{\sqrt{2}}{\csc{\left(x + \frac{\pi}{4} \right)}} - \frac{1}{4 \csc{\left(2 x \right)}} csc ( x + 4 π ) 2 − 4 csc ( 2 x ) 1
___ /x pi\
2*\/ 2 *cot|- + --|
cot(x) \2 8 /
- --------------- + -------------------
/ 2 \ 2/x pi\
2*\1 + cot (x)/ 1 + cot |- + --|
\2 8 /
2 2 cot ( x 2 + π 8 ) cot 2 ( x 2 + π 8 ) + 1 − cot ( x ) 2 ( cot 2 ( x ) + 1 ) \frac{2 \sqrt{2} \cot{\left(\frac{x}{2} + \frac{\pi}{8} \right)}}{\cot^{2}{\left(\frac{x}{2} + \frac{\pi}{8} \right)} + 1} - \frac{\cot{\left(x \right)}}{2 \left(\cot^{2}{\left(x \right)} + 1\right)} cot 2 ( 2 x + 8 π ) + 1 2 2 cot ( 2 x + 8 π ) − 2 ( cot 2 ( x ) + 1 ) cot ( x )
___
sin(2*x) \/ 2 *cos(2*x)
- -------- - -----------------------------------------------------
4 ___________ ___________
___ / ___ / ___
- \/ 2 *cos(x) + \/ 2 + \/ 2 *\/ 2 - \/ 2 *sin(x)
− sin ( 2 x ) 4 − 2 cos ( 2 x ) 2 − 2 2 + 2 sin ( x ) − 2 cos ( x ) - \frac{\sin{\left(2 x \right)}}{4} - \frac{\sqrt{2} \cos{\left(2 x \right)}}{\sqrt{2 - \sqrt{2}} \sqrt{\sqrt{2} + 2} \sin{\left(x \right)} - \sqrt{2} \cos{\left(x \right)}} − 4 sin ( 2 x ) − 2 − 2 2 + 2 sin ( x ) − 2 cos ( x ) 2 cos ( 2 x )
/ 2/x\\ /x\
2 |1 - tan |-||*tan|-|
1 - tan (x) \ \2// \2/
----------------------------------------- - --------------------
/ 2/x\ /x\ \ 2
|1 - tan |-| 2*tan|-| | / 2/x\\
/ 2 \ | \2/ \2/ | |1 + tan |-||
\1 + tan (x)/*|----------- - -----------| \ \2//
| 2/x\ 2/x\|
|1 + tan |-| 1 + tan |-||
\ \2/ \2//
− ( 1 − tan 2 ( x 2 ) ) tan ( x 2 ) ( tan 2 ( x 2 ) + 1 ) 2 + 1 − tan 2 ( x ) ( 1 − tan 2 ( x 2 ) tan 2 ( x 2 ) + 1 − 2 tan ( x 2 ) tan 2 ( x 2 ) + 1 ) ( tan 2 ( x ) + 1 ) - \frac{\left(1 - \tan^{2}{\left(\frac{x}{2} \right)}\right) \tan{\left(\frac{x}{2} \right)}}{\left(\tan^{2}{\left(\frac{x}{2} \right)} + 1\right)^{2}} + \frac{1 - \tan^{2}{\left(x \right)}}{\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)}}{\tan^{2}{\left(\frac{x}{2} \right)} + 1}\right) \left(\tan^{2}{\left(x \right)} + 1\right)} − ( tan 2 ( 2 x ) + 1 ) 2 ( 1 − tan 2 ( 2 x ) ) tan ( 2 x ) + ( t a n 2 ( 2 x ) + 1 1 − t a n 2 ( 2 x ) − t a n 2 ( 2 x ) + 1 2 t a n ( 2 x ) ) ( tan 2 ( x ) + 1 ) 1 − tan 2 ( x )
/ pi\
cos|2*x - --|
\ 2 / ___ / pi\
- ------------- + \/ 2 *cos|x - --|
4 \ 4 /
2 cos ( x − π 4 ) − cos ( 2 x − π 2 ) 4 \sqrt{2} \cos{\left(x - \frac{\pi}{4} \right)} - \frac{\cos{\left(2 x - \frac{\pi}{2} \right)}}{4} 2 cos ( x − 4 π ) − 4 cos ( 2 x − 2 π )
/ pi\
cos|2*x - --| ___
\ 2 / \/ 2 *cos(2*x)
- ------------- + --------------
4 / pi\
2*cos|x + --|
\ 4 /
2 cos ( 2 x ) 2 cos ( x + π 4 ) − cos ( 2 x − π 2 ) 4 \frac{\sqrt{2} \cos{\left(2 x \right)}}{2 \cos{\left(x + \frac{\pi}{4} \right)}} - \frac{\cos{\left(2 x - \frac{\pi}{2} \right)}}{4} 2 cos ( x + 4 π ) 2 cos ( 2 x ) − 4 cos ( 2 x − 2 π )
1 1
------------------------------------ - --------------------
/ 1 1 \ /pi \ /pi \
|----------- - ------|*csc|-- - 2*x| 2*csc(x)*csc|-- - x|
| /pi \ csc(x)| \2 / \2 /
|csc|-- - x| |
\ \2 / /
− 1 2 csc ( x ) csc ( − x + π 2 ) + 1 ( 1 csc ( − x + π 2 ) − 1 csc ( x ) ) csc ( − 2 x + π 2 ) - \frac{1}{2 \csc{\left(x \right)} \csc{\left(- x + \frac{\pi}{2} \right)}} + \frac{1}{\left(\frac{1}{\csc{\left(- x + \frac{\pi}{2} \right)}} - \frac{1}{\csc{\left(x \right)}}\right) \csc{\left(- 2 x + \frac{\pi}{2} \right)}} − 2 csc ( x ) csc ( − x + 2 π ) 1 + ( c s c ( − x + 2 π ) 1 − c s c ( x ) 1 ) csc ( − 2 x + 2 π ) 1
cos(2*x) cos(x)*sin(x)
---------------- - -------------
-sin(x) + cos(x) 2
− sin ( x ) cos ( x ) 2 + cos ( 2 x ) − sin ( x ) + cos ( x ) - \frac{\sin{\left(x \right)} \cos{\left(x \right)}}{2} + \frac{\cos{\left(2 x \right)}}{- \sin{\left(x \right)} + \cos{\left(x \right)}} − 2 sin ( x ) cos ( x ) + − sin ( x ) + cos ( x ) cos ( 2 x )
cos(2*x)/(-sin(x) + cos(x)) - cos(x)*sin(x)/2