Parte trigonométrica
[src]
1
-------------------------
3/2
/ 1 \
8*|---------| *sec(4*x)
| 2 |
\sec (4*x)/
$$\frac{1}{8 \left(\frac{1}{\sec^{2}{\left(4 x \right)}}\right)^{\frac{3}{2}} \sec{\left(4 x \right)}}$$
/ 2 \
___ 2/ pi\ | cos (2*x) |
\/ 2 *cos |2*x - --|*|-1 + --------------|
\ 2 / | 2/ pi\|
| cos |2*x - --||
\ \ 2 //
------------------------------------------
3/2
4*(1 + cos(8*x))
$$\frac{\sqrt{2} \left(\frac{\cos^{2}{\left(2 x \right)}}{\cos^{2}{\left(2 x - \frac{\pi}{2} \right)}} - 1\right) \cos^{2}{\left(2 x - \frac{\pi}{2} \right)}}{4 \left(\cos{\left(8 x \right)} + 1\right)^{\frac{3}{2}}}$$
2
___ / 2 \ 4 / 2 \
\/ 2 *\-1 + cot (x)/ *sin (x)*\1 - tan (2*x)/
---------------------------------------------
3/2
/ 2 / 2 \\
4*\1 + sin (4*x)*\-1 + cot (4*x)//
$$\frac{\sqrt{2} \left(1 - \tan^{2}{\left(2 x \right)}\right) \left(\cot^{2}{\left(x \right)} - 1\right)^{2} \sin^{4}{\left(x \right)}}{4 \left(\left(\cot^{2}{\left(4 x \right)} - 1\right) \sin^{2}{\left(4 x \right)} + 1\right)^{\frac{3}{2}}}$$
/ 2 \
___ | csc (2*x) |
\/ 2 *|-1 + --------------|
| 2/pi \|
| csc |-- - 2*x||
\ \2 //
----------------------------------
3/2
/ 1 \ 2
4*|1 + -------------| *csc (2*x)
| /pi \|
| csc|-- - 8*x||
\ \2 //
$$\frac{\sqrt{2} \left(\frac{\csc^{2}{\left(2 x \right)}}{\csc^{2}{\left(- 2 x + \frac{\pi}{2} \right)}} - 1\right)}{4 \left(1 + \frac{1}{\csc{\left(- 8 x + \frac{\pi}{2} \right)}}\right)^{\frac{3}{2}} \csc^{2}{\left(2 x \right)}}$$
___ 2 4 / 2 \
\/ 2 *cot (x)*sin (x)*\-1 + cot (2*x)/
--------------------------------------
3/2
/ 2 / 2 \\
\1 + sin (4*x)*\-1 + cot (4*x)//
$$\frac{\sqrt{2} \left(\cot^{2}{\left(2 x \right)} - 1\right) \sin^{4}{\left(x \right)} \cot^{2}{\left(x \right)}}{\left(\left(\cot^{2}{\left(4 x \right)} - 1\right) \sin^{2}{\left(4 x \right)} + 1\right)^{\frac{3}{2}}}$$
2
___ / 2 \ / 1 \
\/ 2 *\-1 + cot (x)/ *|1 - ---------|
| 2 |
\ cot (2*x)/
----------------------------------------
3/2
2 / 2 \
/ 2 \ | -1 + cot (4*x)|
4*\1 + cot (x)/ *|1 + --------------|
| 2 |
\ 1 + cot (4*x) /
$$\frac{\sqrt{2} \left(1 - \frac{1}{\cot^{2}{\left(2 x \right)}}\right) \left(\cot^{2}{\left(x \right)} - 1\right)^{2}}{4 \left(\frac{\cot^{2}{\left(4 x \right)} - 1}{\cot^{2}{\left(4 x \right)} + 1} + 1\right)^{\frac{3}{2}} \left(\cot^{2}{\left(x \right)} + 1\right)^{2}}$$
/ 2/ pi\\
| cos |2*x - --||
___ 2 | \ 2 /|
\/ 2 *cos (2*x)*|1 - --------------|
| 2 |
\ cos (2*x) /
------------------------------------
3/2
4*(1 + cos(8*x))
$$\frac{\sqrt{2} \left(1 - \frac{\cos^{2}{\left(2 x - \frac{\pi}{2} \right)}}{\cos^{2}{\left(2 x \right)}}\right) \cos^{2}{\left(2 x \right)}}{4 \left(\cos{\left(8 x \right)} + 1\right)^{\frac{3}{2}}}$$
2/ pi\ / pi\
sin |2*x + --|*cot|2*x + --|
\ 4 / \ 4 /
-------------------------------------
3/2
/ 2/ pi\ 4/ pi\\
32*|cot |2*x + --|*sin |2*x + --||
\ \ 4 / \ 4 //
$$\frac{\sin^{2}{\left(2 x + \frac{\pi}{4} \right)} \cot{\left(2 x + \frac{\pi}{4} \right)}}{32 \left(\sin^{4}{\left(2 x + \frac{\pi}{4} \right)} \cot^{2}{\left(2 x + \frac{\pi}{4} \right)}\right)^{\frac{3}{2}}}$$
___ 2 / 2 \
\/ 2 *cos (2*x)*\1 - tan (2*x)/
-------------------------------
3/2
/ 1 \
4*|1 + -------------|
| /pi \|
| csc|-- - 8*x||
\ \2 //
$$\frac{\sqrt{2} \left(1 - \tan^{2}{\left(2 x \right)}\right) \cos^{2}{\left(2 x \right)}}{4 \left(1 + \frac{1}{\csc{\left(- 8 x + \frac{\pi}{2} \right)}}\right)^{\frac{3}{2}}}$$
___ 2 / 2 \
\/ 2 *cos (2*x)*\1 - tan (2*x)/
-------------------------------
3/2
4*(1 + cos(8*x))
$$\frac{\sqrt{2} \left(1 - \tan^{2}{\left(2 x \right)}\right) \cos^{2}{\left(2 x \right)}}{4 \left(\cos{\left(8 x \right)} + 1\right)^{\frac{3}{2}}}$$
/ 2/pi \\
| csc |-- - 2*x||
___ | \2 /|
\/ 2 *|1 - --------------|
| 2 |
\ csc (2*x) /
---------------------------------------
3/2
/ 1 \ 2/pi \
4*|1 + -------------| *csc |-- - 2*x|
| /pi \| \2 /
| csc|-- - 8*x||
\ \2 //
$$\frac{\sqrt{2} \left(1 - \frac{\csc^{2}{\left(- 2 x + \frac{\pi}{2} \right)}}{\csc^{2}{\left(2 x \right)}}\right)}{4 \left(1 + \frac{1}{\csc{\left(- 8 x + \frac{\pi}{2} \right)}}\right)^{\frac{3}{2}} \csc^{2}{\left(- 2 x + \frac{\pi}{2} \right)}}$$
2
___ / 2 \ 4 / 2 \
\/ 2 *\1 - tan (x)/ *cos (x)*\1 - tan (2*x)/
--------------------------------------------
3/2
/ 2 / 2 \\
4*\1 + cos (4*x)*\1 - tan (4*x)//
$$\frac{\sqrt{2} \left(1 - \tan^{2}{\left(x \right)}\right)^{2} \left(1 - \tan^{2}{\left(2 x \right)}\right) \cos^{4}{\left(x \right)}}{4 \left(\left(1 - \tan^{2}{\left(4 x \right)}\right) \cos^{2}{\left(4 x \right)} + 1\right)^{\frac{3}{2}}}$$
/ 4 \
___ 2 | 4*sin (2*x)|
\/ 2 *cos (2*x)*|1 - -----------|
| 2 |
\ sin (4*x) /
---------------------------------
3/2
/ /pi \\
4*|1 + sin|-- + 8*x||
\ \2 //
$$\frac{\sqrt{2} \left(- \frac{4 \sin^{4}{\left(2 x \right)}}{\sin^{2}{\left(4 x \right)}} + 1\right) \cos^{2}{\left(2 x \right)}}{4 \left(\sin{\left(8 x + \frac{\pi}{2} \right)} + 1\right)^{\frac{3}{2}}}$$
/pi \
sin|-- + 4*x|
\2 /
-------------------
3/2
2/pi \
8*sin |-- + 4*x|
\2 /
$$\frac{\sin{\left(4 x + \frac{\pi}{2} \right)}}{8 \left(\sin^{2}{\left(4 x + \frac{\pi}{2} \right)}\right)^{\frac{3}{2}}}$$
/ pi\
tan|2*x + --|
\ 4 /
--------------------------------------------------
3/2
/ 2/ pi\ \
| tan |2*x + --| |
| \ 4 / | / 2/ pi\\
32*|---------------------| *|1 + tan |2*x + --||
| 2| \ \ 4 //
|/ 2/ pi\\ |
||1 + tan |2*x + --|| |
\\ \ 4 // /
$$\frac{\tan{\left(2 x + \frac{\pi}{4} \right)}}{32 \left(\frac{\tan^{2}{\left(2 x + \frac{\pi}{4} \right)}}{\left(\tan^{2}{\left(2 x + \frac{\pi}{4} \right)} + 1\right)^{2}}\right)^{\frac{3}{2}} \left(\tan^{2}{\left(2 x + \frac{\pi}{4} \right)} + 1\right)}$$
/ 2 \
___ 2 | sin (4*x) |
\/ 2 *sin (2*x)*|-1 + -----------|
| 4 |
\ 4*sin (2*x)/
----------------------------------
3/2
/ /pi \\
4*|1 + sin|-- + 8*x||
\ \2 //
$$\frac{\sqrt{2} \left(-1 + \frac{\sin^{2}{\left(4 x \right)}}{4 \sin^{4}{\left(2 x \right)}}\right) \sin^{2}{\left(2 x \right)}}{4 \left(\sin{\left(8 x + \frac{\pi}{2} \right)} + 1\right)^{\frac{3}{2}}}$$
1
-----------------------------------
3/2
/ 1 \ /pi \
8*|--------------| *csc|-- - 4*x|
| 2/pi \| \2 /
|csc |-- - 4*x||
\ \2 //
$$\frac{1}{8 \left(\frac{1}{\csc^{2}{\left(- 4 x + \frac{\pi}{2} \right)}}\right)^{\frac{3}{2}} \csc{\left(- 4 x + \frac{\pi}{2} \right)}}$$
/ 2 \
___ | sec (2*x) |
\/ 2 *|1 - --------------|
| 2/ pi\|
| sec |2*x - --||
\ \ 2 //
-----------------------------
3/2
/ 1 \ 2
4*|1 + --------| *sec (2*x)
\ sec(8*x)/
$$\frac{\sqrt{2} \left(- \frac{\sec^{2}{\left(2 x \right)}}{\sec^{2}{\left(2 x - \frac{\pi}{2} \right)}} + 1\right)}{4 \left(1 + \frac{1}{\sec{\left(8 x \right)}}\right)^{\frac{3}{2}} \sec^{2}{\left(2 x \right)}}$$
___ / 1 \
\/ 2 *|-1 + ---------|
| 2 |
\ tan (2*x)/
----------------------------------
3/2
/ 1 \ 2
4*|1 + -------------| *csc (2*x)
| /pi \|
| csc|-- - 8*x||
\ \2 //
$$\frac{\sqrt{2} \left(-1 + \frac{1}{\tan^{2}{\left(2 x \right)}}\right)}{4 \left(1 + \frac{1}{\csc{\left(- 8 x + \frac{\pi}{2} \right)}}\right)^{\frac{3}{2}} \csc^{2}{\left(2 x \right)}}$$
/ 2/ pi\\
| sec |2*x - --||
___ | \ 2 /|
\/ 2 *|-1 + --------------|
| 2 |
\ sec (2*x) /
----------------------------------
3/2
/ 1 \ 2/ pi\
4*|1 + --------| *sec |2*x - --|
\ sec(8*x)/ \ 2 /
$$\frac{\sqrt{2} \left(-1 + \frac{\sec^{2}{\left(2 x - \frac{\pi}{2} \right)}}{\sec^{2}{\left(2 x \right)}}\right)}{4 \left(1 + \frac{1}{\sec{\left(8 x \right)}}\right)^{\frac{3}{2}} \sec^{2}{\left(2 x - \frac{\pi}{2} \right)}}$$
___ 2 / 2 \
\/ 2 *sin (2*x)*\-1 + cot (2*x)/
--------------------------------
3/2
4*(1 + cos(8*x))
$$\frac{\sqrt{2} \left(\cot^{2}{\left(2 x \right)} - 1\right) \sin^{2}{\left(2 x \right)}}{4 \left(\cos{\left(8 x \right)} + 1\right)^{\frac{3}{2}}}$$
___ 2 / 1 \
\/ 2 *tan (x)*|-1 + ---------|
| 2 |
\ tan (2*x)/
-------------------------------------
3/2
2 / 2 \
/ 2 \ | 1 - tan (4*x)|
\1 + tan (x)/ *|1 + -------------|
| 2 |
\ 1 + tan (4*x)/
$$\frac{\sqrt{2} \left(-1 + \frac{1}{\tan^{2}{\left(2 x \right)}}\right) \tan^{2}{\left(x \right)}}{\left(\frac{1 - \tan^{2}{\left(4 x \right)}}{\tan^{2}{\left(4 x \right)} + 1} + 1\right)^{\frac{3}{2}} \left(\tan^{2}{\left(x \right)} + 1\right)^{2}}$$
___ / 2 \
\/ 2 *\1 - tan (2*x)/
-----------------------------
3/2
/ 1 \ 2
4*|1 + --------| *sec (2*x)
\ sec(8*x)/
$$\frac{\sqrt{2} \left(1 - \tan^{2}{\left(2 x \right)}\right)}{4 \left(1 + \frac{1}{\sec{\left(8 x \right)}}\right)^{\frac{3}{2}} \sec^{2}{\left(2 x \right)}}$$
/ 4 \
___ 2/pi \ | 4*sin (2*x)|
\/ 2 *sin |-- + 2*x|*|1 - -----------|
\2 / | 2 |
\ sin (4*x) /
--------------------------------------
3/2
/ /pi \\
4*|1 + sin|-- + 8*x||
\ \2 //
$$\frac{\sqrt{2} \left(- \frac{4 \sin^{4}{\left(2 x \right)}}{\sin^{2}{\left(4 x \right)}} + 1\right) \sin^{2}{\left(2 x + \frac{\pi}{2} \right)}}{4 \left(\sin{\left(8 x + \frac{\pi}{2} \right)} + 1\right)^{\frac{3}{2}}}$$
2
___ / 2 \ / 2 \
\/ 2 *\1 - tan (x)/ *\1 - tan (2*x)/
---------------------------------------
3/2
2 / 2 \
/ 2 \ | 1 - tan (4*x)|
4*\1 + tan (x)/ *|1 + -------------|
| 2 |
\ 1 + tan (4*x)/
$$\frac{\sqrt{2} \left(1 - \tan^{2}{\left(x \right)}\right)^{2} \left(1 - \tan^{2}{\left(2 x \right)}\right)}{4 \left(\frac{1 - \tan^{2}{\left(4 x \right)}}{\tan^{2}{\left(4 x \right)} + 1} + 1\right)^{\frac{3}{2}} \left(\tan^{2}{\left(x \right)} + 1\right)^{2}}$$
___ 2 / 1 \
\/ 2 *sin (2*x)*|-1 + ---------|
| 2 |
\ tan (2*x)/
--------------------------------
3/2
/ 1 \
4*|1 + --------|
\ sec(8*x)/
$$\frac{\sqrt{2} \left(-1 + \frac{1}{\tan^{2}{\left(2 x \right)}}\right) \sin^{2}{\left(2 x \right)}}{4 \left(1 + \frac{1}{\sec{\left(8 x \right)}}\right)^{\frac{3}{2}}}$$
___ 2 / 1 \
\/ 2 *sin (2*x)*|-1 + ---------|
| 2 |
\ tan (2*x)/
--------------------------------
3/2
4*(1 + cos(8*x))
$$\frac{\sqrt{2} \left(-1 + \frac{1}{\tan^{2}{\left(2 x \right)}}\right) \sin^{2}{\left(2 x \right)}}{4 \left(\cos{\left(8 x \right)} + 1\right)^{\frac{3}{2}}}$$
___ 4 2 / 1 \
\/ 2 *cos (x)*tan (x)*|-1 + ---------|
| 2 |
\ tan (2*x)/
--------------------------------------
3/2
/ 2 / 2 \\
\1 + cos (4*x)*\1 - tan (4*x)//
$$\frac{\sqrt{2} \left(-1 + \frac{1}{\tan^{2}{\left(2 x \right)}}\right) \cos^{4}{\left(x \right)} \tan^{2}{\left(x \right)}}{\left(\left(1 - \tan^{2}{\left(4 x \right)}\right) \cos^{2}{\left(4 x \right)} + 1\right)^{\frac{3}{2}}}$$
2
1 - tan (2*x)
---------------------------------------
3/2
/ 2\
|/ 2 \ |
|\1 - tan (2*x)/ | / 2 \
8*|----------------| *\1 + tan (2*x)/
| 2|
|/ 2 \ |
\\1 + tan (2*x)/ /
$$\frac{1 - \tan^{2}{\left(2 x \right)}}{8 \left(\frac{\left(1 - \tan^{2}{\left(2 x \right)}\right)^{2}}{\left(\tan^{2}{\left(2 x \right)} + 1\right)^{2}}\right)^{\frac{3}{2}} \left(\tan^{2}{\left(2 x \right)} + 1\right)}$$
2
-1 + cot (2*x)
----------------------------------------
3/2
/ 2\
|/ 2 \ |
|\-1 + cot (2*x)/ | / 2 \
8*|-----------------| *\1 + cot (2*x)/
| 2|
| / 2 \ |
\ \1 + cot (2*x)/ /
$$\frac{\cot^{2}{\left(2 x \right)} - 1}{8 \left(\frac{\left(\cot^{2}{\left(2 x \right)} - 1\right)^{2}}{\left(\cot^{2}{\left(2 x \right)} + 1\right)^{2}}\right)^{\frac{3}{2}} \left(\cot^{2}{\left(2 x \right)} + 1\right)}$$
___ 2 / 2 \
\/ 2 *cot (x)*\-1 + cot (2*x)/
--------------------------------------
3/2
2 / 2 \
/ 2 \ | -1 + cot (4*x)|
\1 + cot (x)/ *|1 + --------------|
| 2 |
\ 1 + cot (4*x) /
$$\frac{\sqrt{2} \left(\cot^{2}{\left(2 x \right)} - 1\right) \cot^{2}{\left(x \right)}}{\left(\frac{\cot^{2}{\left(4 x \right)} - 1}{\cot^{2}{\left(4 x \right)} + 1} + 1\right)^{\frac{3}{2}} \left(\cot^{2}{\left(x \right)} + 1\right)^{2}}$$
/ pi\
cot|2*x + --|
\ 4 /
--------------------------------------------------
3/2
/ 2/ pi\ \
| cot |2*x + --| |
| \ 4 / | / 2/ pi\\
32*|---------------------| *|1 + cot |2*x + --||
| 2| \ \ 4 //
|/ 2/ pi\\ |
||1 + cot |2*x + --|| |
\\ \ 4 // /
$$\frac{\cot{\left(2 x + \frac{\pi}{4} \right)}}{32 \left(\frac{\cot^{2}{\left(2 x + \frac{\pi}{4} \right)}}{\left(\cot^{2}{\left(2 x + \frac{\pi}{4} \right)} + 1\right)^{2}}\right)^{\frac{3}{2}} \left(\cot^{2}{\left(2 x + \frac{\pi}{4} \right)} + 1\right)}$$
cot(2*x + pi/4)/(32*(cot(2*x + pi/4)^2/(1 + cot(2*x + pi/4)^2)^2)^(3/2)*(1 + cot(2*x + pi/4)^2))