Parte trigonométrica
[src]
tan(x) 1 4/5 2 4
------ - --------- - x *csc (x) + --------------
2 2 5 ___
x x*cos (x) 5*\/ x *tan(x)
$$- x^{\frac{4}{5}} \csc^{2}{\left(x \right)} - \frac{1}{x \cos^{2}{\left(x \right)}} + \frac{\tan{\left(x \right)}}{x^{2}} + \frac{4}{5 \sqrt[5]{x} \tan{\left(x \right)}}$$
2 4/5
tan(x) sec (x) x 4
------ - ------- - ------- + --------------
2 x 2 5 ___
x sin (x) 5*\/ x *tan(x)
$$- \frac{x^{\frac{4}{5}}}{\sin^{2}{\left(x \right)}} - \frac{\sec^{2}{\left(x \right)}}{x} + \frac{\tan{\left(x \right)}}{x^{2}} + \frac{4}{5 \sqrt[5]{x} \tan{\left(x \right)}}$$
/ pi\
2 4*sec|x - --|
sec (x) 4/5 2/ pi\ sec(x) \ 2 /
- ------- - x *sec |x - --| + -------------- + --------------
x \ 2 / 2 / pi\ 5 ___
x *sec|x - --| 5*\/ x *sec(x)
\ 2 /
$$- x^{\frac{4}{5}} \sec^{2}{\left(x - \frac{\pi}{2} \right)} - \frac{\sec^{2}{\left(x \right)}}{x} + \frac{\sec{\left(x \right)}}{x^{2} \sec{\left(x - \frac{\pi}{2} \right)}} + \frac{4 \sec{\left(x - \frac{\pi}{2} \right)}}{5 \sqrt[5]{x} \sec{\left(x \right)}}$$
2/pi \
csc |-- - x|
\2 /
1 + ------------ /pi \
/ 2 \ 2 csc|-- - x|
4/5 | csc (x) | csc (x) \2 / 4*csc(x)
x *|-1 - ------------| - ---------------- + ----------- + -------------------
| 2/pi \| x 2 5 ___ /pi \
| csc |-- - x|| x *csc(x) 5*\/ x *csc|-- - x|
\ \2 // \2 /
$$x^{\frac{4}{5}} \left(- \frac{\csc^{2}{\left(x \right)}}{\csc^{2}{\left(- x + \frac{\pi}{2} \right)}} - 1\right) - \frac{1 + \frac{\csc^{2}{\left(- x + \frac{\pi}{2} \right)}}{\csc^{2}{\left(x \right)}}}{x} + \frac{\csc{\left(- x + \frac{\pi}{2} \right)}}{x^{2} \csc{\left(x \right)}} + \frac{4 \csc{\left(x \right)}}{5 \sqrt[5]{x} \csc{\left(- x + \frac{\pi}{2} \right)}}$$
2
sec (x)
1 + ------------
/ 2/ pi\\ 2/ pi\ / pi\
| sec |x - --|| sec |x - --| 4*sec|x - --|
4/5 | \ 2 /| \ 2 / sec(x) \ 2 /
x *|-1 - ------------| - ---------------- + -------------- + --------------
| 2 | x 2 / pi\ 5 ___
\ sec (x) / x *sec|x - --| 5*\/ x *sec(x)
\ 2 /
$$x^{\frac{4}{5}} \left(-1 - \frac{\sec^{2}{\left(x - \frac{\pi}{2} \right)}}{\sec^{2}{\left(x \right)}}\right) - \frac{\frac{\sec^{2}{\left(x \right)}}{\sec^{2}{\left(x - \frac{\pi}{2} \right)}} + 1}{x} + \frac{\sec{\left(x \right)}}{x^{2} \sec{\left(x - \frac{\pi}{2} \right)}} + \frac{4 \sec{\left(x - \frac{\pi}{2} \right)}}{5 \sqrt[5]{x} \sec{\left(x \right)}}$$
4/5
tan(x) 2 2*x 4*cot(x)
------ - ---------------- - ------------ + --------
2 x*(1 + cos(2*x)) 1 - cos(2*x) 5 ___
x 5*\/ x
$$- \frac{2 x^{\frac{4}{5}}}{1 - \cos{\left(2 x \right)}} - \frac{2}{x \left(\cos{\left(2 x \right)} + 1\right)} + \frac{\tan{\left(x \right)}}{x^{2}} + \frac{4 \cot{\left(x \right)}}{5 \sqrt[5]{x}}$$
2/pi \ /pi \
csc |-- - x| csc|-- - x|
\2 / 4/5 2 \2 / 4*csc(x)
- ------------ - x *csc (x) + ----------- + -------------------
x 2 5 ___ /pi \
x *csc(x) 5*\/ x *csc|-- - x|
\2 /
$$- x^{\frac{4}{5}} \csc^{2}{\left(x \right)} - \frac{\csc^{2}{\left(- x + \frac{\pi}{2} \right)}}{x} + \frac{\csc{\left(- x + \frac{\pi}{2} \right)}}{x^{2} \csc{\left(x \right)}} + \frac{4 \csc{\left(x \right)}}{5 \sqrt[5]{x} \csc{\left(- x + \frac{\pi}{2} \right)}}$$
2 2
/ 2/x\\ 4/5 / 2/x\\
|1 + cot |-|| x *|1 + cot |-||
1 4*cot(x) \ \2// \ \2//
--------- + -------- - ----------------- - -------------------
2 5 ___ 2 2/x\
x *cot(x) 5*\/ x / 2/x\\ 4*cot |-|
x*|-1 + cot |-|| \2/
\ \2//
$$- \frac{x^{\frac{4}{5}} \left(\cot^{2}{\left(\frac{x}{2} \right)} + 1\right)^{2}}{4 \cot^{2}{\left(\frac{x}{2} \right)}} - \frac{\left(\cot^{2}{\left(\frac{x}{2} \right)} + 1\right)^{2}}{x \left(\cot^{2}{\left(\frac{x}{2} \right)} - 1\right)^{2}} + \frac{1}{x^{2} \cot{\left(x \right)}} + \frac{4 \cot{\left(x \right)}}{5 \sqrt[5]{x}}$$
4/5
tan(x) 1 x 1
------ - --------- - ------- + 4*-------*cot(x)
2 2 2 5 ___
x x*cos (x) sin (x) 5*\/ x
$$4 \frac{1}{5 \sqrt[5]{x}} \cot{\left(x \right)} - \frac{x^{\frac{4}{5}}}{\sin^{2}{\left(x \right)}} - \frac{1}{x \cos^{2}{\left(x \right)}} + \frac{\tan{\left(x \right)}}{x^{2}}$$
2
sin (x)
1 + -------
/ 2 \ 2
4/5 | cos (x)| cos (x) sin(x) 4*cos(x)
x *|-1 - -------| - ----------- + --------- + --------------
| 2 | x 2 5 ___
\ sin (x)/ x *cos(x) 5*\/ x *sin(x)
$$x^{\frac{4}{5}} \left(-1 - \frac{\cos^{2}{\left(x \right)}}{\sin^{2}{\left(x \right)}}\right) - \frac{\frac{\sin^{2}{\left(x \right)}}{\cos^{2}{\left(x \right)}} + 1}{x} + \frac{\sin{\left(x \right)}}{x^{2} \cos{\left(x \right)}} + \frac{4 \cos{\left(x \right)}}{5 \sqrt[5]{x} \sin{\left(x \right)}}$$
/ pi\
4/5 cos|x - --|
1 x \ 2 / 4*cos(x)
- --------- - ------------ + ----------- + -------------------
2 2/ pi\ 2 5 ___ / pi\
x*cos (x) cos |x - --| x *cos(x) 5*\/ x *cos|x - --|
\ 2 / \ 2 /
$$- \frac{x^{\frac{4}{5}}}{\cos^{2}{\left(x - \frac{\pi}{2} \right)}} - \frac{1}{x \cos^{2}{\left(x \right)}} + \frac{\cos{\left(x - \frac{\pi}{2} \right)}}{x^{2} \cos{\left(x \right)}} + \frac{4 \cos{\left(x \right)}}{5 \sqrt[5]{x} \cos{\left(x - \frac{\pi}{2} \right)}}$$
4/5
tan(x) 2 2*x 4
------ - ---------------- - ------------ + --------------
2 x*(1 + cos(2*x)) 1 - cos(2*x) 5 ___
x 5*\/ x *tan(x)
$$- \frac{2 x^{\frac{4}{5}}}{1 - \cos{\left(2 x \right)}} - \frac{2}{x \left(\cos{\left(2 x \right)} + 1\right)} + \frac{\tan{\left(x \right)}}{x^{2}} + \frac{4}{5 \sqrt[5]{x} \tan{\left(x \right)}}$$
2/ pi\
cos |x - --|
\ 2 /
1 + ------------ / pi\
/ 2 \ 2 cos|x - --|
4/5 | cos (x) | cos (x) \ 2 / 4*cos(x)
x *|-1 - ------------| - ---------------- + ----------- + -------------------
| 2/ pi\| x 2 5 ___ / pi\
| cos |x - --|| x *cos(x) 5*\/ x *cos|x - --|
\ \ 2 // \ 2 /
$$x^{\frac{4}{5}} \left(- \frac{\cos^{2}{\left(x \right)}}{\cos^{2}{\left(x - \frac{\pi}{2} \right)}} - 1\right) - \frac{1 + \frac{\cos^{2}{\left(x - \frac{\pi}{2} \right)}}{\cos^{2}{\left(x \right)}}}{x} + \frac{\cos{\left(x - \frac{\pi}{2} \right)}}{x^{2} \cos{\left(x \right)}} + \frac{4 \cos{\left(x \right)}}{5 \sqrt[5]{x} \cos{\left(x - \frac{\pi}{2} \right)}}$$
4/5 2
1 x 2*sin (x) 2*sin(2*x)
- -------------- - ------- + ----------- + ---------------
2/ pi\ 2 2 5 ___ 2
x*sin |x + --| sin (x) x *sin(2*x) 5*\/ x *sin (x)
\ 2 /
$$- \frac{x^{\frac{4}{5}}}{\sin^{2}{\left(x \right)}} - \frac{1}{x \sin^{2}{\left(x + \frac{\pi}{2} \right)}} + \frac{2 \sin^{2}{\left(x \right)}}{x^{2} \sin{\left(2 x \right)}} + \frac{2 \sin{\left(2 x \right)}}{5 \sqrt[5]{x} \sin^{2}{\left(x \right)}}$$
2
sec (x)
1 + -------
/ 2 \ 2
4/5 | csc (x)| csc (x) sec(x) 4*csc(x)
x *|-1 - -------| - ----------- + --------- + --------------
| 2 | x 2 5 ___
\ sec (x)/ x *csc(x) 5*\/ x *sec(x)
$$x^{\frac{4}{5}} \left(- \frac{\csc^{2}{\left(x \right)}}{\sec^{2}{\left(x \right)}} - 1\right) - \frac{1 + \frac{\sec^{2}{\left(x \right)}}{\csc^{2}{\left(x \right)}}}{x} + \frac{\sec{\left(x \right)}}{x^{2} \csc{\left(x \right)}} + \frac{4 \csc{\left(x \right)}}{5 \sqrt[5]{x} \sec{\left(x \right)}}$$
4/5
tan(x) 1 x 4
------ - --------- - ------- + --------------
2 2 2 5 ___
x x*cos (x) sin (x) 5*\/ x *tan(x)
$$- \frac{x^{\frac{4}{5}}}{\sin^{2}{\left(x \right)}} - \frac{1}{x \cos^{2}{\left(x \right)}} + \frac{\tan{\left(x \right)}}{x^{2}} + \frac{4}{5 \sqrt[5]{x} \tan{\left(x \right)}}$$
4/5
tan(x) 1 x 4*cot(x)
------ - --------- - ------- + --------
2 2 2 5 ___
x x*cos (x) sin (x) 5*\/ x
$$- \frac{x^{\frac{4}{5}}}{\sin^{2}{\left(x \right)}} - \frac{1}{x \cos^{2}{\left(x \right)}} + \frac{\tan{\left(x \right)}}{x^{2}} + \frac{4 \cot{\left(x \right)}}{5 \sqrt[5]{x}}$$
4
4*sin (x)
1 + ---------
/ 2 \ 2 2
4/5 | sin (2*x)| sin (2*x) 2*sin (x) 2*sin(2*x)
x *|-1 - ---------| - ------------- + ----------- + ---------------
| 4 | x 2 5 ___ 2
\ 4*sin (x)/ x *sin(2*x) 5*\/ x *sin (x)
$$x^{\frac{4}{5}} \left(-1 - \frac{\sin^{2}{\left(2 x \right)}}{4 \sin^{4}{\left(x \right)}}\right) - \frac{\frac{4 \sin^{4}{\left(x \right)}}{\sin^{2}{\left(2 x \right)}} + 1}{x} + \frac{2 \sin^{2}{\left(x \right)}}{x^{2} \sin{\left(2 x \right)}} + \frac{2 \sin{\left(2 x \right)}}{5 \sqrt[5]{x} \sin^{2}{\left(x \right)}}$$
2 2
/ 2/x\\ 4/5 / 2/x\\
|1 + tan |-|| x *|1 + tan |-||
tan(x) 4 \ \2// \ \2//
------ + -------------- - ---------------- - -------------------
2 5 ___ 2 2/x\
x 5*\/ x *tan(x) / 2/x\\ 4*tan |-|
x*|1 - tan |-|| \2/
\ \2//
$$- \frac{x^{\frac{4}{5}} \left(\tan^{2}{\left(\frac{x}{2} \right)} + 1\right)^{2}}{4 \tan^{2}{\left(\frac{x}{2} \right)}} - \frac{\left(\tan^{2}{\left(\frac{x}{2} \right)} + 1\right)^{2}}{x \left(1 - \tan^{2}{\left(\frac{x}{2} \right)}\right)^{2}} + \frac{\tan{\left(x \right)}}{x^{2}} + \frac{4}{5 \sqrt[5]{x} \tan{\left(x \right)}}$$
1
1 + -------
2
1 4/5 / 2 \ cot (x) 4*cot(x)
--------- + x *\-1 - cot (x)/ - ----------- + --------
2 x 5 ___
x *cot(x) 5*\/ x
$$x^{\frac{4}{5}} \left(- \cot^{2}{\left(x \right)} - 1\right) - \frac{1 + \frac{1}{\cot^{2}{\left(x \right)}}}{x} + \frac{1}{x^{2} \cot{\left(x \right)}} + \frac{4 \cot{\left(x \right)}}{5 \sqrt[5]{x}}$$
2
tan(x) 4/5 / 1 \ 1 + tan (x) 4
------ + x *|-1 - -------| - ----------- + --------------
2 | 2 | x 5 ___
x \ tan (x)/ 5*\/ x *tan(x)
$$x^{\frac{4}{5}} \left(-1 - \frac{1}{\tan^{2}{\left(x \right)}}\right) - \frac{\tan^{2}{\left(x \right)} + 1}{x} + \frac{\tan{\left(x \right)}}{x^{2}} + \frac{4}{5 \sqrt[5]{x} \tan{\left(x \right)}}$$
tan(x)/x^2 + x^(4/5)*(-1 - 1/tan(x)^2) - (1 + tan(x)^2)/x + 4/(5*x^(1/5)*tan(x))