1 1
------- - ------
___ 2 / ___ \
2*\/ x 1 + x \2*\/ x + 2*acot(x)/*sin(x)
---------------- + ----------------------------
2 3
cos (x) cos (x)
$$\frac{\sin{\left (x \right )}}{\cos^{3}{\left (x \right )}} \left(2 \sqrt{x} + 2 \operatorname{acot}{\left (x \right )}\right) + \frac{- \frac{1}{x^{2} + 1} + \frac{1}{2 \sqrt{x}}}{\cos^{2}{\left (x \right )}}$$
(-1/(1.0 + x^2) + 0.5*x^(-0.5))/cos(x)^2 + 2.0*(x^0.5 + acot(x))*sin(x)/cos(x)^3
Рациональный знаменатель
[src] ___ 3 5/2 3 3 3/2 2 7/2 2 2 3 2
\/ x *cos (x) + x *cos (x) - 2*x*cos (x) + 4*x *cos (x)*sin(x) + 4*x *cos (x)*sin(x) + 4*x*cos (x)*acot(x)*sin(x) + 4*x *cos (x)*acot(x)*sin(x)
-----------------------------------------------------------------------------------------------------------------------------------------------------
/ 2\ 5
2*x*\1 + x /*cos (x)
$$\frac{1}{2 x \left(x^{2} + 1\right) \cos^{5}{\left (x \right )}} \left(4 x^{\frac{7}{2}} \sin{\left (x \right )} \cos^{2}{\left (x \right )} + x^{\frac{5}{2}} \cos^{3}{\left (x \right )} + 4 x^{\frac{3}{2}} \sin{\left (x \right )} \cos^{2}{\left (x \right )} + \sqrt{x} \cos^{3}{\left (x \right )} + 4 x^{3} \sin{\left (x \right )} \cos^{2}{\left (x \right )} \operatorname{acot}{\left (x \right )} + 4 x \sin{\left (x \right )} \cos^{2}{\left (x \right )} \operatorname{acot}{\left (x \right )} - 2 x \cos^{3}{\left (x \right )}\right)$$
Объединение рациональных выражений
[src]/ 2 ___\ ___ / 2\ / ___ \
\1 + x - 2*\/ x /*cos(x) + 4*\/ x *\1 + x /*\\/ x + acot(x)/*sin(x)
---------------------------------------------------------------------
___ / 2\ 3
2*\/ x *\1 + x /*cos (x)
$$\frac{1}{2 \sqrt{x} \left(x^{2} + 1\right) \cos^{3}{\left (x \right )}} \left(4 \sqrt{x} \left(\sqrt{x} + \operatorname{acot}{\left (x \right )}\right) \left(x^{2} + 1\right) \sin{\left (x \right )} + \left(- 2 \sqrt{x} + x^{2} + 1\right) \cos{\left (x \right )}\right)$$
/ 2 ___\ ___ / 2\ / ___ \
\1 + x - 2*\/ x /*cos(x) + 4*\/ x *\1 + x /*\\/ x + acot(x)/*sin(x)
---------------------------------------------------------------------
___ / 2\ 3
2*\/ x *\1 + x /*cos (x)
$$\frac{1}{2 \sqrt{x} \left(x^{2} + 1\right) \cos^{3}{\left (x \right )}} \left(4 \sqrt{x} \left(\sqrt{x} + \operatorname{acot}{\left (x \right )}\right) \left(x^{2} + 1\right) \sin{\left (x \right )} + \left(- 2 \sqrt{x} + x^{2} + 1\right) \cos{\left (x \right )}\right)$$
/ 2 \
2 | 1 2 x | 2 / ___ \
sec (x)*|---------------- - -------- + ----------------| + sec (x)*\2*\/ x + 2*acot(x)/*tan(x)
| ___ 5/2 2 ___ 5/2|
\2*\/ x + 2*x 2 + 2*x 2*\/ x + 2*x /
$$\left(2 \sqrt{x} + 2 \operatorname{acot}{\left (x \right )}\right) \tan{\left (x \right )} \sec^{2}{\left (x \right )} + \left(\frac{x^{2}}{2 x^{\frac{5}{2}} + 2 \sqrt{x}} + \frac{1}{2 x^{\frac{5}{2}} + 2 \sqrt{x}} - \frac{2}{2 x^{2} + 2}\right) \sec^{2}{\left (x \right )}$$
2 ___ 3 ___ 5/2
x *cos(x) - 2*\/ x *cos(x) + 4*x*sin(x) + 4*x *sin(x) + 4*\/ x *acot(x)*sin(x) + 4*x *acot(x)*sin(x) + cos(x)
---------------------------------------------------------------------------------------------------------------
___ / 2\ 3
2*\/ x *\1 + x /*cos (x)
$$\frac{1}{2 \sqrt{x} \left(x^{2} + 1\right) \cos^{3}{\left (x \right )}} \left(4 x^{\frac{5}{2}} \sin{\left (x \right )} \operatorname{acot}{\left (x \right )} + 4 \sqrt{x} \sin{\left (x \right )} \operatorname{acot}{\left (x \right )} - 2 \sqrt{x} \cos{\left (x \right )} + 4 x^{3} \sin{\left (x \right )} + x^{2} \cos{\left (x \right )} + 4 x \sin{\left (x \right )} + \cos{\left (x \right )}\right)$$
2 ___ 3 ___ 5/2
x *cos(x) - 2*\/ x *cos(x) + 4*x*sin(x) + 4*x *sin(x) + 4*\/ x *acot(x)*sin(x) + 4*x *acot(x)*sin(x) + cos(x)
---------------------------------------------------------------------------------------------------------------
___ 3 5/2 3
2*\/ x *cos (x) + 2*x *cos (x)
$$\frac{1}{2 x^{\frac{5}{2}} \cos^{3}{\left (x \right )} + 2 \sqrt{x} \cos^{3}{\left (x \right )}} \left(4 x^{\frac{5}{2}} \sin{\left (x \right )} \operatorname{acot}{\left (x \right )} + 4 \sqrt{x} \sin{\left (x \right )} \operatorname{acot}{\left (x \right )} - 2 \sqrt{x} \cos{\left (x \right )} + 4 x^{3} \sin{\left (x \right )} + x^{2} \cos{\left (x \right )} + 4 x \sin{\left (x \right )} + \cos{\left (x \right )}\right)$$
Тригонометрическая часть
[src] 1 1
------- - ------
___ 2 / ___ \
2*\/ x 1 + x \2*\/ x + 2*acot(x)/*sin(x)
---------------- + ----------------------------
2 3
cos (x) cos (x)
$$\frac{\sin{\left (x \right )}}{\cos^{3}{\left (x \right )}} \left(2 \sqrt{x} + 2 \operatorname{acot}{\left (x \right )}\right) + \frac{- \frac{1}{x^{2} + 1} + \frac{1}{2 \sqrt{x}}}{\cos^{2}{\left (x \right )}}$$
1 1
------- - ------
___ 2 / ___ \
2*\/ x 1 + x \2*\/ x + 2*acot(x)/*sin(x)
---------------- + ----------------------------
2 3
cos (x) cos (x)
$$\frac{\sin{\left (x \right )}}{\cos^{3}{\left (x \right )}} \left(2 \sqrt{x} + 2 \operatorname{acot}{\left (x \right )}\right) + \frac{- \frac{1}{x^{2} + 1} + \frac{1}{2 \sqrt{x}}}{\cos^{2}{\left (x \right )}}$$