/ 2 \
1 log\-1 + sin (x)/
- --------- - ----------------- + log(sin(x))
2 2
2*sin (x)
$$- \frac{1}{2} \log{\left (\sin^{2}{\left (x \right )} - 1 \right )} + \log{\left (\sin{\left (x \right )} \right )} - \frac{1}{2 \sin^{2}{\left (x \right )}}$$
-0.5/sin(x)^2 - 0.5*log(sin(x)^2 - 1) + log(sin(x))
Рациональный знаменатель
[src] 2 / 2 \ 2
-2 - 2*sin (x)*log\-1 + sin (x)/ + 4*sin (x)*log(sin(x))
--------------------------------------------------------
2
4*sin (x)
$$\frac{1}{4 \sin^{2}{\left (x \right )}} \left(- 2 \log{\left (\sin^{2}{\left (x \right )} - 1 \right )} \sin^{2}{\left (x \right )} + 4 \log{\left (\sin{\left (x \right )} \right )} \sin^{2}{\left (x \right )} - 2\right)$$
Объединение рациональных выражений
[src] 2 / / 2 \ \
-1 + sin (x)*\- log\-1 + sin (x)/ + 2*log(sin(x))/
--------------------------------------------------
2
2*sin (x)
$$\frac{1}{2 \sin^{2}{\left (x \right )}} \left(\left(- \log{\left (\sin^{2}{\left (x \right )} - 1 \right )} + 2 \log{\left (\sin{\left (x \right )} \right )}\right) \sin^{2}{\left (x \right )} - 1\right)$$
/ 2 \
1 log\-1 + sin (x)/
- --------- - ----------------- + log(sin(x))
2 2
2*sin (x)
$$- \frac{1}{2} \log{\left (\sin^{2}{\left (x \right )} - 1 \right )} + \log{\left (\sin{\left (x \right )} \right )} - \frac{1}{2 \sin^{2}{\left (x \right )}}$$
/ 1 cos(2*x)\
log|- - - --------|
1 \ 2 2 / cos(2*x)
- - - ------------------- + -------- + log(sin(x))
4 2 4
$$- \frac{1}{2} \log{\left (- \frac{1}{2} \cos{\left (2 x \right )} - \frac{1}{2} \right )} + \log{\left (\sin{\left (x \right )} \right )} + \frac{1}{4} \cos{\left (2 x \right )} - \frac{1}{4}$$
2 / 2 \
sin (x) log\-1 + sin (x)/
- ------- - ----------------- + log(sin(x))
2 2
$$- \frac{1}{2} \log{\left (\sin^{2}{\left (x \right )} - 1 \right )} + \log{\left (\sin{\left (x \right )} \right )} - \frac{1}{2} \sin^{2}{\left (x \right )}$$
2 / 2 \ 2
-1 - sin (x)*log\-1 + sin (x)/ + 2*sin (x)*log(sin(x))
------------------------------------------------------
2
2*sin (x)
$$\frac{1}{2 \sin^{2}{\left (x \right )}} \left(- \log{\left (\sin^{2}{\left (x \right )} - 1 \right )} \sin^{2}{\left (x \right )} + 2 \log{\left (\sin{\left (x \right )} \right )} \sin^{2}{\left (x \right )} - 1\right)$$
/ 2 \
1 log\-1 + sin (x)/
- --------- - ----------------- + log(sin(x))
2 2
2*sin (x)
$$- \frac{1}{2} \log{\left (\sin^{2}{\left (x \right )} - 1 \right )} + \log{\left (\sin{\left (x \right )} \right )} - \frac{1}{2 \sin^{2}{\left (x \right )}}$$
Тригонометрическая часть
[src] / 2 \
1 log\-cos (x)/
- --------- - ------------- + log(sin(x))
2 2
2*sin (x)
$$\log{\left (\sin{\left (x \right )} \right )} - \frac{1}{2} \log{\left (- \cos^{2}{\left (x \right )} \right )} - \frac{1}{2 \sin^{2}{\left (x \right )}}$$
2 / 2 \
sin (x) log\-1 + sin (x)/
- ------- - ----------------- + log(sin(x))
2 2
$$- \frac{1}{2} \log{\left (\sin^{2}{\left (x \right )} - 1 \right )} + \log{\left (\sin{\left (x \right )} \right )} - \frac{1}{2} \sin^{2}{\left (x \right )}$$