∫ sinmxcosnx wrt x eching

$$\int \sin m x \cos n x d x$$

Baholash

$$\left\{\begin{matrix}\frac{n\cos(x\left(m+n\right))-m\cos(x\left(m+n\right))-m\cos(x\left(m-n\right))-n\cos(x\left(m-n\right))}{2\left(m^{2}-n^{2}\right)}+С,&|m|\neq |n|\\\frac{\left(\cos(nx)\right)^{2}}{2n}+С,&n\neq 0\text{ and }m=-n\\С,&n=0\text{ and }m=0\\-\frac{\left(\cos(nx)\right)^{2}}{2n}+С,&n\neq 0\text{ and }m=n\end{matrix}\right,$$

x ga nisbatan hosilani topish

$$\left\{\begin{matrix}\frac{\sin(x\left(m+n\right))+\sin(x\left(m-n\right))}{2},&|m|\neq |n|\\-\frac{\sin(2nx)}{2},&m=-n\\\frac{\sin(2nx)}{2},&n\neq 0\text{ and }m=n\end{matrix}\right,$$