What is the int “cos2x”?

What is the integration of cos(2x)?

$$\begin{aligned}\mathrm{I}=\int \cos (2 \mathrm{x}) \mathrm{dx} \\\Rightarrow \text { Subtitute, } \mathrm{t} &=2 \mathrm{x} \\\frac{\mathrm{dt}}{\mathrm{dx}} &=2 \\\therefore \frac{\mathrm{dt}}{2} &=\mathrm{dx}\end{aligned}$$From equations 1, $2 \& 3$$$\begin{aligned}&I=\int \cos (t) \frac{d t}{2} \\&I=\frac{1}{2} \int \cos (t) d t \\&I=\frac{\sin (2 x)}{2}+\frac{C}{2} \\&I=\frac{\sin (2 x)}{2}+C^{\prime} \quad \text { Ans. }\end{aligned}$$

Author: Gaurav Kumar