Question

Evaluate : $\int \cos 2xdx.$

Answer 1

$\begin{array}{c}I={\int }^{}\cos \left(2x\right)dx.....\left(1\right)\\ \Rightarrow subtitute,t=2x.....\left(2\right)\\ \frac{dt}{dx}=2\\ \therefore \frac{dt}{2}=dx.....\left(3\right)\\ fromequation1,2\&3\\ I={\int }^{}\cos \left(t\right)\frac{dt}{2}\\ I=\frac{1}{2}{\int }^{}\cos \left(t\right)dt\\ I=\frac{\sin \left(2x\right)}{2}+\frac{C}{2}\\ I=\frac{\sin \left(2x\right)}{2}+C\end{array}$