Question

what is the integration of sin^2x ?

Answer 1

$$\begin{gathered} \mathrm{Let}\mathrm{I}=\int {\sin }^{2}xdx \\ =\int \left[\frac{1-\cos 2x}{2}\right]dx \\ =\frac{1}{2}\int \left(1-\cos 2x\right)dx \\ =\frac{1}{2}\left[x-\frac{\sin 2x}{2}\right]+\mathrm{C} \end{gathered}$$