Question

Solve: $\int x-{\sin }^{2}xdx$

Answer 1

$\int (x-{\sin }^{2}x)dx$

$=\int xdx-\int {\sin }^{2}xdx$

$=\frac{x^2}{2}-\int \frac{1}{2}-\frac{\cos 2x}{2}dx(\cos 2\theta =1-2{\sin }^2\theta )$

$\frac{x^2}{2}-\frac{x}{2}+\frac{\sin 2x}{4}+C$

$\therefore \int (x-{\sin }^{2}x)dx=\frac{x^2}{2}-\frac{x}{2}+\frac{\sin 2x}{4}+C$