Question

Evaluate $\int {\sin }^2(2x+5)dx$.

Answer 1

$I=\int {\sin }^2(2x+5)dx$

$I=\int \frac{1-\cos 2(2x-5)}{2}dx$ .......... $(\because$ $1-cos2A=2si{n}^{2}A)$

$I=\frac{1}{2}\int 1-\cos (4x+10)dx$

$I=\frac{1}{2}[x-\frac{\sin (4x+10)}{4}+C]$

$I=\frac{x}{2}-\frac{1}{8}\sin (4x+10)+C$