Question

Find the integrals of the functions.
$\int si{n}^2(2x+5)dx.$

Answer 1

$\int si{n}^2(2x+5)dx=\int \frac{1-cos2(2x+5)}{2}dx=\int \frac{1-cos(4x+10)}{2}dx(\therefore si{n}^{2}x=\frac{1-cos2x}{2})=\int \frac{1}{2}dx-\frac{1}{2}\int cos(4x+10)dx=\frac{1}{2}x-\frac{1}{2}\frac{sin(4x+10)}{4}+C[\because \int cos(ax+b)dx=\frac{sin(ax+b)}{a}]=\frac{1}{2}x-\frac{sin(4x+10)}{8}+C$