Question

Find $\int \sin \left(ax+b\right)\cos \left(ax+b\right)dx$.

Answer 1

$\begin{array}{c}\int \frac{\sin \left(ax+\right)\cos \left(ax+b\right)\times 2}{2}dx\\ \frac{1}{2}\int \sin \left(2\left(ax+b\right)\right)dx\\ =\frac{-\cos \left(2\left(ax+b\right)\right)}{2\times 2a}+C\\ =\frac{-\cos \left(2ax+2b\right)}{4a}+C\end{array}$