Question

Integrate the function: sin(ax + b) cos(ax + b)

Answer 1

sin(ax + b) cos(ax + b) = $\frac{2 \sin (ax+b) \cos (ax+b)}{2}=\frac{\sin 2(ax+b)}{2}$

Let 2(ax + b) = t

∴ 2adx = dt

$\Rightarrow \int \frac{\sin 2(ax+b)}{2}dx = \frac{1}{2}\int \frac{\sin t dt}{2a}$

=$\frac{1}{4a}$ [-cost] + C

= -$\frac{1}{4a}$ cos2(ax + b) +C