Question

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

Answer 1

Answer:

Step-by-step explanation:

$Concept:\\\\1.If \int{f(x)}\:dx=g(x)+c, then \int{f(ax+b)}\;dx=\frac{1}{a}g(ax+b)+c\\\\2.sin2A=2.sinA.cosA$

$Now,\\\\\int{sin(ax+b).cos(ax+b)}\:dx\\\\=\frac{1}{2}\int{2.sin(ax+b).cos(ax+b)}\:dx\\\\=\frac{1}{2}\int{sin2(ax+b)}\:dx\\\\=\frac{1}{2}\int{sin(2ax+2b)}\:dx\\\\=\frac{1}{2}\frac{(-cos(2ax+2b))}{2a}+c\\\\=\frac{-1}{4a}cos2(ax+b)+c$