Integrate the functions in Exercises: (ax+b) (ax+b) - Vidyadip

Question

Integrate the functions in Exercises:
$\sin(\text{ax+b})\cos(\text{ax+b})$

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Answer

$\int\sin(\text{ax+b})\cos(\text{ax+b})\text{ dx}$
$=\frac{1}{2}\int2\sin(\text{ax+b})\cos(\text{ax+b})\text { dx} $
$=\frac{1}{2}\int\sin2(\text{ax+b})\text{ dx} $
$=\frac{1}{2}\int\sin(2\text{ax+2b})\text{ dx} $
$=\frac{1}{2}\frac{[-\cos(2\text{ax}+2\text{b})]}{2\text{a}\rightarrow\text{Coeff. of x}}+\text{c} $
$=\frac{-1}{4\text{a}}\cos2(\text{ax+b})+\text{c} $

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