Integrate :
$sin (a x + b) cos (a x + b)$

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Solution

$sin (a x + b) cos (a x + b) \frac{1}{2} (2 sin (a x + b) cos (a x + b)) \frac{1}{2} {sin 2 a x + 2 b} I = \frac{1}{2} \int {sin 2 a x + 2 b} d x = \frac{1}{4 a} (- cos (2 a x)) + b x + C$

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