Integrate the following function: $sin (a x + b) cos (a x + b)$

\frac{cos (2 a x + 2 b)}{4 a} + c

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\frac{sin (2 a x + 2 b)}{4 a} + c

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\frac{- cos (2 a x + 2 b)}{4 a} + c

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\frac{- sin (2 a x + 2 b)}{4 a} + c

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Solution

The correct option is B $\frac{- cos (2 a x + 2 b)}{4 a} + c$

$\int sin (a x + b) cos (a x + b) d x$

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

$= \frac{1}{2} \int sin (2 a x + 2 b) d x$

$= - \frac{1}{2} \times \frac{cos (2 a x + 2 b)}{2 a} + c$

$= \frac{- cos (2 a x + 2 b)}{4 a} + c$

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α

β

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[α] + [β]

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