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Q5  Integrate the functions  \sin ( ax + b ) \cos ( ax + b )

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Given to integrate \sin ( ax + b ) \cos ( ax + b ) function,

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

Let us assume 2(ax+b) = t

we get, 2adx =dt

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

= \frac{1}{4a}[-cos t] +C

Now, by back substituting the value of t,

= \frac{-1}{4a}[cos 2(ax+b)] +C                                                     

Posted by

Divya Prakash Singh

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