The Integral of $\int \sin(ax) \cos(ax) dx$

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What is the integral of:$$I=\int \sin(ax) \cos(ax) dx$$

My approach is down below. I have attempted the problem and posted it as an answer. I did the problem using trigonometric substitution.$$u=ax$$$$\frac{du}a=dx$$$$\frac{1}a\int\sin u \cos u \ du$$$$g=\sin u$$$$dg = \cos u \ du$$ $$\frac{1}a\int g\ dg$$$$I=\frac{1}a\frac{\sin^2ax}{2}+C$$

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2 Answers

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$$\sin(ax) \cos(ax)=\frac{1}{2}\sin(2ax)$$

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$$u=ax$$$$\frac{du}a=dx$$$$\frac{1}a\int\sin u \cos u \ du$$$$g=\sin u$$$$dg = \cos u \ du$$ $$\frac{1}a\int g\ dg$$$$I=\frac{1}a\frac{\sin^2ax}{2}+C$$

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