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Simplify $\sin\left(ax\right)\cos\left(ax\right)$ using the trigonometric identity: $\sin(2x)=2\sin(x)\cos(x)$
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$\int\frac{\sin\left(2ax\right)}{2}dx$
Learn how to solve problems step by step online. Solve the trigonometric integral int(sin(ax)cos(ax))dx. Simplify \sin\left(ax\right)\cos\left(ax\right) using the trigonometric identity: \sin(2x)=2\sin(x)\cos(x). Take the constant \frac{1}{2} out of the integral. Divide 1 by 2. We can solve the integral \int\sin\left(2ax\right)dx by applying integration by substitution method (also called U-Substitution). First, we must identify a section within the integral with a new variable (let's call it u), which when substituted makes the integral easier. We see that 2ax it's a good candidate for substitution. Let's define a variable u and assign it to the choosen part.