Solve the trigonometric integral $\int\sin\left(ax\right)\cos\left(ax\right)dx$

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$\int\frac{1}{2}\sin\left(2ax\right)dx$

Learn how to solve trigonometric integrals problems step by step online. Solve the trigonometric integral int(sin(ax)cos(ax))dx. Simplify \sin\left(ax\right)\cos\left(ax\right) into \frac{1}{2}\sin\left(2ax\right) by applying trigonometric identities. The integral of a function times a constant (\frac{1}{2}) is equal to the constant times the integral of the function. 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. Now, in order to rewrite dx in terms of du, we need to find the derivative of u. We need to calculate du, we can do that by deriving the equation above.