# Step-by-step Solution

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## Step-by-step Solution

Problem to solve:

$\int\sin\left(4x\right)\cdot\cos\left(2x\right)dx$

Solving method

Learn how to solve problems step by step online.

$\int\frac{\sin\left(6x\right)+\sin\left(2x\right)}{2}dx$

Learn how to solve problems step by step online. Solve the trigonometric integral int(sin(4x)cos(2x))dx. Rewrite the trigonometric expression \sin\left(4x\right)\cos\left(2x\right) inside the integral. The integral \frac{1}{2}\int\sin\left(6x\right)dx results in: -\frac{1}{12}\cos\left(6x\right). The integral \frac{1}{2}\int\sin\left(2x\right)dx results in: -\frac{1}{4}\cos\left(2x\right). Gather the results of all integrals.

$-\frac{1}{12}\cos\left(6x\right)-\frac{1}{4}\cos\left(2x\right)+C_0$