Final Answer
$-\frac{1}{12}\cos\left(6x\right)-\frac{1}{4}\cos\left(2x\right)+C_0$
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Step-by-step Solution
Problem to solve:
$\int\sin\left(4x\right)\cos\left(2x\right)dx$
Specify the solving method
1
Rewrite the trigonometric expression $\sin\left(4x\right)\cos\left(2x\right)$ inside the integral
$\int\frac{\sin\left(6x\right)+\sin\left(2x\right)}{2}dx$
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. Take the constant \frac{1}{2} out of the integral. Simplify the expression inside the integral. The integral \frac{1}{2}\int\sin\left(6x\right)dx results in: -\frac{1}{12}\cos\left(6x\right).
Final Answer
$-\frac{1}{12}\cos\left(6x\right)-\frac{1}{4}\cos\left(2x\right)+C_0$