Final Answer
$\frac{1}{2}\left(\frac{1}{10}\sin\left(10x\right)+\frac{1}{2}\sin\left(2x\right)\right)+C_0$
Step-by-step solution
Problem to solve:
$\int\cos\left(4x\right)\cdot\cos\left(6x\right)dx$
Solving method
1
Reduce $\cos\left(4x\right)\cos\left(6x\right)$ by applying trigonometric identities
$\int\frac{\cos\left(10x\right)+\cos\left(2x\right)}{2}dx$
2
As the integral that we are solving is an indefinite integral, when we finish integrating we must add the constant of integration $C$
$\frac{1}{2}\left(\frac{1}{10}\sin\left(10x\right)+\frac{1}{2}\sin\left(2x\right)\right)+C_0$
Final Answer
$\frac{1}{2}\left(\frac{1}{10}\sin\left(10x\right)+\frac{1}{2}\sin\left(2x\right)\right)+C_0$