Step-by-step Solution

Solve the trigonometric integral $\int\cos\left(4x\right)\cos\left(6x\right)dx$

Go!
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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

$\frac{1}{2}\left(\frac{1}{10}\sin\left(10x\right)+\frac{1}{2}\sin\left(2x\right)\right)+C_0$