# Step-by-step Solution

## Integral of cos(4*x)cos(6*x)

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### Videos

$\frac{1}{20}\sin\left(10x\right)-\frac{1}{4}\sin\left(-2x\right)+C_0$

## Step-by-step explanation

Problem to solve:

$\int\cos\left(4x\right)\cdot\cos\left(6x\right)dx$
1

Applying the rule of the product of two cosines $\cos\left(a\right)\cdot\cos\left(b\right)=\frac{\cos\left(a+b\right)+\cos\left(a-b\right)}{2}$

$\int\frac{\cos\left(4x+6x\right)+\cos\left(4x-6x\right)}{2}dx$
2

Take the constant out of the integral

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

$\frac{1}{20}\sin\left(10x\right)-\frac{1}{4}\sin\left(-2x\right)+C_0$
$\int\cos\left(4x\right)\cdot\cos\left(6x\right)dx$

### Main topic:

Integration by substitution

~ 1.1 seconds

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