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

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

Answer

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

Step-by-step explanation

Problem

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

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

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

Unlock this step-by-step solution!

Answer

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

Main topic:

Integration by substitution

Used formulas:

5. See formulas

Time to solve it:

~ 0.55 seconds