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Step-by-step Solution

Trigonometric integral $\int\cos\left(5x\right)\cos\left(2x\right)dx$

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Answer

$\frac{1}{14}\sin\left(7x\right)+\frac{1}{6}\sin\left(3x\right)+C_0$

Step-by-step explanation

Problem to solve:

$\int\cos\left(5x\right)\cdot\cos\left(2x\right)dx$
1

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

$\int\frac{\cos\left(5x+2x\right)+\cos\left(5x-2x\right)}{2}dx$
2

Take the constant out of the integral

$\frac{1}{2}\int\left(\cos\left(5x+2x\right)+\cos\left(5x-2x\right)\right)dx$

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Answer

$\frac{1}{14}\sin\left(7x\right)+\frac{1}{6}\sin\left(3x\right)+C_0$
$\int\cos\left(5x\right)\cdot\cos\left(2x\right)dx$

Main topic:

Integration by substitution

Used formulas:

5. See formulas

Time to solve it:

~ 1.16 seconds