What is the integral of cos(pi)xcos(4pi)x ?

The integral of cos(pi)xcos(4pi)x is -(x^3)/3+C

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integral of cos(pi)xcos(4pi)x

\int cos (π) x cos (4 π) x d x

- \frac{x ^{3}}{3} + C

Solution steps

\int cos (π) x cos (4 π) x d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= cos (π) cos (4 π) \cdot \int xx d x

cos (π) cos (4 π) = - 1

= (- 1) \cdot \int xx d x

Simplify

xx : x^{2}

= (- 1) \cdot \int x^{2} d x

Apply the Power Rule

: \frac{x ^{3}}{3}

= (- 1) \frac{x ^{3}}{3}

Simplify

= - \frac{x ^{3}}{3}

Add a constant to the solution

= - \frac{x ^{3}}{3} + C

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What is the integral of cos(pi)xcos(4pi)x ?
The integral of cos(pi)xcos(4pi)x is -(x^3)/3+C