What is the integral of xcos(3pi)x^2 ?

The integral of xcos(3pi)x^2 is -(x^4)/4+C

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integral of xcos(3pi)x^2

\int x cos (3 π) x^{2} d x

- \frac{x ^{4}}{4} + C

Solution steps

\int x cos (3 π) x^{2} d x

Take the constant out:

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

= cos (3 π) \cdot \int x x^{2} d x

cos (3 π) = - 1

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

Simplify

x x^{2} : x^{3}

= (- 1) \cdot \int x^{3} d x

Apply the Power Rule

: \frac{x ^{4}}{4}

= (- 1) \frac{x ^{4}}{4}

Simplify

= - \frac{x ^{4}}{4}

Add a constant to the solution

= - \frac{x ^{4}}{4} + C

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What is the integral of xcos(3pi)x^2 ?
The integral of xcos(3pi)x^2 is -(x^4)/4+C