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

The integral of xcos(3)x^2 is 1/4 cos(3)x^4+C

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integral of xcos(3)x^2

\int x cos (3) x^{2} d x

\frac{1}{4} cos (3) x^{4} + C

Solution steps

\int x cos (3) x^{2} d x

Take the constant out:

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

= cos (3) \cdot \int x x^{2} d x

Simplify

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

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

Apply the Power Rule

= cos (3) \frac{x ^{4}}{4}

Simplify

cos (3) \frac{x ^{4}}{4} : \frac{1}{4} cos (3) x^{4}

= \frac{1}{4} cos (3) x^{4}

Add a constant to the solution

= \frac{1}{4} cos (3) x^{4} + C

What is the integral of xcos(3)x^2 ?
The integral of xcos(3)x^2 is 1/4 cos(3)x^4+C