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

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

= 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

\frac{d}{d x} (5 x^{4} + 3 x^{2} - 9 x + 16)

f (x) = 7 e^{x} + x, (0, 7)

\int \frac{2 - v}{v ^{2} - 1} d v

f (x) = x - 2, g (x) = - x^{2} + x + 2

\int x^{2} x - 4 d x

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