What is the integral of xcos(5)x^2 ?

The integral of xcos(5)x^2 is 1/4 cos(5)x^4+C

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integral of xcos(5)x^2

\int x cos (5) x^{2} d x

\frac{1}{4} cos (5) x^{4} + C

Solution steps

\int x cos (5) x^{2} d x

Take the constant out:

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

= cos (5) \cdot \int x x^{2} d x

Simplify

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

= cos (5) \cdot \int x^{3} d x

Apply the Power Rule

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

= cos (5) \frac{x ^{4}}{4}

Simplify

cos (5) \frac{x ^{4}}{4} : \frac{1}{4} cos (5) x^{4}

= \frac{1}{4} cos (5) x^{4}

Add a constant to the solution

= \frac{1}{4} cos (5) x^{4} + C

\int \frac{4 x}{x ^{2} + 9} d x

y = 2 x sin (x) + x^{2} e^{x}

\frac{d}{d x} (- 2 x^{2} - 5 x + 2)

\int \frac{1}{x ^{2} - 81} d x

y^{^{'}} = - \frac{3 y}{t} - 2 - t^{- 4}, y (1) = 4

What is the integral of xcos(5)x^2 ?
The integral of xcos(5)x^2 is 1/4 cos(5)x^4+C