What is the integral of 8xcos(4)x^2 ?

The integral of 8xcos(4)x^2 is 2cos(4)x^4+C

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integral of 8xcos(4)x^2

\int 8 x cos (4) x^{2} d x

2 cos (4) x^{4} + C

Solution steps

\int 8 x cos (4) x^{2} d x

Take the constant out:

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

= 8 cos (4) \cdot \int x x^{2} d x

Simplify

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

= 8 cos (4) \cdot \int x^{3} d x

Apply the Power Rule

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

= 8 cos (4) \frac{x ^{4}}{4}

Simplify

8 cos (4) \frac{x ^{4}}{4} : 2 cos (4) x^{4}

= 2 cos (4) x^{4}

Add a constant to the solution

= 2 cos (4) x^{4} + C

\frac{d}{d y} (e^{x - y})

\frac{\partial}{\partial x} (cos (3 x + 6 y))

\frac{d y}{d x} + 0.8 x y = 4 x

\frac{\partial}{\partial x} (x \cdot i)

What is the integral of 8xcos(4)x^2 ?
The integral of 8xcos(4)x^2 is 2cos(4)x^4+C