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Popular >

integral of-4x^3

Solution

\int - 4 x^{3} d x

Solution

- x^{4} + C

Solution steps

\int - 4 x^{3} d x

Take the constant out:

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

= - 4 \cdot \int x^{3} d x

Apply the Power Rule

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

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

Simplify

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

= - x^{4}

Add a constant to the solution

= - x^{4} + C

Popular Examples

integral from 0 to 1 of (6x^2-1)e^x

\int_{0}^{1} (6 x^{2} - 1) e^{x} d x

limit as x approaches-1 of 1/(x^2)+3x-1

x \to - 1 lim (\frac{1}{x ^{2}} + 3 x - 1)

(dy)/(dx)=(y+1)^{(-1)}

\frac{d y}{d x} = (y + 1)^{(- 1)}

x^{^{''}} + 25 x = 0

derivative of e^xcos(sqrt(x))

\frac{d}{d x} (e^{x} cos (x))

Frequently Asked Questions (FAQ)

What is the integral of-4x^3 ?
The integral of-4x^3 is -x^4+C