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Popular Calculus >

integral of-4z^3

Solution

\int - 4 z^{3} d z

Solution

- z^{4} + C

Solution steps

\int - 4 z^{3} d z

Take the constant out:

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

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

Apply the Power Rule

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

Simplify

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

= - z^{4}

Add a constant to the solution

= - z^{4} + C

Graph

Popular Examples

integral of (5x^3+20x^2-4x+4)/(x^2+4x)

\int \frac{5 x ^{3} + 20 x ^{2} - 4 x + 4}{x ^{2} + 4 x} d x

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\int \frac{1}{9 x lo g _{3} ( x )} d x

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\int (2 sin (x) + cos (x)) d x

integral of xarctan(x+1)

\int x arctan (x + 1) d x

integral of e^{-st}cos(3t)

\int e^{- s t} cos (3 t) d t

Frequently Asked Questions (FAQ)

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