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Popular >

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

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

= - 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

integral of (y^2+2y)/(sqrt(y^3+3y^2+4))

\int \frac{y ^{2} + 2 y}{y ^{3} + 3 y ^{2} + 4} d y

integral of 1/(9xlog_{3)(x)}

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

integral of \sqrt[3]{4x}

\int 3 4 x d x

integral of 1/16 cos^3(x)sin^2(x)

\int \frac{1}{16} cos^{3} (x) sin^{2} (x) d x

Frequently Asked Questions (FAQ)

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