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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

Popular Examples

(d^2)/(dx^2)(e^{-2x^2})

\frac{d ^{2}}{d x ^{2}} (e^{- 2 x^{2}})

derivative of-1/(cos(x))

\frac{d}{d x} (- \frac{1}{cos ( x )})

sum from n=0 to infinity of cos(pi/2)

n = 0 \sum \infty cos (\frac{π}{2})

tangent of f(x)=4x^2-5x,(-1,9)tangent of

f (x) = 4 x^{2} - 5 x, (- 1, 9)

sum from n=1 to infinity of (3^n)/(n^3)

n = 1 \sum \infty \frac{3 ^{n}}{n ^{3}}

Frequently Asked Questions (FAQ)

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