en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (z+2)^2

Solution

\int (z + 2)^{2} d z

Solution

\frac{z ^{3}}{3} + 2 z^{2} + 4 z + C

Solution steps

\int (z + 2)^{2} d z

Expand

(z + 2)^{2} : z^{2} + 4 z + 4

= \int z^{2} + 4 z + 4 d z

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int z^{2} d z + \int 4 z d z + \int 4 d z

\int z^{2} d z = \frac{z ^{3}}{3}

\int 4 z d z = 2 z^{2}

\int 4 d z = 4 z

= \frac{z ^{3}}{3} + 2 z^{2} + 4 z

Add a constant to the solution

= \frac{z ^{3}}{3} + 2 z^{2} + 4 z + C

Popular Examples

derivative of sqrt(cos(2^x*x^5))

\frac{d}{d x} (cos (2^{x} \cdot x^{5}))

derivative of sqrt(9+\sqrt{9-x)}

\frac{d}{d x} (9 + 9 - x)

integral of (15sqrt(x)+sqrt(2))

\int (15 x + 2) d x

limit as x approaches-3+of 8x+5

x \to - 3 + lim (8 x + 5)

integral of 1/(4y^2+1)

\int \frac{1}{4 y ^{2} + 1} d y

Frequently Asked Questions (FAQ)

What is the integral of (z+2)^2 ?
The integral of (z+2)^2 is (z^3)/3+2z^2+4z+C