en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular Calculus >

integral of (4x+2)^2

Solution

\int (4 x + 2)^{2} d x

Solution

\frac{16 x ^{3}}{3} + 8 x^{2} + 4 x + C

Solution steps

\int (4 x + 2)^{2} d x

Expand

(4 x + 2)^{2} : 16 x^{2} + 16 x + 4

= \int 16 x^{2} + 16 x + 4 d x

Apply the Sum Rule:

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

= \int 16 x^{2} d x + \int 16 x d x + \int 4 d x

\int 16 x^{2} d x = \frac{16 x ^{3}}{3}

\int 16 x d x = 8 x^{2}

\int 4 d x = 4 x

= \frac{16 x ^{3}}{3} + 8 x^{2} + 4 x

Add a constant to the solution

= \frac{16 x ^{3}}{3} + 8 x^{2} + 4 x + C

Graph

Popular Examples

limit as x approaches 0 of (sin(x+pi))/x

(dy)/(dx)=-(1+y^2)/(1+x^2)

d/(dt)(1-2cos(t))

integral of (8x+9)/((x^2+9)(8-x))

integral of 1/(6y)

Frequently Asked Questions (FAQ)

What is the integral of (4x+2)^2 ?
The integral of (4x+2)^2 is (16x^3)/3+8x^2+4x+C