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+7)^2

Solution

\int (4 x + 7)^{2} d x

Solution

\frac{16 x ^{3}}{3} + 28 x^{2} + 49 x + C

Solution steps

\int (4 x + 7)^{2} d x

Expand

(4 x + 7)^{2} : 16 x^{2} + 56 x + 49

= \int 16 x^{2} + 56 x + 49 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 56 x d x + \int 49 d x

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

\int 56 x d x = 28 x^{2}

\int 49 d x = 49 x

= \frac{16 x ^{3}}{3} + 28 x^{2} + 49 x

Add a constant to the solution

= \frac{16 x ^{3}}{3} + 28 x^{2} + 49 x + C

Graph

Popular Examples

integral of (3x-4)/(x^2-1)

integral of 1 (v)

integral of 1/(sqrt((1+x^2)*ln(x+\sqrt{1+x^2)))}

integral of 5x^4e^{8x^5}

integral of log_{7}(x)

Frequently Asked Questions (FAQ)

What is the integral of (4x+7)^2 ?
The integral of (4x+7)^2 is (16x^3)/3+28x^2+49x+C