What is the integral of (sqrt(x)+2)^2 ?

The integral of (sqrt(x)+2)^2 is (x^2)/2+8/3 x^{3/2}+4x+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

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

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

Solution steps

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

Expand

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

= \int x + 4 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 x d x + \int 4 x d x + \int 4 d x

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

\int 4 x d x = \frac{8}{3} x^{\frac{3}{2}}

\int 4 d x = 4 x

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

Add a constant to the solution

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

\int - 7 x^{5} e^{x^{6}} d x

\int \frac{y}{4 - y} d y

\int 3^{x} \cdot e^{x} d x

\int \frac{12}{3 - 8 x - x ^{2}} d x

\int (3 sin (y) - 2 sec^{2} (y)) d y

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