What is the integral of (x+2)sqrt(4x+x^2) ?

The integral of (x+2)sqrt(4x+x^2) is 1/3 (4x+x^2)^{3/2}+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (x+2)sqrt(4x+x^2)

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

\frac{1}{3} (4 x + x^{2})^{\frac{3}{2}} + C

Solution steps

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

Apply u-substitution

: \int u^{2} d u

= \int u^{2} d u

Apply the Power Rule

: \frac{u ^{3}}{3}

= \frac{u ^{3}}{3}

Substitute back

u = 4 x + x^{2}

= \frac{( 4 x + x ^{2} ) ^{3}}{3}

Simplify

\frac{( 4 x + x ^{2} ) ^{3}}{3} : \frac{1}{3} (4 x + x^{2})^{\frac{3}{2}}

= \frac{1}{3} (4 x + x^{2})^{\frac{3}{2}}

Add a constant to the solution

= \frac{1}{3} (4 x + x^{2})^{\frac{3}{2}} + C

\frac{\partial}{\partial z} (2 x^{2} + 2 yz)

x \to - 1 lim (2 x^{3} - 4)

\frac{12}{( 3 s - 5 )}

\int \frac{1}{n ^{3}}

(- 5, - 8), (5, 2)

What is the integral of (x+2)sqrt(4x+x^2) ?
The integral of (x+2)sqrt(4x+x^2) is 1/3 (4x+x^2)^{3/2}+C