What is the integral of (14x+4)sqrt(7x^2+4x) ?

The integral of (14x+4)sqrt(7x^2+4x) is 2/3 (7x^2+4x)^{3/2}+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral of (14x+4)sqrt(7x^2+4x)

\int (14 x + 4) 7 x^{2} + 4 x d x

\frac{2}{3} (7 x^{2} + 4 x)^{\frac{3}{2}} + C

Solution steps

\int (14 x + 4) 7 x^{2} + 4 x d x

Apply u-substitution

= \int u d u

Apply the Power Rule

= \frac{2}{3} u^{\frac{3}{2}}

Substitute back

u = 7 x^{2} + 4 x

= \frac{2}{3} (7 x^{2} + 4 x)^{\frac{3}{2}}

Add a constant to the solution

= \frac{2}{3} (7 x^{2} + 4 x)^{\frac{3}{2}} + C

What is the integral of (14x+4)sqrt(7x^2+4x) ?
The integral of (14x+4)sqrt(7x^2+4x) is 2/3 (7x^2+4x)^{3/2}+C