What is the integral of 6x(x+2) ?

The integral of 6x(x+2) is 6((x^3)/3+x^2)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of 6x(x+2)

\int 6 x (x + 2) d x

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

Solution steps

\int 6 x (x + 2) d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 6 \cdot \int x (x + 2) d x

Expand

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

= 6 \cdot \int x^{2} + 2 x 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

= 6 (\int x^{2} d x + \int 2 x d x)

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

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

= 6 (\frac{x ^{3}}{3} + x^{2})

Add a constant to the solution

= 6 (\frac{x ^{3}}{3} + x^{2}) + C

\int 5 x^{2} e^{2 x} d x

\int e^{3} cos (2 x) sin (2 x) d x

\int \frac{x ^{4} + 3 x}{x ^{2}} d x

\int sin (3 x) e^{3 x} d x

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