en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of x(2x+3)

Solution

\int x (2 x + 3) d x

Solution

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

Solution steps

\int x (2 x + 3) d x

Expand

x (2 x + 3) : 2 x^{2} + 3 x

= \int 2 x^{2} + 3 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

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

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

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

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

Add a constant to the solution

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

Popular Examples

slope of (3)(0.4)slope

(3) (0.4)

limit as x approaches-1-of (x+1)/(|x+1|)

x \to - 1 - lim (\frac{x + 1}{∣ x + 1 ∣})

implicit (dy)/(dx),xy=45 implicit derivative

\frac{d y}{d x}, x y = 45

integral from 0 to 4 of sqrt(4-x)

\int_{0}^{4} 4 - x d x

tangent of f(x)=e^x,\at x=1 tangent of

f (x) = e^{x}, at x = 1

Frequently Asked Questions (FAQ)

What is the integral of x(2x+3) ?
The integral of x(2x+3) is (2x^3)/3+(3x^2)/2+C