What is the integral of (x+2)(x+3) ?

The integral of (x+2)(x+3) is (x^3)/3+(5x^2)/2+6x+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)(x+3)

\int (x + 2) (x + 3) d x

\frac{x ^{3}}{3} + \frac{5 x ^{2}}{2} + 6 x + C

Solution steps

\int (x + 2) (x + 3) d x

Expand

(x + 2) (x + 3) : x^{2} + 5 x + 6

= \int x^{2} + 5 x + 6 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^{2} d x + \int 5 x d x + \int 6 d x

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

\int 5 x d x = \frac{5 x ^{2}}{2}

\int 6 d x = 6 x

= \frac{x ^{3}}{3} + \frac{5 x ^{2}}{2} + 6 x

Add a constant to the solution

= \frac{x ^{3}}{3} + \frac{5 x ^{2}}{2} + 6 x + C

\int_{\frac{π}{6}}^{\frac{π}{2}} cot (x) d x

\int π x cos (n x) d x

\frac{d}{d x} (2 x^{\frac{4}{3}} - 3 x^{\frac{2}{3}})

((1 + arctan (x)) e^{2 x})^{^{'}}

(\frac{1}{y})^{^{'}}

What is the integral of (x+2)(x+3) ?
The integral of (x+2)(x+3) is (x^3)/3+(5x^2)/2+6x+C