What is the integral of (2x-5)(6-x) ?

The integral of (2x-5)(6-x) is -x^3+(x^3)/3+6x^2+(5x^2)/2-30x+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral of (2x-5)(6-x)

\int (2 x - 5) (6 - x) d x

- x^{3} + \frac{x ^{3}}{3} + 6 x^{2} + \frac{5 x ^{2}}{2} - 30 x + C

Solution steps

\int (2 x - 5) (6 - x) d x

Apply Integration By Parts

= 12 x^{2} - x^{3} - 30 x + \frac{5 x ^{2}}{2} - \int 12 x - x^{2} d x

\int 12 x - x^{2} d x = 6 x^{2} - \frac{x ^{3}}{3}

= 12 x^{2} - x^{3} - 30 x + \frac{5 x ^{2}}{2} - (6 x^{2} - \frac{x ^{3}}{3})

Simplify

= - x^{3} + \frac{x ^{3}}{3} + 6 x^{2} + \frac{5 x ^{2}}{2} - 30 x

Add a constant to the solution

= - x^{3} + \frac{x ^{3}}{3} + 6 x^{2} + \frac{5 x ^{2}}{2} - 30 x + C

What is the integral of (2x-5)(6-x) ?
The integral of (2x-5)(6-x) is -x^3+(x^3)/3+6x^2+(5x^2)/2-30x+C