What is the integral of (4x-5)(2x+1) ?

The integral of (4x-5)(2x+1) is 4x^3-(4x^3)/3-3x^2-5x+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral of (4x-5)(2x+1)

\int (4 x - 5) (2 x + 1) d x

4 x^{3} - \frac{4 x ^{3}}{3} - 3 x^{2} - 5 x + C

Solution steps

\int (4 x - 5) (2 x + 1) d x

Apply Integration By Parts

= (2 x + 1) (2 x^{2} - 5 x) - \int 2 (2 x^{2} - 5 x) d x

\int 2 (2 x^{2} - 5 x) d x = \frac{4 x ^{3}}{3} - 5 x^{2}

= (2 x + 1) (2 x^{2} - 5 x) - (\frac{4 x ^{3}}{3} - 5 x^{2})

Simplify

(2 x + 1) (2 x^{2} - 5 x) - (\frac{4 x ^{3}}{3} - 5 x^{2}) : 4 x^{3} - \frac{4 x ^{3}}{3} - 3 x^{2} - 5 x

= 4 x^{3} - \frac{4 x ^{3}}{3} - 3 x^{2} - 5 x

Add a constant to the solution

= 4 x^{3} - \frac{4 x ^{3}}{3} - 3 x^{2} - 5 x + C

What is the integral of (4x-5)(2x+1) ?
The integral of (4x-5)(2x+1) is 4x^3-(4x^3)/3-3x^2-5x+C