What is the integral of (3x-4)(2x+3) ?

The integral of (3x-4)(2x+3) is 2x^3-4x^2+(9x^2)/2-12x+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (3x-4)(2x+3)

\int (3 x - 4) (2 x + 3) d x

2 x^{3} - 4 x^{2} + \frac{9 x ^{2}}{2} - 12 x + C

Solution steps

\int (3 x - 4) (2 x + 3) d x

Apply Integration By Parts

: 3 x^{3} - 8 x^{2} + \frac{9 x ^{2}}{2} - 12 x - \int 3 x^{2} - 8 x d x

= 3 x^{3} - 8 x^{2} + \frac{9 x ^{2}}{2} - 12 x - \int 3 x^{2} - 8 x d x

\int 3 x^{2} - 8 x d x = x^{3} - 4 x^{2}

= 3 x^{3} - 8 x^{2} + \frac{9 x ^{2}}{2} - 12 x - (x^{3} - 4 x^{2})

Simplify

3 x^{3} - 8 x^{2} + \frac{9 x ^{2}}{2} - 12 x - (x^{3} - 4 x^{2}) : 2 x^{3} - 4 x^{2} + \frac{9 x ^{2}}{2} - 12 x

= 2 x^{3} - 4 x^{2} + \frac{9 x ^{2}}{2} - 12 x

Add a constant to the solution

= 2 x^{3} - 4 x^{2} + \frac{9 x ^{2}}{2} - 12 x + C

\int e^{2 x - 9} d x

\int (x^{2} - x + 3) d x

\int (x^{2} + 4) (x - 4) d x

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

\int \frac{8}{x ln ( 4 x )} d x

What is the integral of (3x-4)(2x+3) ?
The integral of (3x-4)(2x+3) is 2x^3-4x^2+(9x^2)/2-12x+C