What is the integral of (x+6)(3x-4) ?

The integral of (x+6)(3x-4) is x^3+7x^2-24x+C

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integral of (x+6)(3x-4)

\int (x + 6) (3 x - 4) d x

x^{3} + 7 x^{2} - 24 x + C

Solution steps

\int (x + 6) (3 x - 4) d x

Expand

(x + 6) (3 x - 4) : 3 x^{2} + 14 x - 24

= \int 3 x^{2} + 14 x - 24 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 3 x^{2} d x + \int 14 x d x - \int 24 d x

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

\int 14 x d x = 7 x^{2}

\int 24 d x = 24 x

= x^{3} + 7 x^{2} - 24 x

Add a constant to the solution

= x^{3} + 7 x^{2} - 24 x + C

\int_{- 2}^{0} 3 x 4 - x^{2} d x

\frac{\partial}{\partial x} (ln (2 + x^{2} + y^{2}))

\frac{\partial}{\partial y} (ln (y - 3 x))

\int - 24 t e^{- 3 t} d t

What is the integral of (x+6)(3x-4) ?
The integral of (x+6)(3x-4) is x^3+7x^2-24x+C