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

The integral of (x-2)(3x-4) is (3x^3)/2-(x^3)/2-5x^2+8x+C

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

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

\frac{3 x ^{3}}{2} - \frac{x ^{3}}{2} - 5 x^{2} + 8 x + C

Solution steps

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

Apply Integration By Parts

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

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

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

= (3 x - 4) (\frac{x ^{2}}{2} - 2 x) - 3 (\frac{x ^{3}}{6} - x^{2})

Simplify

(3 x - 4) (\frac{x ^{2}}{2} - 2 x) - 3 (\frac{x ^{3}}{6} - x^{2}) : \frac{3 x ^{3}}{2} - \frac{x ^{3}}{2} - 5 x^{2} + 8 x

= \frac{3 x ^{3}}{2} - \frac{x ^{3}}{2} - 5 x^{2} + 8 x

Add a constant to the solution

= \frac{3 x ^{3}}{2} - \frac{x ^{3}}{2} - 5 x^{2} + 8 x + C

\int 3 y sin (x y) d x

\frac{d y}{d x} = 7 x^{5} + 6

f (x) = 7 e^{- x} - 4 e^{- 7 x}

\frac{\partial}{\partial x} (3 sec^{2} (3 x - 2 y + 1))

\frac{d}{d x} ((2 x + 3)^{5} + 10 x (2 x + 3)^{4})

What is the integral of (x-2)(3x-4) ?
The integral of (x-2)(3x-4) is (3x^3)/2-(x^3)/2-5x^2+8x+C