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

The integral of (x+5)(4x-2) is (4x^3)/3+9x^2-10x+C

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

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

\frac{4 x ^{3}}{3} + 9 x^{2} - 10 x + C

Solution steps

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

Expand

(x + 5) (4 x - 2) : 4 x^{2} + 18 x - 10

= \int 4 x^{2} + 18 x - 10 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 4 x^{2} d x + \int 18 x d x - \int 10 d x

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

\int 18 x d x = 9 x^{2}

\int 10 d x = 10 x

= \frac{4 x ^{3}}{3} + 9 x^{2} - 10 x

Add a constant to the solution

= \frac{4 x ^{3}}{3} + 9 x^{2} - 10 x + C

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What is the integral of (x+5)(4x-2) ?
The integral of (x+5)(4x-2) is (4x^3)/3+9x^2-10x+C