What is the integral of (5x+5)(3x-3) ?

The integral of (5x+5)(3x-3) is 15((x^3)/3-x)+C

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integral of (5x+5)(3x-3)

\int (5 x + 5) (3 x - 3) d x

15 (\frac{x ^{3}}{3} - x) + C

Solution steps

\int (5 x + 5) (3 x - 3) d x

(5 x + 5) (3 x - 3) = 5 \cdot 3 (x + 1) (x - 1)

= \int 5 \cdot 3 (x + 1) (x - 1) d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 5 \cdot 3 \cdot \int (x + 1) (x - 1) d x

Simplify

= 15 \cdot \int (x + 1) (x - 1) d x

Expand

(x + 1) (x - 1) : x^{2} - 1

= 15 \cdot \int x^{2} - 1 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

= 15 (\int x^{2} d x - \int 1 d x)

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

\int 1 d x = x

= 15 (\frac{x ^{3}}{3} - x)

Add a constant to the solution

= 15 (\frac{x ^{3}}{3} - x) + C

What is the integral of (5x+5)(3x-3) ?
The integral of (5x+5)(3x-3) is 15((x^3)/3-x)+C