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

The integral of (x+3)(x-5) is (x^3)/3-x^2-15x+C

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

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

\frac{x ^{3}}{3} - x^{2} - 15 x + C

Solution steps

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

Expand

(x + 3) (x - 5) : x^{2} - 2 x - 15

= \int x^{2} - 2 x - 15 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 x^{2} d x - \int 2 x d x - \int 15 d x

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

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

\int 15 d x = 15 x

= \frac{x ^{3}}{3} - x^{2} - 15 x

Add a constant to the solution

= \frac{x ^{3}}{3} - x^{2} - 15 x + C

\int_{2}^{6} \frac{1}{3 x - 2} d x

\frac{d}{d t} (2 cos (t) + 2 sin (t))

F (x) = (9 x^{6} + 4 x^{3})^{4}

y^{^{''}} - 2 y^{^{'}} - 3 y = 16 x^{2} e^{- x}

y^{^{''}} + 4 y^{^{'}} + 5 y = e^{x} + 5 x

What is the integral of (x+3)(x-5) ?
The integral of (x+3)(x-5) is (x^3)/3-x^2-15x+C