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

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

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

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

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

Solution steps

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

Expand

(x + 4) (x + 2) : x^{2} + 6 x + 8

= \int x^{2} + 6 x + 8 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 6 x d x + \int 8 d x

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

\int 6 x d x = 3 x^{2}

\int 8 d x = 8 x

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

Add a constant to the solution

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

\int (4 x^{2}) d x

y = 13 x, y = x^{2}

\int \frac{( 2 + x + x )}{x} d x

\int \frac{1}{7 ( x ^{2} + 1 )} d x

\frac{d}{d x} ((x^{3} + 7)^{6})

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