What is the integral of (x+3)(x+7) ?

The integral of (x+3)(x+7) is (x^3)/3+5x^2+21x+C

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integral of (x+3)(x+7)

\int (x + 3) (x + 7) d x

\frac{x ^{3}}{3} + 5 x^{2} + 21 x + C

Solution steps

\int (x + 3) (x + 7) d x

Expand

(x + 3) (x + 7) : x^{2} + 10 x + 21

= \int x^{2} + 10 x + 21 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 10 x d x + \int 21 d x

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

\int 10 x d x = 5 x^{2}

\int 21 d x = 21 x

= \frac{x ^{3}}{3} + 5 x^{2} + 21 x

Add a constant to the solution

= \frac{x ^{3}}{3} + 5 x^{2} + 21 x + C

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What is the integral of (x+3)(x+7) ?
The integral of (x+3)(x+7) is (x^3)/3+5x^2+21x+C