What is the integral of (3x+5)^2(3) ?

The integral of (3x+5)^2(3) is 3(3x^3+15x^2+25x)+C

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integral of (3x+5)^2(3)

\int (3 x + 5)^{2} (3) d x

3 (3 x^{3} + 15 x^{2} + 25 x) + C

Solution steps

\int (3 x + 5)^{2} \cdot 3 d x

Take the constant out:

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

= 3 \cdot \int (3 x + 5)^{2} d x

Expand

(3 x + 5)^{2} : 9 x^{2} + 30 x + 25

= 3 \cdot \int 9 x^{2} + 30 x + 25 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

= 3 (\int 9 x^{2} d x + \int 30 x d x + \int 25 d x)

\int 9 x^{2} d x = 3 x^{3}

\int 30 x d x = 15 x^{2}

\int 25 d x = 25 x

= 3 (3 x^{3} + 15 x^{2} + 25 x)

Add a constant to the solution

= 3 (3 x^{3} + 15 x^{2} + 25 x) + C

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What is the integral of (3x+5)^2(3) ?
The integral of (3x+5)^2(3) is 3(3x^3+15x^2+25x)+C