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Popular Calculus >

integral of (3x+5)^2

Solution

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

Solution

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

Solution steps

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

Expand

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

= \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

= \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 x^{3} + 15 x^{2} + 25 x

Add a constant to the solution

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

Graph

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Frequently Asked Questions (FAQ)

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