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Popular >

integral of (2x+3)^2

Solution

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

Solution

\frac{4 x ^{3}}{3} + 6 x^{2} + 9 x + C

Solution steps

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

Expand

(2 x + 3)^{2} : 4 x^{2} + 12 x + 9

= \int 4 x^{2} + 12 x + 9 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 4 x^{2} d x + \int 12 x d x + \int 9 d x

\int 4 x^{2} d x = \frac{4 x ^{3}}{3}

\int 12 x d x = 6 x^{2}

\int 9 d x = 9 x

= \frac{4 x ^{3}}{3} + 6 x^{2} + 9 x

Add a constant to the solution

= \frac{4 x ^{3}}{3} + 6 x^{2} + 9 x + C

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Frequently Asked Questions (FAQ)

What is the integral of (2x+3)^2 ?
The integral of (2x+3)^2 is (4x^3)/3+6x^2+9x+C