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Popular Calculus >

integral of (3+2x)^2

Solution

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

Solution

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

Solution steps

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

Expand

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

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

\int 9 d x = 9 x

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

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

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

Add a constant to the solution

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

Graph

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\int e^{\frac{5}{x}} d x

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\int 5 ln (6 x) d x

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\int x in x d x

integral of 2/(sqrt(x+1))

\int \frac{2}{x + 1} d x

Frequently Asked Questions (FAQ)

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