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Popular >

integral of (3x+4)^2

Solution

\int (3 x + 4)^{2} d x

Solution

3 x^{3} + 12 x^{2} + 16 x + C

Solution steps

\int (3 x + 4)^{2} d x

Expand

(3 x + 4)^{2} : 9 x^{2} + 24 x + 16

= \int 9 x^{2} + 24 x + 16 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 24 x d x + \int 16 d x

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

\int 24 x d x = 12 x^{2}

\int 16 d x = 16 x

= 3 x^{3} + 12 x^{2} + 16 x

Add a constant to the solution

= 3 x^{3} + 12 x^{2} + 16 x + C

Popular Examples

limit as x approaches 2 of (|x-2|)/(2-x)

x \to 2 lim (\frac{∣ x - 2 ∣}{2 - x})

limit as x approaches 0 of-2x^2

x \to 0 lim (- 2 x^{2})

inverse oflaplace 2/(s(s+2)(s+3))inverse laplace

\frac{2}{s ( s + 2 ) ( s + 3 )}

sum from n=1 to infinity of (-2/3)^{n-1}

n = 1 \sum \infty (- \frac{2}{3})^{n - 1}

integral from 3 to 9 of 1/(x^2-1)

\int_{3}^{9} \frac{1}{x ^{2} - 1} d x

Frequently Asked Questions (FAQ)

What is the integral of (3x+4)^2 ?
The integral of (3x+4)^2 is 3x^3+12x^2+16x+C