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Popular Calculus >

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

Graph

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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