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Popular >

integral of (9x-6)^2

Solution

\int (9 x - 6)^{2} d x

Solution

27 x^{3} - 54 x^{2} + 36 x + C

Solution steps

\int (9 x - 6)^{2} d x

Expand

(9 x - 6)^{2} : 81 x^{2} - 108 x + 36

= \int 81 x^{2} - 108 x + 36 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 81 x^{2} d x - \int 108 x d x + \int 36 d x

\int 81 x^{2} d x = 27 x^{3}

\int 108 x d x = 54 x^{2}

\int 36 d x = 36 x

= 27 x^{3} - 54 x^{2} + 36 x

Add a constant to the solution

= 27 x^{3} - 54 x^{2} + 36 x + C

Graph

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Frequently Asked Questions (FAQ)

What is the integral of (9x-6)^2 ?
The integral of (9x-6)^2 is 27x^3-54x^2+36x+C