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Popular Calculus >

integral of (6x-1)^2

Solution

\int (6 x - 1)^{2} d x

Solution

12 x^{3} - 6 x^{2} + x + C

Solution steps

\int (6 x - 1)^{2} d x

Expand

(6 x - 1)^{2} : 36 x^{2} - 12 x + 1

= \int 36 x^{2} - 12 x + 1 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 36 x^{2} d x - \int 12 x d x + \int 1 d x

\int 36 x^{2} d x = 12 x^{3}

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

\int 1 d x = x

= 12 x^{3} - 6 x^{2} + x

Add a constant to the solution

= 12 x^{3} - 6 x^{2} + x + C

Graph

Popular Examples

integral of 12x^3-6x^2+4x

\int 12 x^{3} - 6 x^{2} + 4 x d x

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\int cos (x + 90) d x

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\int sin^{2} (\frac{x}{6}) d x

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\int 2 sec^{2} (2 x) tan (2 x) d x

integral of (7e^{7sqrt(x)})/(sqrt(x))

\int \frac{7 e ^{7 x}}{x} d x

Frequently Asked Questions (FAQ)

What is the integral of (6x-1)^2 ?
The integral of (6x-1)^2 is 12x^3-6x^2+x+C