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Popular >

integral of (2x-1)^2

Solution

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

Solution

\frac{4 x ^{3}}{3} - 2 x^{2} + x + C

Solution steps

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

Expand

(2 x - 1)^{2} : 4 x^{2} - 4 x + 1

= \int 4 x^{2} - 4 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 4 x^{2} d x - \int 4 x d x + \int 1 d x

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

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

\int 1 d x = x

= \frac{4 x ^{3}}{3} - 2 x^{2} + x

Add a constant to the solution

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

Graph

Popular Examples

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\frac{\partial}{\partial x} (x^{2} y^{3} + 2 x^{4} y)

limit as x approaches infinity of 2/x-6

x \to \infty lim (\frac{2}{x} - 6)

derivative of 3x^4-5x^2+1

\frac{d}{d x} (3 x^{4} - 5 x^{2} + 1)

d/(dy)((2x)/(x^2+y^2))

\frac{d}{d y} (\frac{2 x}{x ^{2} + y ^{2}})

derivative of (4-x^2^3)

\frac{d}{d x} ((4 - x^{2})^{3})

Frequently Asked Questions (FAQ)

What is the integral of (2x-1)^2 ?
The integral of (2x-1)^2 is (4x^3)/3-2x^2+x+C