What is the integral of (x-1)^2x ?

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

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integral of (x-1)^2x

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

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

Solution steps

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

Expand

(x - 1)^{2} x : x^{3} - 2 x^{2} + x

= \int x^{3} - 2 x^{2} + x 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 x^{3} d x - \int 2 x^{2} d x + \int x d x

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

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

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

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

Add a constant to the solution

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

\frac{d}{d x} (\frac{1 - x}{1 + x})

x \to 0 lim (\frac{4}{x} - \frac{4}{e ^{x} - 1})

\frac{\partial}{\partial x} ((6 x + 3 y) ey)

\int \frac{1}{( x - 3 ) ( x + 2 )} d x

f (x) = x^{2} + 6, (4, 22)

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