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

The integral of (2x^2-x)^2 is (4x^5)/5-x^4+(x^3)/3+C

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integral of (2x^2-x)^2

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

\frac{4 x ^{5}}{5} - x^{4} + \frac{x ^{3}}{3} + C

Solution steps

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

Expand

(2 x^{2} - x)^{2} : 4 x^{4} - 4 x^{3} + x^{2}

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

\int 4 x^{4} d x = \frac{4 x ^{5}}{5}

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

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

= \frac{4 x ^{5}}{5} - x^{4} + \frac{x ^{3}}{3}

Add a constant to the solution

= \frac{4 x ^{5}}{5} - x^{4} + \frac{x ^{3}}{3} + C

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

f (x) = x^{4} - 32 x^{2} + 256, at x = - 1

\int arctan (7 x) d x

3 e^{t}

What is the integral of (2x^2-x)^2 ?
The integral of (2x^2-x)^2 is (4x^5)/5-x^4+(x^3)/3+C