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

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

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integral of (x+2)(2x-1)

\int (x + 2) (2 x - 1) d x

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

Solution steps

\int (x + 2) (2 x - 1) d x

Apply Integration By Parts

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

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

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

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

Simplify

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

Add a constant to the solution

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

\frac{d}{d x} (3 x^{2} + 6)

\frac{d}{d x} (1 - (\frac{a}{x})^{b - 1})

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

x^{11} arccot (x)

t \to (0) lim (ln (t))

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