What is the integral of (x+3)(2x-1) ?

The integral of (x+3)(2x-1) is (2x^3)/3+(5x^2)/2-3x+C

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integral of (x+3)(2x-1)

\int (x + 3) (2 x - 1) d x

\frac{2 x ^{3}}{3} + \frac{5 x ^{2}}{2} - 3 x + C

Solution steps

\int (x + 3) (2 x - 1) d x

Expand

(x + 3) (2 x - 1) : 2 x^{2} + 5 x - 3

= \int 2 x^{2} + 5 x - 3 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 2 x^{2} d x + \int 5 x d x - \int 3 d x

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

\int 5 x d x = \frac{5 x ^{2}}{2}

\int 3 d x = 3 x

= \frac{2 x ^{3}}{3} + \frac{5 x ^{2}}{2} - 3 x

Add a constant to the solution

= \frac{2 x ^{3}}{3} + \frac{5 x ^{2}}{2} - 3 x + C

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\int - ∣ x ∣ d x

\frac{d}{d x} (\frac{4 x ^{5} - 15}{x ^{4}})

What is the integral of (x+3)(2x-1) ?
The integral of (x+3)(2x-1) is (2x^3)/3+(5x^2)/2-3x+C