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

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

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

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

x^{2} - 3 x - 2 ln ∣ x ∣ + C

Solution steps

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

Expand

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

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

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

\int 3 d x = 3 x

\int \frac{2}{x} d x = 2 ln ∣ x ∣

= x^{2} - 3 x - 2 ln ∣ x ∣

Add a constant to the solution

= x^{2} - 3 x - 2 ln ∣ x ∣ + C

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