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

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

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

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

x^{2} + x - ln ∣ x + 2 ∣ + C

Solution steps

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

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

\int 1 d x = x

\int \frac{1}{x + 2} d x = ln ∣ x + 2 ∣

= x^{2} + x - ln ∣ x + 2 ∣

Add a constant to the solution

= x^{2} + x - ln ∣ x + 2 ∣ + C

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