What is the integral of 3-4/(2x+1) ?

The integral of 3-4/(2x+1) is 3x-2ln|2x+1|+C

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integral of 3-4/(2x+1)

\int 3 - \frac{4}{2 x + 1} d x

3 x - 2 ln ∣ 2 x + 1 ∣ + C

Solution steps

\int 3 - \frac{4}{2 x + 1} 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 3 d x - \int \frac{4}{2 x + 1} d x

\int 3 d x = 3 x

\int \frac{4}{2 x + 1} d x = 2 ln ∣ 2 x + 1 ∣

= 3 x - 2 ln ∣ 2 x + 1 ∣

Add a constant to the solution

= 3 x - 2 ln ∣ 2 x + 1 ∣ + C

What is the integral of 3-4/(2x+1) ?
The integral of 3-4/(2x+1) is 3x-2ln|2x+1|+C