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

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

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

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

3 x + \frac{1}{2} ln ∣ 2 x + 2 ∣ + C

Solution steps

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

\int 3 d x = 3 x

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

= 3 x + \frac{1}{2} ln ∣ 2 x + 2 ∣

Add a constant to the solution

= 3 x + \frac{1}{2} ln ∣ 2 x + 2 ∣ + C

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