What is the integral of ln(2x+2) ?

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

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integral of ln(2x+2)

\int ln (2 x + 2) d x

x ln (2 x + 2) - x - 1 + ln ∣ x + 1 ∣ + C

Solution steps

\int ln (2 x + 2) d x

Apply Integration By Parts

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

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

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

= x ln (2 x + 2) - (x + 1 - ln ∣ x + 1 ∣)

Simplify

= x ln (2 x + 2) - x - 1 + ln ∣ x + 1 ∣

Add a constant to the solution

= x ln (2 x + 2) - x - 1 + ln ∣ x + 1 ∣ + C

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