# How do you integrate intln(2x+1)dx?

I would set $2 x + 1 = t$
$2 \mathrm{dx} = \mathrm{dt}$
$\int \ln \left(t\right) \frac{\mathrm{dt}}{2} =$ by parts:
$= \frac{1}{2} \left[t \ln \left(t\right) - \int t \cdot \frac{1}{t} \mathrm{dt}\right] =$
$= \frac{1}{2} \left[t \ln \left(t\right) - t + c\right]$
but $t = 2 x + 1$
$= \frac{1}{2} \left[\left(2 x + 1\right) \ln | 2 x + 1 | - \left(2 x + 1\right) + c\right]$