Question

√(2x+1) Evaluate the integral 2 (2x + 1) In (2x + 1) dx.

Answer 1

Substitute $y=\ln(2x+1)$ and $dy=\frac2{2x+1}\,dx$, so that

$\displaystyle \int \frac2{(2x+1) \ln(2x+1)} \, dx = \int \frac{dy}y = \ln|y| + C = \boxed{\ln|\ln(2x+1)| + C}$