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 + C`