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

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36 votes

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

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20 votes

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

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

Bzo answered May 29, 2023

by Bzo

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