SOLUTION: Evaluate the integral using integration by parts with explanations. ln (2x+1) dx

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Question 407767: Evaluate the integral using integration by parts with explanations.
ln (2x+1) dx

Found 2 solutions by Tatiana_Stebko, richard1234:
Answer by Tatiana_Stebko(1539)   (Show Source): You can put this solution on YOUR website!

Use formula =
Let
then
=====

Answer by richard1234(7193)   (Show Source): You can put this solution on YOUR website!
This is an alternative approach which can still use integration by parts, but is slightly easier.

Let , , . If we replace 2x+1, we obtain

. We can integrate via parts, or by a formula which you can (and should) memorize.

Letting , , we obtain and . Applying the parts formula,

. Note that we have to multiply by 1/2, since we want . Back-substitute to obtain




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