The discussion revolves around finding the integral of the function ln(2x+1) with respect to x. Participants are exploring various techniques for integration, particularly focusing on integration by parts and substitution methods.
The discussion is active, with participants sharing their attempts and suggesting alternative methods. There is no explicit consensus on the best approach, but multiple strategies are being explored, indicating a productive exchange of ideas.
Participants are working under the constraints of a homework assignment, which may limit the information they can provide or the methods they can use. The original poster's attempts and suggestions from others reflect a focus on understanding the integration process rather than arriving at a final answer.
So far, so good. The last integral can be turned into a simpler one by dividing 2x by 2x + 1, using polynomial long division. If you don't know that technique, it works out to 1 + -1/(2x + 1) in this problem.Sczisnad said:Homework Statement
integral ln(2x+1)dx
Homework Equations
N/A
The Attempt at a Solution
I tried integration by parts,
Let u = ln(2x+1), dv = dx, du = 2/(2x+1)dx, v = x
ln(2x+1)dx = ln(2x+1)*x-(integral)x*(2/(2x+1))dx