The integral of ln(2x+1) can be solved using integration by parts. By letting u = ln(2x+1) and dv = dx, the solution simplifies to ln(2x+1)*x - ∫(x*(2/(2x+1)))dx. Further simplification through polynomial long division yields a simpler integral, resulting in the expression 1 - 1/(2x + 1). This method effectively breaks down the problem into manageable components.
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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