The integral of (ln(e^x + 1))^(1/3) / (e^x + 1) presents a challenge that involves substitution and integration by parts. The substitution k = ln(e^x + 1) leads to dk = dx(e^x)/(e^x + 1). However, attempts to solve using integration by parts result in a repetitive loop, indicating the need for a different approach or simplification. Participants in the discussion suggest further exploration of the derivative of the substitution to eliminate the variable x from the integral.
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ravenea said:Homework Statement
Integral of (ln(e^x + 1))^(1/3) / (e^x + 1)
See http://www2.wolframalpha.com/input/?i=integral+of+(ln(e**x+++1))**(1/3)/(e**x+++1)"
Homework Equations
N/A
The Attempt at a Solution
First, substitute k = ln(e^x + 1) dk = dx(e^x)/(e^x + 1)
Then, used integration by parts, but got to a loop...