I suggest to close math.stackexchange.com/q/5024942/42969 as a duplicate. OP already reduced the task to integrating ln(1+x^n)/x, which is solved in the duplicate target. Both answers here correspond directly to answers to the duplicate target.
OP claims that it is a different question, but accepted one of the answers.
@MartinR voted to close. OP says "my purpose for asking this question is to find if a u-sub is possible or how can I proceed through the u-sub" but accepted the answer with the power series of log