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I tried regular u substitution but that didn't let me get rid of all the x's.

I also just tried long division but that gave me an answer that didn't match with the actual answer to the problem.

The actual answer is 6[1/7 x^(7/6) - 1/5 x^(5/6) + 1/3 x^(1/6) - x^(1/6) + arctan(x^(1/6)) ] + C

How do I go about doing this?