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The two ideas I'd come up with was trying to substitute w^4+1 with u but that results in a 0 in the numerator.

Then I thought maybe I have to put w/w^4+1 into the 1/1+w^2 form and integrate into 1/k tan^-1kx + C but I'm not sure how to keep the original function while making the w^4 a w^2.

Help please? Am I at least going in the right direction with any of these ideas?