Let x^2-(f(x))^2=t-1/t and x^4+(f(x))^4=...

Let `x^2-(f(x))^2=t-1/t and x^4+(f(x))^4=t^2+1/t^2.` Then the value of `int_- 2012^2012(x^3f(x)f^(prime)(x)+x)dx` is (i) `x^4/4+C` (ii)`{f(x)}^4/4+C` (iii) `-4024` (iv) `{f'(x)}/(3f(x))+C`

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