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Problem Let x 2 − ( f ( x ) ) 2 = t − 1 t x^2 - (f(x))^2 = t - \frac{1}{t} x 2 − ( f ( x ) ) 2 = t − t 1 x 4 + ( f ( x ) ) 4 = t 2 + 1 t 2 x^4 + (f(x))^4 = t^2 + \frac{1}{t^2} x 4 + ( f ( x ) ) 4 = t 2 + t 2 1 ∫ − 2012 2012 ( x 3 ⋅ f ( x ) ⋅ f ′ ( x ) + x ) d x \int_{-2012}^{2012} (x^3 \cdot f(x) \cdot f'(x) + x)\, dx ∫ − 2012 2012 ( x 3 ⋅ f ( x ) ⋅ f ′ ( x ) + x ) d x x 4 4 + C \frac{x^4}{4} + C 4 x 4 + C { f ( x ) } 4 4 + C \frac{\{f(x)\}^4}{4} + C 4 { f ( x ) } 4 + C − 4024 -4024 − 4024 f ′ ( x ) 3 f ( x ) + C \frac{f'(x)}{3f(x)} + C 3 f ( x ) f ′ ( x ) + C Browse the problem library