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Calculus Level 4

If f(x)=x332x2+x+14f(x)=x^{3}-\frac{3}{2}x^{2}+x+\frac{1}{4}

Find 1434f(f(x)) dx\displaystyle {\int^{\frac{3}{4}}_{\frac{1}{4}} f(f(x)) \text{ d}x}

This problem is part of my set Some JEE problems

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