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Question:

If f(x) = ∫(5x⁸ + 7x⁶)/(x² + 1 + 2x⁷)² dx, (x ≥ 0) and f(0) = 0, then the value of f(1) is:

2

4

12

14

Solution:

∫(5x⁸ + 7x⁶)/(x² + 1 + 2x⁷)² dx
∫5x⁸ + 7x⁶(1x⁷ + 1x⁵ + 2)² dx = 12 + 1x⁵ + 1x⁷ + C
As f(0) = 0, f(x) = x⁷/(2x⁷ + x² + 1)
f(1) = 14