The value of the integral ∫₁⁰⁴[x²]dx/[x² - 8x + 196] + [x²], where [x] denotes the greatest integer less than or equal to x, is:

I = ∫₁⁰⁴[x²][x² - 8x + 196] + [x²]dx. (1)
Use ∫ₐᵇf(a + b - x)dx = ∫ₐᵇf(x)dx
I = ∫₁⁰⁴[(4 - x)²][(4 - x)²] + [(4 - x)²]dx. (2)
(1) + (2)
2I = ∫₁⁰⁴[(4 - x)² + x²][x²] + [(4 - x)²]dx
2I = ∫₁⁰⁴dx
2I = 6
I = 3