integral 8x(x^3+6x^2+x+6) dx =

8 ∫x(x³ + 6x² + x + 6) dx
= 8 ∫(x⁴ + 6x³ + x² + 6x) dx
= 8 (x^5 /5 + 6x⁴/4 + x³/3 + 6x²/2 ) + C
= 8/5 x^5 + 12x⁴ + 8/3 x³ + 24x² + C