integral 8x^2/(x^3 -2)^5=.....

misal u = x³-2
du = 3x² dx
dx = du/(3x²)

∫8x²u^5 dx
∫8x² u^5 du/3x²
∫8/3 u^5 du
(8/3+1) u^6
u^6
(x³-2)^6

misalkan
u = x³-2
du= 3x² dx
dx= du/(3x²)

∫8x²/u⁵ dx
=∫8x²/u⁵ du/3x²
=∫8/3 1/u⁵ du
=8/3 ∫u⁻⁵ du
=8/3 -1/4u⁻⁴ +C
=-2/3 u⁻⁴ +C
=-2/3 (x³-2)⁻⁴ +C
=-2/(3(x³-2)⁴) +C