Penyelesaian hasil dari ∫6x(3x-1)⁻1/3 dx =
Misal:
U = 6x →du = 6dx
dv = (3x – 1)⁻1/3dx →
v = ∫(3x – 1)1/3 dx
= ∫1/3(3x – 1) 1/3 3dx
= 1/3:2/3(3x – 1)2/3 + C
= 1/2 (3x – 1)2/3 + C
Jadi ∫6x(3x-1)⁻1/3 dx
= 6x.1/2(3x-1)2/3 – ∫1/2(3x-1)2/3.6dx
= 3x . (3x – 1)2/3 – ∫(3x-1)2/3 . 3dx
= 3x .(3x – 1)2/3 – 3/5(3x – 1)5/3 + C