I forgot to do it properly. So I put here as my own reminder. Here goes. $∫ 2x∛(6x - 1) dx$ Integration by Parts $∫ u.dv = u.v - ∫ v du$ Start $u = 2x$ $dv = ∛(6x - 1) dx$ We need the $du$ and $v$: ${du}/{dx} = 2$ $du = 2 dx$ $v = ∫ ∛(6x - 1) dx$ $= ∫ (6x - 1)^{1/3} dx$ $= {1/6} × 1/{1/3 + 1} × (6x - 1)^{1/3 + 1}$ $= 1/6 × 1/{4/3} × (6x - 1)^{4/3}$ $= 1/6 × 3/4 × (6x - 1)^{4/3}$ $= 1/8 × (6x - 1)^{4/3}$ We have these variables: u — du — dv — v. Let's use images then, as you can see below: Plug Continue 👍 Another Form of Solution Expand it once again. 👍 Other Technique We can also use tabular integration by parts method. It's faster. How to decide whether using integral by parts or substitution ? I usually observe the difference of the exponents. If like so: Then use substitution . But if like this: Use integration by parts.