Find a substitution w and constants k,n so that the integral x^2sqrt(1-4x^3)dx has the form ∫kw^n dw .

Answer 1

let w = 1-4x^3
then dw = -12x^2 dx
That is, x^2 dx = -1/12 dw

Then ∫x^2 √(1-4x^3) dx = ∫ -1/12 w^(1/2) dw