another Calculus "indefinite integral" problem help?

Question

integrate the expression

(1 - 2X)^1/3(-2dx)

Answer 1

Integrate with u = (1 - 2x). Note that du/dx = -2, so du = -2dx, which you happen to have right there. You should be able to integrate u^(1/3)du pretty easily, and then substitute (1 - 2x) back in for u once you're done. You should get the result provided by the answerer immediately below me by haidar b. This is integration by substitution, a standard solution approach for integrals.

Answer 2

take t=1-2x

dt/dx = -2 --> dt=2dx

integral (1 - 2x)^1/3 (-2dx) = integral t^1/3 dt =
= t^(1+1/3)/(1+1/3) + C = [3t^(1+1/3)]/4 + C =
= [3(1 - 2x)^(1 + 1/3)]/4 + C