text: Let u = 1-4x^3\nthen du = -12x^2 dx\n\nYou have to add a -1/6 outside the integral and a -6 inside so that you end up with a -12x inside.  Substitution gives you\n\n=(-1/6) int {u^3/2 du}\n=(-1/6)(2/5)u^(5/2)\n=(-1/15)u^(5/2)\n\nAnd substituting back in for u gives you\n=(-1/15)(1-4x^3)^(5/2) + C   <---add the constant for indefinite integrals