50. Correct. The
answer is false. In general, integration by substitution is performed as
follows: ∫f(x)dx = ∫u(du/dx)dx
= ∫udu =
F(u) +c. Therefore, set u=x3+1, then du/dx = 3x2 and dx =
du/3x2. Substitute this into the integrand: ∫16x2(x3+1)dx
= ∫15x2*udu/3x2
= ∫5udu =
5*0.5u2 + c = 2.5u2 +c = 2.5(x3+1)2 +
c.