**50. Incorrect. The
answer is false, not true.** In general, integration by substitution is
performed as follows: ∫f(x)dx = ∫u(du/dx)dx = ∫udu = F(u) +c. Therefore, set u=x^{3}+1, then du/dx = 3x^{2} and dx =
du/3x^{2}. Substitute this into the integrand: ∫16x^{2}(x^{3}+1)dx = ∫15x^{2}*udu/3x^{2}
= ∫5udu =
5*0.5u^{2} + c = 2.5u^{2 }+c = 2.5(x^{3}+1)^{2 }+
c.