Evaluate the following integrals showing each step. displaymode int x e^x dx. displaymode int x sin 2x dx. displaymode int e^(-x) x^2 dx. displaymode int [ln x]/[x^2] dx. find the center of mass of the region bounded by y = sin x between x = 0 and x = pi above the x-axis. displaymode integral from 0^pi t sin 2t dt. displaymode integral from (0)^(pi^2n^2) sin root(x) dx. (first substitution, then by parts)