Evaluate ∫1exln(x)dx\int_1^e x \ln(x) dx∫1exln(x)dx using integration by parts, where u=ln(x)u = \ln(x)u=ln(x) and dv=xdxdv = x dxdv=xdx.
e2+14\frac{e^2+1}{4}4e2+1
e2−14\frac{e^2-1}{4}4e2−1
e2+12\frac{e^2+1}{2}2e2+1
e2−12\frac{e^2-1}{2}2e2−1