Use the method of integration by parts to determine the primitives for this function: x^1/2 ln x?

Integrate the original integrand by parts:

∫ x¹lnx / 2 dx = ∫ xlnx / 2 dx

Let f'(x) = x / 2

f(x) = x² / 4

Let g(x) = lnx

g'(x) = 1 / x

∫ f'(x)g(x) dx = f(x)g(x) - ∫ f(x)g'(x) dx

∫ x¹lnx / 2 dx = x²lnx / 4 - ∫ x / 4 dx

∫ x¹lnx / 2 dx = x²lnx / 4 - x² / 8 + C

∫ x¹lnx / 2 dx = x²(2lnx - 1) / 8 + C

?(ln x)/x² dx enable z = ln x => dz = dx/x ?ze^(-z) dz enable u = z => du = dz dv = e^(-z) dz => v = -e^(-z) uv - ?v du -ze^(-z) + ?e^(-z) dz = -ze^(-z) - e^(-z) + C = (-ln x)/x - a million/x + C i do no longer consider Rapidfire's way of integrating by potential of things and locate it puzzling.

oh thats easy...you can do it...