Question

Integral de ln(x)/raiz de x

Answer 1

∫udv = uv - ∫vdu
∫㏑x/√x dx = ∫㏑x.x⁻¹/²dx =
Sejam lnx = u => 1/x dx = du=> x⁻1dx = du e x⁻¹/²dx = dv => x¹/²:1/2 = v =>2√x = v
∫㏑x.x⁻¹/²dx = lnx.2x¹/² -∫2x¹/² . x⁻¹dx = lnx.2√x -2∫x⁻¹/²dx =
= lnx.2√x -2.(x¹/²):1/2 + C = 2√x.lnx - 4√x + C = 2√x(lnx -2)+ C