∫tan^{3}x - xtan^{2}x. dx

∫tan^{2}x (tan x - x).dx

∫sec^{2}x - 1(tan x - x).dx

∫sec^{2}x.tan x.dx - ∫x.sec^{2}x.dx - ∫tan x.dx + ∫x.dx

Let tanx = t then sec^{2}x.dx = dt . the break u.v in ∫x.sec^{2}x.dx

directly

(tan^{2}x)/2 - xtanx + ∫tan x.dx - ∫tan x.dx + (x^{2})/2

(tan^{2}x)/2 - xtanx + (x^{2})/2