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Rewrite as x sec² x - x and on the 1st use integration by parts with u = x and dv = sec² x dx..next integral is tan x which is a ln |sin x | answer
∫ xtan^(2)x dx =
∫ x d(tan x)-∫ x dx =
xtan x - ∫tan x dx -(1/2)x^2 =
xtan x + ∫1/cos x d(cos x) -(1/2)x^2 =
xtan x +ln|cos x|+(1/2)x^2 +C
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