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

Thank you very much Shashanmohore. It was very helpful.

Sir, Which will be the efficient method A,B,C,D,or E?

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