Question 3 which is the efficient method

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Mathematics

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Explanation & Answer

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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