f-x-xtan-2-x-find-one-primitive-of-f-x-

Question Number 132832 by mathocean1 last updated on 16/Feb/21

f (x) = {x t a n}^{2} x

f i n d o n e p r i m i t i v e o f f (x) .

Answered by Olaf last updated on 17/Feb/21

F (x) = \int f (x) d x

F (x) = \int x \tan^{2} x d x

F (x) = \int [x (1 + \tan^{2} x) - x] d x

F (x) = x \tan x - \int \tan x d x - \frac{x^{2}}{2}

F (x) = x \tan x + \ln ∣ \cos x ∣ - \frac{x^{2}}{2} (+ C)

Answered by EDWIN88 last updated on 16/Feb/21

F (x) = \int x (\sec^{2} x - 1) dx

= \int x d (\tan x) - \frac{1}{2} x^{2}

= x \tan x - \int \tan x dx - \frac{1}{2} x^{2}

= x \tan x - \frac{1}{2} x^{2} + \ln ∣ \cos x ∣ + C

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