I=∫ x ( x +tan x )dx =∫ ( ^ 2 x + x tan x )dx =∫ ^ 2 x dx +∫ x tan x dx =tan x + x +C ...

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Integrating Factor

∫ secxsecx+ta...

Question

$\int s e c x (s e c x + t a n x) d x$

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Solution

$I = \int sec x (sec x + tan x) d x = \int ({sec}^{2} x + sec x tan x) d x = \int {sec}^{2} x d x + \int sec x tan x d x = tan x + sec x + C$

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