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Antiderivative of 2tan x sec x Compute tan x sec 2 x dx in two different ways a) By substituting u = tan x b) By substituting v = sec x c) Compare the two results Solution a) Compute tan x sec 2 x dx by substituting u = tan x If u = tan x 2then du = sec x dx and tan x sec 2 x dx = u du = 1 u2 c 2 = 1 tan2 x0702Consider the following indefinite integral I= ∫ tan(x)sec^2(x) dx Part 1 of the question was to evaluate I using substitution, u=sec(x) my answer (sec^2(x))/2 C Part 2 evaluate I using substitution, u=tan(x) my answer tan^2(x)/2 C Part 3 is to explain why the solutions to parts 1 and 2 are seemingly different I would like to know whether my answers for part 1 and 2 are correctX d x 2 ∫ sec 2 ⁡ x tan 2 ⁡ x d x = t a n 2 x c, c ∈ R Note that once we have a side without an integral on it you need to include a constant of integration I have used c The two expressions on the left hand side are the same so you can add them giving 3 ∫ sec 2 Finding The Antiderivative Of 1 Cos X Video Le...