Evaluate the following integrals. (4 marks each) 4sec x dx cot3, dx
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Integral of 4sec x dx: We can use the substitution u = sec x + tan x, du/dx = sec x tan x + sec x, and rewrite the integral as: ∫ 4sec x dx = ∫ 4(sec x)(sec x + tan x)/(sec x + tan x) dx = ∫ 4(u/sec x)(du/dx) dx = ∫ 4u du = 2u^2 + C = 2(sec x + tan x)^2 + C Show more…
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