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39 Cards in this Set

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 ∫ xⁿ dx (x^(n + 1) / n + 1) + C ∫ e^x dx e^x + C ∫ sin x dx -cos x + C ∫ sec² x dx tan x + C ∫ sec x tan x dx sec x + C ∫ u dv uv - ∫ v du ∫ tan x dx ln |sec x| + C ∫ 1 / x dx ln |x| + C ∫ a ^x dx (a^x / ln a) + C ∫ cos x dx sin x + C ∫ csc² x dx -cot x + C ∫ csc x cot x dx -csc x + C ∫ cot x dx ln |sin x| + C ∫ 1 / √(a² - x²) dx arcsin (x/a) + C ∫ 1 / (x² + a²) dx 1/a arctan (x/a) + C trig identity sin² = 1 - cos² x trig identity cos² = 1 - sin² x trig half angle identity sin² = ½ - ½ cos 2x trig half angle identity cos² = ½ + ½ cos 2x trig identity sec² x tan² + 1 trig identity tan² x sec² x - 1 Strategy for solving ∫ sin³(x) cos²(x) where sin is odd save one sin factor and use sin²x = 1 - cos²x, then substitute u = cos x Strategy for solving ∫ sin²(x) cos³(x) where cos is odd save one cos factor and use cos²x = 1 - sin²x, then substitute u = sin x Strategy for solving ∫ sin²(x) cos²(x) where both are even use half angle identities sin²x = ½(1 - cos 2x) or cos²x = ½(1 + cos 2x) Strategy for solving ∫ tan³(x) sec²(x) where tan is odd save a factor of sec x tan x and use tan²x = sec²x - 1, then substitute u = sec x Strategy for solving ∫ tan³(x) sec²(x) where sec is even save a factor of sec²x and use sec²x = 1 + tan²x, then substitute u = tan x ∫ csc x dx ln |csc x - cot x| + C ∫ sec x dx ln |sec x + tan x| + C trig identity sin A cos B ½[sin(A - B) + sin(A + B)] trig identity sin A sin B ½[cos(A - B) - cos(A + B)] trig identity cos A cos B ½[cos(A - B) + cos(A + B) trig identity sin x cos x ½ sin 2x √(a² - x²) x = a sin Θ; dx = a cos Θ dΘ Θ = sin^-1 x/a -π/2 - π/2 -> 1 - sin² Θ = cos² Θ √(a² + x²) x = a tan Θ; dx = a sec² Θ dΘ Θ = tan ^-1 x/a -π/2 - π/2 -> 1 + tan² Θ = sec² Θ √(x² - a²) x = a sec Θ; dx = a sec Θ tan Θ dΘ 0 - π/2 -> sec² Θ - 1 = tan² Θ sin 2Θ 2sin Θ cos Θ ∫ sin² x ½x - ¼sin(2x) ∫ cos² x ½x + ¼sin(2x) ∫ tan² x tan(x) - x