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