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39 Cards in this Set

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  • Back
∫ 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