Formules d’intégration de base Flashcards

1
Q

∫ 1 dx

A

x + C

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2
Q

∫ k dx

A

kx + C

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3
Q

∫ x^n dx

A

x^n+1 / n + 1 + C

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4
Q

∫ 1/x dx

A

ln|x| + C

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5
Q

∫ e^x dx

A

e^x + C

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6
Q

∫ a^x dx

A

a^x / ln a + C

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7
Q

∫ e^kx dx

A

e^kx / k + C

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8
Q

∫ a^kx dx

A

a^kx / k ln a + C

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9
Q

∫ sin x dx

A

-cos x + C

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10
Q

∫ cos x dx

A

sin x + C

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11
Q

∫ sec^2 x dx

A

tan x + C

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12
Q

∫ csc^2 x dx

A

-cotan x + C

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13
Q

∫ sec x tan x dx

A

sec x + C

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14
Q

∫ csc x cot x dx

A

-csc x + C

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15
Q

∫ sin (kx) dx

A

-cos (kx) / k + C

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16
Q

∫ cos (kx) dx

A

sin kx / k + C

17
Q

∫ sec^2 (kx) dx

A

tan kx / k + C

18
Q

∫ csc^2 (kx) dx

A

-cot kx / k + C

19
Q

∫ sec (kx) tan (kx) dx

A

sec kx / k + C

20
Q

∫ csc (kx) cot (kx) dx

A

-csc (kx) / k + C

21
Q

∫ (1 / √1-x^2) dx

A

arcsin x

22
Q

∫ (1/1+x^2) dx

A

arctan x

23
Q

∫ sec x dx

A

ln|sec x + tan x| + C

24
Q

∫ tan x dx

A

ln|sec x| + C

25
Q

∫ csc x dx

A

ln|csc x - cot x| + C

26
Q

∫ cot x dx

A

ln|sin x| + C

27
Q

rapport trigo = tan x

A

tan x = sin x
cos x

28
Q

rapport trigo = csc x

A

csc x = 1 / sin x

29
Q

rapport trigo = sec x

A

sec x = 1 / cos x

30
Q

rapport trigo = cot x

A

cot x = 1/ tan x

cot x = cos x / sinx

31
Q

rapport trigo = 1

A

cos^2 x + sin^2 x = 1

32
Q

rapport trigo = sec^2 x

A

1 + tan^2 x = sec^2 x

33
Q

rapport trigo = csc^2 x

A

cot^2 x + 1 = csc^2 x

34
Q

1/x√x^2-1

A

arcsec|x| + C