Integration Flashcards

1
Q

x

A

xⁿ⁺¹/n+1 + c

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2
Q

(ax+b)ⁿ

A

1/a ((ax+b)ⁿ⁺¹/n+1) + c

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3
Q

1/x

A

ln |x| + c

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4
Q

1/ax+b

A

1/a ln |ax+b| + c

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5
Q

A

eˣ + c

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6
Q

e ᵃˣ⁺ᵇ

A

1/a eᵃˣ⁺ᵇ +c

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7
Q

sinx

A

-cosx + c

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8
Q

sinax+b

A

-1/a cos(ax+b) + c

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9
Q

cosx

A

sinx + c

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10
Q

cos( ax+b)

A

1/a sin(ax+b) + c

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11
Q

tanx

A
  • ln|cosx| + c or ln |secx| + c
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12
Q

tan ax + b

A

1/a lnsec(ax+b )

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13
Q

secx

A

ln |secxtanx| +c

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14
Q

sec²x

A

tan x + c

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15
Q

cosecx

A

ln | tan(x/2) |+ c

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16
Q

cot x

A

ln |sin x | +c

17
Q

f ‘x / f x

A

ln |f (x) | + c

18
Q

f ‘x (f x)ⁿ

A

( f x )ⁿ⁺¹/n+ 1 + c

19
Q

f ‘ x eᶠ ˣ

A

eᶠ ˣ + c

20
Q

1/ √(a² -x² )

A

sin⁻¹(x/a) + c

21
Q

1/ (a² +x² )

A

1/a tan⁻¹(x/a) + c