integration formulas and other deriv. Flashcards

1
Q

(pythagorean identities) sin²x + cos²x=

A

1

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2
Q

(pythagorean identities) sec²x=

A

1 + tan²x

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3
Q

(pythagorean identities) csc²x=

A

1 + cot²x

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4
Q

∫a^u du=

A

(1/lna)*a^u + C

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5
Q

∫e^u du=

A

e^u + C

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6
Q

∫sinu du=

A

-cosu + C

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7
Q

∫cosu du=

A

sinu + C

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8
Q

∫tanu du=

A

-ln|cosu| + C

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9
Q

∫cotu du=

A

ln|sinu| + C

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10
Q

∫secu du =

A

ln|secu + tanu| + C

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11
Q

∫cscu du=

A

-ln|cscu + cotu| + C

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12
Q

∫sec²u du=

A

tanu + C

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13
Q

∫csc²u du=

A

-cotu + C

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14
Q

∫secutanu du=

A

secu + C

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15
Q

∫cscucotu du=

A

-cscu + C

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16
Q

d/dx [logau]=

A

u’/(lna)u

17
Q

d/dx[a^u]=

A

(lna)a^u*u’

18
Q

d/dx[tanu]=

A

(sec^2u)u’

19
Q

d/dx[cotu]=

A

-(csc^2u)u’

20
Q

d/dx[secu]=

A

(secutanu)u’

21
Q

d/dx[cscu] =

A

-(cscucotu)u’

22
Q

d/dx[arcsinu]=

A

u’/√(1-u^2)

23
Q

d/dx[arccosu]=

A

-u’/√(1-u^2)

24
Q

d/dx[arctanu]=

A

u’/ (1 + u^2)

25
Q

d/dx[arccotu]=

A

-u’/ (1 + u^2)

26
Q

d/dx[arcsecu]=

A

u’/ |u|√(u^2-1)

27
Q

d/dx[arccscu]=

A

-u’/ |u|√(u^2-1)