Basic Differentation/Integation Rules

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1

/dx (C)

0

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2

/dx (kx)

K

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3

/dx kf(x)

Kf’(x)

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4

/dx (xn)

nxn-1

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5

/dx (f(x)±g(x))

f’(x)±g’(x)

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6

∫(f(x)±g(x))dx

∫f(x)± ∫g(x)

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7

∫(0)dx

C

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8

∫(K)dx

kx+c

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9

∫kf(x)dx

k∫f(x)dx

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10

∫(xn)dx

(xn+1)/(n+1) +c

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11

/dx (sin x)

cos x

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12

/dx (cos x)

-sin x

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13

/dx (tan x)

Sec2x

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14

/dx (cot x)

-csc2x

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15

/dx (sec x)

Sec x tan x

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16

/dx (csc x)

-csc x cot x

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17

∫(sin x)dx

-cos x + c

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18

∫(cos x)dx

sin x + c

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19

∫(sec2 x)dx

tan x + c

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20

∫(csc2 x)dx

-cot x + c

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21

∫(sec x tan x)dx

sec x + c

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22

∫(csc x cot x)dx

-csc x + c

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23

/dx eu

eu·u’

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24

/dx au

au · u’ · ln a

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25

/dx Ln u

1/U · u’

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26

/dx Logau

1/U · u’ · 1/ln a

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27

/dx arcsin u

u’/√ 1-u²

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28

/dx arccos u

-u’/√ 1-u²

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29

/dx arctan u

u’/1+u²

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30

/dx arccot u

-u’/1+u²

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31

/dx arcsec u

u’/|u|√ u²-1

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32

/dx arccsc u

-u’/|u|√ u²-1

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33

1/√ a²-u² du

arcsin u/a + C

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34

1/a²+u² du

1/aarctan u/a + C

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35

1/u√ a²-u² du

1/aarcsec |u|/a + C

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36

∫ tan u du

-ln|cos u| + C

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37

∫ cot u du

ln|sin u| + C

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38

∫ sec u du

ln|sec u + tan u| + C

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39

∫ csc u du

-ln|csc u + cot u| + C

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40

1/u du

ln|u| + C

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41

∫au du

au · 1/ln a + C

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42

∫eu du

eu + C

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43

What is the Trig sub of a²-x²

x=asinθ

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44

What is the Trig sub of a²+x²

x=atanθ

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45

What is the Trig sub of x²-a²

x=asecθ

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