formulas

Question 1

integral sec x tan x dx=

Answer 1

sec x+C

Question 2

integral 0 dx=

Answer 2

C

Question 3

integral 1 dx=

Answer 3

x+C

Question 4

integral e x dx=

Answer 4

e x+C

Question 5

integral 1/x dx=

Answer 5

ln x+C

Question 6

integral n^xdx

Answer 6

n^x / ln x+C

Question 7

integral cos x dx=

Answer 7

sin x+C

Question 8

integral sin x dx=

Answer 8

_cos x+C

Question 9

integral sec^2 x dx=

Answer 9

tan x+C

Question 10

integral csc^2 x dx=

Answer 10

_cot x+C

Question 11

integral sec x tan x dx=

Answer 11

sec x+C

Question 12

integral csc x cot x dx=

Answer 12

_csc x+C

Question 13

d/dx ln x

Answer 13

1/x

Question 14

d/dx sinh u=

Answer 14

cosh u

Question 15

d/dx cosh u=

Answer 15

sinh u

Question 16

d/dx tanh u=

Answer 16

Sech^2 u

Question 17

integral sinhu du=

Answer 17

cosh u + C

Question 18

integral cosh u du=

Answer 18

sinh u + C

Question 19

integral sech^2 u du=

Answer 19

tanh u + C

Question 20

integral csch^2 u du=

Answer 20

-coth u + C

Question 21

integral sech u tanh u du=

Answer 21

-sech u + C

Question 22

integral csch u coth u du=

Answer 22

-csch u + C

Question 23

d/dx coth u=

Answer 23

-csch^2 u

Question 24

d/dx sech u =

Answer 24

-sech u tanh u

Question 25

d/dx csch u =

Answer 25

-csch u coth u

Question 26

d/dx of ln(x)=

Answer 26

1/x

Question 27

d/dx ln ( f(x) ) =

Answer 27

1/f(x) (f”(x))

Question 28

d/dx loga(X)=

Answer 28

1/xlna

Question 29

d/dx log a (f(x))=

Answer 29

1/(f(x) lna )

Question 30

product rule g(f(x))=

Answer 30

g’f x f’g

Question 31

Chain rule

Answer 31

getting the derivative of out side and leave inside alone and then multiplying by the derivative of inside

Question 32

you an write the square root of X as X to the power 1/2, how about ln of square root of X

Answer 32

ln of square root of x we can rewrite as ln of x to the power 1/2 and then rewrite as 1/2lnx

Question 33

ln (abcd)=

Answer 33

(lna)(lnb)(lnc)(lnd)

Question 34

Log a (x)=y

Answer 34

a^y=x

Question 35

loga (xy)=

Answer 35

loga (x) + loga (y)

Question 36

loga (x/y)=

Answer 36

loga (x) - loga (y)

Question 37

loga (a^x)=

Answer 37

x

Question 38

lnx=e then e^lnx=e^e

Answer 38

x=e^e

Question 39

change base formula

Answer 39

loga (b) = ln(b) / ln(a) remember base goes to the basement (bottom)

Question 40

d/dx a^x=

Answer 40

a^x lna

Question 41

d/dx a^x=

Answer 41

a^x lna

Question 42

d/dx a^f(x)

Answer 42

a^f(x) lna f’(x)

Question 43

d/dx of ln(x)=

Answer 43

1/x

Question 44

d/dx ln ( f(x) ) =

Answer 44

1/f(x) (f”(x))

Question 45

d/dx loga(X)=

Answer 45

1/xlna

Question 46

d/dx log a (f(x))=

Answer 46

1/(f(x) lna )

Question 47

product rule g(f(x))=

Answer 47

g’f x f’g

Question 48

Chain rule

Answer 48

getting the derivative of out side and leave inside alone and then multiplying by the derivative of inside

Question 49

you an write the square root of X as X to the power 1/2, how about ln of square root of X

Answer 49

ln of square root of x we can rewrite as ln of x to the power 1/2 and then rewrite as 1/2lnx

Question 50

ln (abcd)=

Answer 50

(lna)(lnb)(lnc)(lnd)

Question 51

Log a (x)=y

Answer 51

a^y=x

Question 52

loga (xy)=

Answer 52

loga (x) + loga (y)

Question 53

loga (x/y)=

Answer 53

loga (x) - loga (y)

Question 54

loga (a^x)=

Answer 54

x

Question 55

lnx=e then e^lnx=e^e

Answer 55

x=e^e

Question 56

change base formula

Answer 56

loga (b) = ln(b) / ln(a) remember base goes to the basement (bottom)

Question 57

d/dx a^x=

Answer 57

a^x lna

Question 58

d/dx a^x=

Answer 58

a^x lna

Question 59

d/dx a^f(x)

Answer 59

a^f(x) lna f’(x)

Question 60

Half life

Answer 60

Ln2/k or Ln0.5/k

Question 61

Decay and growth

Answer 61

A(t)=A0e^rt Y=Y0e^kt R is the interest or percent T is number of years A0 is initial value

Question 62

Temp formula

Answer 62

T-Ts=(T0-Ts)e^-kt T is the current temp or the one we want to get to and Ts is the room temp and T0 is the initial temp

Question 63

Hyperbolic sinh

Answer 63

(e^x - e^-x) / 2

Question 64

Hyperbolic cosh

Answer 64

(e^x + e^-x) / 2

Question 65

Cosh^2x - sinh^2x=

Answer 65

1

Question 66

Sinh2x

Answer 66

2sinhx

Question 67

what do we use if we have squer root of (a² - X²)

Answer 67

then we put X= a sin

Question 68

what do we use if we have squer root of (a² + X²)

Answer 68

then we put X=a tan Ø

Question 69

what do we use if we have squer root of (X² - a²)

Answer 69

then we put X = a Sec

Question 70

sin2X=

Answer 70

2 sinX cosX

Question 71

integral of Sec X dx=

Answer 71

ln I secx+tanx I + c

Question 72

integral of Csc x dx=

Answer 72

ln I csc x - cot x I + c

Question 73

Sec²X - 1

Answer 73

tan²X

Question 74

integral of (tan x) dx=

Answer 74

ln I sec x I + c

Question 75

integral of Sec X dx=

Answer 75

ln I sec x + tan x I + c

Question 76

Cos ²X =

Answer 76

1/2 ( 1 + cos (2x))

Question 77

sin²X=

Answer 77

1/2 ( 1 - cos (2x))

Question 78

1+ tan²X =

Answer 78

sec²X

Question 79

integral of sin (mx) Cos (nx) dx=

we have to use Sine A Cos B =

Answer 79

1/2 [sin (A-B) + sin ( A+B)]

Question 80

integral of sin (mx) sin (nx) dx=

we have to use Sine A sin B =

Answer 80

1/2 [cos (A-B) - cos ( A+B)]

Question 81

integral of cos (mx) Cos (nx) dx=

we have to use cos A Cos B =

Answer 81

1/2 [cos (A-B) + cos (A+B)]