Test 1 Flashcards
Integration by Parts Formula
∫ udv = [uv - ∫( vdu )]
d/dx C=
0
d/dx x=
1
d/dx (x^n)
n*x^(n-1)
d/dx (Cx)=
C d/dx (x)
d/dx (x*v)=
x * d/dx[v] + v* d/dx[x]
d/dx (x/v)=
(( v * d/dx[x] - x * d/dx[v] )) / 2
d/dx [(f*g)(x)]=
chain rule
f’(g(x)) * g’(x)
d/dx e^x=
e^x
d/dx (1/x)
-1/x^2
d/dx a^x=
a^x * ln(a)
d/dx ln |x|=
1/x
d/dx loga |x|=
1 / (ln(a))x
Lim as x-> ∞ of (f(x)/g(x))=
LH’opital’s Rule
f’(x)/ g’(x)
∫x^n dx=
( x^(n+1) ) / (n+1)
∫ 1/x^2 dx =
-1/x + C
∫1/x dx=
ln (x) + c
∫ 1/(x+3) =
ln (|x+3|) + C
1
1
d/dx [sinx] =
cos x
∫ cos x dx=
sin x + C
d/dx [cos x]=
- sin x
∫-sin x dx=
cos x + C
∫ sin x dx =
-cos x + C
d/dx [tan x] =
sec^2 x
∫ sec^2 x=
tan x + C
d/dx [cot x] =
-csc^2 x
∫ csc^2 (x) dx =
-cot x + C
∫ -csc^2 (x) dx=
cot x + C
d/dx sec x=
sec x tan x
∫ sec x tan x dx=
sec x + C
d/dx [csc x] =
-csc x cot x
∫ [-csc x cot x ] dx =
csc x
∫ [csc x cot x] dx =
-csc x
∫ [a^x] dx =
(a^x) /ln a
∫ sec^3 (x) dx =
1/2 (sec x tan x + ln(|sec x + tan x|) + C
∫ tan x dx=
ln (| sec x |) + C
∫ cot x dx =
ln (| sin x |) + C
∫ tan x dx =
ln (| sec x |) + C
∫ cot x dx =
ln (| sin x |) + C
∫ sec x dx =
ln (| sec x + tan x |) + C
∫ csc x dx =
- ln (| css x + cot x |) + C = (( ln (| csc x - cot x |) + C ))
∫csc^3 (x) dx =
- 1/2 (csc x cot x + ln (|csc x + cot x|) + C
cos^2 (x )=
1/2 (1+cos (2x))
sin^2 (x) =
1/2 (1 - cos(2x))
