Primitives Flashcards
1
Q
x^n,nϵN
R
A
x^(n+1)/(n+1)+C,CϵR
2
Q
1/x^n,nϵN{0,1}
]-∞,0[ou]0,+∞[
A
-1/(n-1)*x^(n-1)+C,CϵR
3
Q
1/x
]0,+∞[
A
ln(x)+C,CϵR
4
Q
1/√x
R
A
2√x+C,CϵR
5
Q
exp(x)
R
A
exp(x)+C,CϵR
6
Q
cos(x)
A
sin(x)+C,CϵR
7
Q
sin(x)
A
-cos(x)+C,CϵR
8
Q
f′/√f
A
2√f+C,CϵR
9
Q
f′*exp(f)
A
exp(f)+C,CϵR
10
Q
f’*cos(f)
A
sin(f)+C,CϵR
11
Q
f′*sin(f)
A
−cos(f)+C,CϵR
12
Q
f′*f^n, nϵN
A
f^(n+1)/(n+1)+C,CϵR
13
Q
f′/f^n, nϵN
f ne s’annulle pas sur I
A
-1/(n-1)*f^(n-1)+C,CϵR
14
Q
f′/f
f est strictement positive sur I
A
ln(f)+C,CϵR
15
Q
1/x-a
A
ln|x-a|
16
Q
1/(x-a)^n
A
(1/(1-n))*(1/(x-a)^n-1
17
Q
1/
1-x^2
A
1/*ln|1+x|/
2 |1-x|
18
Q
1/
1+x^2
A
arctan(x)
19
Q
u’/
1+u^2
A
arctan u
20
Q
exp(αx)
A
exp(αx)/α
21
Q
tan(x)
A
-ln |cos(x)|
22
Q
1/cos(x)^2 = 1 + tan(x)^2
A
tan(x)
23
Q
-1/√(1-x^2)
A
Arcsin (x) ou -Arccos (x)
