Primitives

Question 1

x^n,nϵN

R

Answer 1

x^(n+1)/(n+1)+C,CϵR

Question 2

1/x^n,nϵN{0,1}

]-∞,0[ou]0,+∞[

Answer 2

-1/(n-1)*x^(n-1)+C,CϵR

Question 3

1/x

]0,+∞[

Answer 3

ln(x)+C,CϵR

Question 4

1/√x

R

Answer 4

2√x+C,CϵR

Question 5

exp(x)

R

Answer 5

exp(x)+C,CϵR

Question 6

cos(x)

Answer 6

sin(x)+C,CϵR

Question 7

sin(x)

Answer 7

-cos(x)+C,CϵR

Question 8

f′/√f

Answer 8

2√f+C,CϵR

Question 9

f′*exp(f)

Answer 9

exp(f)+C,CϵR

Question 10

f’*cos(f)

Answer 10

sin(f)+C,CϵR

Question 11

f′*sin(f)

Answer 11

−cos(f)+C,CϵR

Question 12

f′*f^n, nϵN

Answer 12

f^(n+1)/(n+1)+C,CϵR

Question 13

f′/f^n, nϵN

f ne s’annulle pas sur I

Answer 13

-1/(n-1)*f^(n-1)+C,CϵR

Question 14

f′/f

f est strictement positive sur I

Answer 14

ln(f)+C,CϵR

Question 15

1/x-a

Answer 15

ln|x-a|

Question 16

1/(x-a)^n

Answer 16

(1/(1-n))*(1/(x-a)^n-1

Question 17

1/

1-x^2

Answer 17

1/*ln|1+x|/

2 |1-x|

Question 18

1/

1+x^2

Answer 18

arctan(x)

Question 19

u’/

1+u^2

Answer 19

arctan u

Question 20

exp(αx)

Answer 20

exp(αx)/α

Question 21

tan(x)

Answer 21

-ln |cos(x)|

Question 22

1/cos(x)^2 = 1 + tan(x)^2

Answer 22

tan(x)

Question 23

-1/√(1-x^2)

Answer 23

Arcsin (x) ou -Arccos (x)