Formulário Primitivas Imediatas

DMCT, Universidade do Minho C´alculo A e B / An´alise Matem´atica I

2007/2008 MIEEIC, MIECOM. MIEMAT, MIEPOL, MIEMEC / LEC

Primitivas Imediatas Na lista de primitivas que se segue, f : I −→ R ´e uma fun¸c˜ao deriv´avel no intervalo I e C denota uma constante real arbitr´ aria.

 3. P

f0 f

 = log |f | + C

5. P (f 0 cos f ) = sen f + C  7. P

f0 cos2 f

11. P

f0 cos f

p 

15. P



1 = log + tg f + C cos f = arcsen f + C

1 − f2

f0 1 + f2



p 

 12. P

f0 sen f

p 

= arctg f + C

16. P

= argsh f + C

20. P

1 = log − cotg f + C sen f ! = arccos f + C

1 − f2 

= arccotg f + C

f0 sh2 f

p 

24. P

 = − coth f + C !

f0

22. P

 = argth f + C



−f 0 1 + f2

!

f2 + 1

= − cotg f + C

18. P (f 0 sh f ) = ch f + C 

= th f + C



−f 0

14. P



f0 1 − f2

f0 sen2 f

10. P (f 0 cotg f ) = log |sen f | + C



f0

21. P

23. P

f0 ch2 f

8. P

!

17. P (f 0 ch f ) = sh f + C 19. P

6. P (f 0 sen f ) = − cos f + C 

= tg f + C

f0

13. P


af 4. P af f 0 = + C (a ∈ R+ \1) log a



9. P (f 0 tg f ) = − log |cos f | + C 

f α+1 + C (α 6= −1) α+1

2. P (f 0 f α ) =

1. P (a) = ax + C

f2 − 1

f0 1 − f2

= argch f + C

 = argcoth f + C