Tabla de Integrales y Formas de Integrar

 

Qgidg ao a o fbtoergdos fbko fbkoafgtgs afgtgs..   hubmfýb hubmfýb

 

aorfv ao rfv a

fb toer toer d

3





∙

 ∕7 ∙ ;   7 √  9√    ∙ √  7 ()  db () 7  ()     ()  ()  ()  ()  ()  ()  ()  ()  () ()mlt ()  () ()tgb ()  () 9 () mls ()  () (9)   () 9tgb()()  () 9()mlt()  () 9()mlt()  () 9 ()tgb() 7   {≣·7}  ∙() √7   

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

∙   7   {≣·7} ∙ ()  √77 7 

alkfb al kfbfl fl

∠   ;    − 4  4 − − 4  4 − − ∠   ;  9    +  ∠   ∠;7  7;db( )  {≣7} ≣7}  {3}  ∠ √ ;  ; 9=      P3 , −) √    ∠ √   ;      +       . ∠  () ()  ;  ()  db()   P3 ,−) ∠  ()   ;  ; xdb()     P3 ,−) ∠    ; 7    ∠  ()  ; mls ( )    − 4  4 − ∠  ()  ; sob ( )    − 4  4 − ∠  () ()  ; db db (|mls ()|)   − 4  4 − 0  ≣ 9   ∠  () ()  ; db (|sob ()|)   − 4  4 − 0 {≣} ∠  () ;  ; db db (|msm()  mlmltt () ()|)    {≣} ∠  (())  ; db (|som()  tgb ()|)     ≣    ∠ (); 9  sob(9) 1   ∠  (); 9  sob(9) 1   ∠  (); 7 tgb ( )     ≣    ∠  ();mlt()  {≣} ∠  (); 7 mlt()  {≣} ∠ (); 7 tgb (())    ≣    ∠  ∙ (); ∙ ()   7      7 ≡  ≡ 7 ∠  ∙ ();∙ ()   7      7 ≡ ≡ 77 ∠  ∙();∙()  79 db (7(7  )   − 4 4 −

 

 

 ∙()  ∙ () ∙ ())  

   

 

7  ∙(); ∙()  7 db (7(7  )   ∠  9 7 7   {≣·7,3} ∠  ∙();∙()   7  9    √   7 7   {≣·7,3} ∠ ∙();∙()      9  7    √   7

− 4  4 − − (−,7[∪P7,−) (−,7[∪P7,−)

 



Bl tlag hubmfýb puoao fbtoergrso, yg quo ostgs bl plsoob gbtf aorfvgag mlkl dl os od mgsl ao



Bl slb pldfblkfls pldfblkfls

 

 hubmflbos ao dg hlrkg .     √   · 

.

Ltrgs hlrkgs ao fbtoergr Fbtoergmfýb plr pgrtos.

∠;∠  D legrftkls F bvorsg trfelblkætrfmg

   

  D.F.G.Q.O   hçmfd ao fbtoergr

↙ ↙

deoirgfmg (pld (pldfblkfl) fblkfl)

Q rfelblkætrfmg

xplbobmfgd

Fbtoergmfýb ao pltobmfgs ao hubmflbos trfelblkætrfmgs.

∠ ()() : 

  ]o usg dg sustftumfýb ;mls ()

↙

() () ; 

:       ↙

]o usg dg sustftumfýb

  ]o usg

↙

  ↙

    ∠((); )(()) : ::       

;()

 () ; + ()  () ; ∙ () ;tgb(() ;tgb ;  

]o usg dg sustftumfýb

↙

]o usg dg sustftumfýb



Mugbal tlals slb fkpgros fkpgros (prfkor mgsl), so osmleo dg koblr koblr pltobmfg pgrg ngmor dg sustftumfýb.



Mugbal gkigs gkigs slb plsfidos (soeubal m gsl), so osmleo dg kgyl kgylrr pltobmfg. Ob mgsl ao quo quo fkpgr, fkpg r, bl so puoao rogdfzg rogdfzgrr bfbeubg a o dgs sustftumflbos.

]ustftumfýb trfelblkætrfmg



          

    

   ∙

     



 

     √



4



2



 sog fkpgr y 4

2

 

     

  ;   0 ; 

 ;   0 ;     

   ;  () ; () ;;   

   ;  () ; () ;;   

 

 

 

 

 ;     0  ;;       

 

 

   ;()   ; () ;;   

   

Qfps o fbtoergdos pgrg tobor ob muobtg

∠  (()) ; ;77 () ∠  ()  ; 7 ()

 

∠ som() ();()

∠  7  ; 7 (|(| |)|) 7   ; 7 ∕ 7 ∠ ( )   ∠ msm( )  () ;()

Aosmlkplsfmfýb ob hrgmmflbos pgrmfgdos

() 0

Dfbogdos ↙ 

]o ngmob

Mu garçtfmg garçtfmgs s b l h gm gmtlrfzgid tlrfzgidos os

4b2

hrgmmflbos pgrmfgdos ao dg hlrkg

od afsmrfkfbgbto

 1

∠ √ 7   ; 7  ∙ ቎||ቆ ∠ √7   ; ∙ ቉ቍ ∠   7   ; 7  ∙ ቉ቍ  

 

 (+). 

 os  o s boegtfvl boegtfvl,, so fbtoergb ao dg hlrkg

+   (++) 



Od búkorl ao mlbstgbtos quo so aoiob aotorkfbgr os feugd gd ergal aod ao blkf blkfbgalr. bgalr.



Sgrg dg hubmfýb frrgmflbgd frrgmflbgd fkprlpfg fkprlpfg,, albao o d ergal aod aoblkfbg aoblkfbgalr alr os koblr l feugd, so ngmo prfkorl dg afvfsfýb sfbtætfmg gbtos a o aosmlkplbor ob hrgmmflbos pgrmfgdos. pgrmfgdos.