Básico para llevar cálculo diferencial e integral.

1. 13.
du
a u
u a u C2 2
2 2
+
= + + +∫ ln
14
du
u a
u u a C2 2
2 2
−
= + − +∫ ln
15. a u du
u
a u
a u
a
C2 2 2 2
2
1
2 2
− = − + +−
∫ sen
16.
∫ +−+−−=− Cauu
a
au
u
duau 22
2
2222
ln
22
17.
a u du
u
a u
a
u a u C2 2 2 2
2
2 2
2 2
+ = + + + + +∫ ln
18.
du
u u a a
u
a
C2 2
11
−
= +−
∫ sec
TERCERAS FORMULAS BASICAS DE INTEGRACION
19. sen cosudu u C= − +∫
20. ∫ += Cuduu sencos
21. ∫ += Cuduu seclntan
22. cot ln senudu u C= +∫
23. Cuuduu ++=∫ tanseclnsec
24. csc ln csc cotudu u u C= − +∫
25. ∫ += Cuduu tansec2
26. csc cot2
udu u C= − +∫
27. ∫ += Cuduuu sectansec
28. csc cot cscu udu u C= − +∫
CUARTAS FORMULAS BASICAS DE INTEGRACION
29. senh coshudu u C= +∫
30. cosh senhudu u C= +∫
31. ∫ += Cuduu coshlntanh
32. coth ln senhudu u C= +∫
33. ∫ += −
Cutanduu senhsech 1
34. ∫ += Cuduu tanhsech2
35. ∫ +−= Cuduu cothcsch2
36. ∫ +−= Cuduuu sechtanhsech
37. ∫ +−= Cuduuu cschcothcsch
INTEGRAL POR PARTES
38. ∫ ∫−= duvvudvu ···
FORMULAS ELEMENTALES
DERIVADAS ELEMENTALES
1. ( ) 0=c
dx
d
2. 1
)(
=
dx
xd
3. ( )
d
dx
cx c=
4. ( )
d
dx
cx ncxn n
= −1
5. ( )
d
dx
u v w
du
dx
dv
dx
dw
dx
± ± ± = ± ±L L
6. ( ) )(')()().(')().( xgxfxgxfxgxf
dx
d
⋅+=
7. 2
)(
)(').()().('
)(
)(
xg
xgxfxgxf
xg
xf
dx
d −
=





DERIVADAS DE FUNCIONES TRIGONOMÉTRICAS
8. ( ) )('))()(( xfxfCosxfSen
dx
d
⋅(=
9. ( ) )('))(()(( xfxfSenxfCos
dx
d
⋅−=
10. ( ) )('))(()(( 2
xfxfSecxfTan
dx
d
⋅=
11. ( ) )('))(()( 2
xfxfCscfxCot
dx
d
⋅−=
12. ( ) )('))(())(()(( xfxfTanxfSecxfSec
dx
d
⋅⋅=
13.
( ) )('))(())(()(( xfxfCotxfCscxfCsc
dx
d
⋅⋅−=
Arcx Log-Ln Polin(x) Exponenc trigon. ALPES

2. @Aplika2 @Aplika2 @Aplika2
Efrain Cupe Alarcón
DERIVADAS DE LAS FUNCIONES
TRIGONOMÉTRICAS INVERSAS
14. ( ) )('
)(1
1
)(( 2
xf
xf
xfarcSen
dx
d
⋅
−
=
15. ( ) )('
)(1
1
)(( 2
xf
xf
xfarcCos
dx
d
⋅
−
−=
16. ( ) )('
)(1
1
)(( 2
xf
xf
xfarcTan
dx
d
⋅
+
=
17. ( ) )('
)(1
1
)(( 2
xf
xf
xfarcCot
dx
d
⋅
+
−=
18. ( ) )('
1)().(
1
)(( 2
xf
xfxf
xfarcSec
dx
d
⋅
−
=
19. ( ) )('
1)().(
1
)(( 2
xf
xfxf
xfarcCsc
dx
d
⋅
−
−=
DERIVADAS DE FUNCIONES EXPONENCIALES Y
LOGARITMICAS
20. ( ) )('
)(
log
)(log xf
xf
e
xf
dx
d a
a ⋅=
21. ( )
)(
)('
)((
xf
xf
xfLn
dx
d
=
22. ( ) Lnaxfaa
dx
d xfxf
).(')()(
⋅=
23.
( )
)(')())((
)(')().()(
)(
1)()(
xgxfxfLn
xfxfxgxf
dx
d
xg
xgxg
⋅⋅+
⋅= −
24. ( ) ).(')()(
xfee
dx
d xfxf
⋅=
DERIVADAS DE FUNCIONES HIPERBÓLICAS
25 ( ) )('))(()(( xfxfCoshxfSenh
dx
d
⋅=
26 ( ) )(')(()(( xfxfSenhxfCosh
dx
d
⋅=
27 ( ) )('))(()(( 2
xfxfSechxfTanh
dx
d
⋅=
28 ( ) )('))(()(( 2
xfxfCschxfCoth
dx
d
⋅−=
29.
( ) )('))(())(()(( xfxfTanhxfSechxfSech
dx
d
⋅⋅−=
30.
( ) )('))(())(()(( xfxfCothxfCschxfCsch
dx
d
⋅⋅−=
TRIGONOMETRIA
sen cos2 2
1A A+ =
sec tan2 2
1A A− =
csc cot2 2
1A A− =
tan
sen
cos
A
A
A
=
cos cos sen2 2 2
A A A= −
sen cos2 1
2
1
2 2A A= −
INTEGRALES BASICAS
1. Cxdx +=∫
2. ∫ ∫= dxxfadxxaf )()(
3. ∫ −≠
+
=
+
1cuando
1
1
m
m
x
dxx
m
m
4. ∫ ∫ ∫ ∫−+=−+ wdxvdxudxdxwvu )(
5. u du
n
u C nn n
=
+
+ ≠ −+
∫
1
1
11
6.
du
u
u C= +∫ ln
7. e du e Cu u
= +∫
8. a du
a
a
Cu
u
= +∫ ln
INTEGRALES BASICAS ADICIONALES
9. ∫ +=
+
−
C
a
u
aua
du 1
22
tan
1
10.
du
u a a
u a
u a
C2 2
1
2−
=
−
+
+∫ ln
11.
du
a u a
u a
u a
C2 2
1
2−
=
+
−
+∫ ln
SEGUNDAS FORMULAS BASICAS DE INTEGRACION
12.
du
a u
u
a
C2 2
1
−
= +−
∫ sen
sen sen cos2 2A A A=