formulario

1. FORMULARIO DE CALCULO DIFERENCIAL EN INTEGRAL I.Q. Jaime Carrillo Pérez Fórmula General de Derivación
Exponenciales y
Logaritmicas
Trigonométricas directas
= + Algebraicas Formas ±
Integralporpartes
=−
lim
∆ →
( + ∆ ) − ( )
∆ =
=
= ∙ + ∙
( ) =
1
( ) =
1
( )
=
=
+ 1
+ − =
2
− +
2
+ Derivadas Algebraicas
( )
= −
=
+ 1
+ + =
2
+ +
2
+ + + = 0
( )
=
( + − ) = + − − =
2
− −
2
+ − + = 1
( )
= − ∙
Exponencialesy
logarítmicas
= +
+
=
1
+ Sustitución trigonométrica =
( )
= ∙
= +
−
=
1
2
−
+
+ =
( + − )
= + −
( )
= −
= +
−
=
1
2
+
−
+ − = = De Arcos
Trigonométricas
∙ = − +
√ +
= + − + ∙
( ∙ )
= +
( ) =
√1 −
( ) = −
√ − 1
( ) = −
√1 −
( ) =
√ − 1
( ) =
1 +
( ) = −
1 +
∙ = +
√ +
= + + + = =
−
∙ = ln| | +
√ −
= + − = √
=
2√
∙ = +
√ −
=
1
+ ∙ √
= √
∙ = | − | +
Identidades
Pitagóricas
+ = 1 = Suma de ángulos Relaciones Trigonométricas
∙ ∙ = + − = 1 + =
( ± ) = ∙ ± ∙
( ± ) = ∙ ∓ ∙
( ± ) =
±
1 + ∙
= = = =
1
=
= = = =
1
=
= = = =
1
=
∙ ∙ = − + − = 1 ∙
Integral de funciones trigonométricas a la “n”
Función Integral n=2 Integral n “par” Integral n=3 o n “impar”
+
1
2
−
1
2
2 (1 − )
2
+
1
4
2 +
1
2
+
1
2
2 (1 − ) Producto de ángulos
=
1
2
+
1
2
2
=
1
2
−
1
2
2
2 = 2 ∙
2 = −
Signos de ángulos
(− ) = −
(− ) =
(− ) = −
(− ) = −
(− ) =
(− ) = −
− + ( − 1) ( − 1)
∙ =
1
2
[ ( − ) + ( + )]
∙ =
1
2
[ ( − ) − ( + )]
∙ =
1
2
[ ( − ) + ( + )]
− + ( + 1)
1
2
[− + ln ( − )] +
+ ( + 1)
1
2
[ + ln ( + )] +
− − + ( − 1) ( − 1)
−
−