calculo integral

c dx = cx + C, c ∈ R
c dx = cx + C, c ∈ R
xn+1
xn dx = n+1 + C, n = 1
n+1
x
xn dx c R
c dx = cx + C, = ∈ + 1 + C, n = 1
1
n
dx = ln x + C
x
1
xn+1 dx = ln x + C
xn dx =
x + C, n = 1
n+1
1
dx =Funciones Exponenciales
ln x + C
x

´
Funciones Hiperbolicas

sen x dx = − cos x + C

tan x dx = ln | sec x| + C
sec x dx = ln | sec x + tan x| + C
csc x dx = ln | csc x − cot x|+ C
cot x dx = ln | sen x| + C

´
Funciones Trigonometricas Inversas

Derivadas:

1
1 − x2
1
√ −1
√
1 − x2
1 − x2
−1
√1
1 xx
1 +− 2 2
11
√ 2
1 +x2 − 1
x x
1
√ −1
√ 2
x x2 − 1
x x −1
−1
−1
√
x +xx2− 1
1 2
−1
1 + x2

Dx (cos−1 x) =
Dx (tan−1 x) =
Dxx(tan−1 x) =
D (sec−1
Dx (sec−1 x) =
Dx (csc−1 x) =
Dx (csc−1 x) =
Dx (cot−1 x) =
Dx (cot−1 x) =Integrales:

Dx (tan x) = sec2 x

Dx (sec x) = sec x tan x
Dx (csc x) = − csc x cot x

Dx (cot x) = − csc2 x

Integrales:
Integrales:

x
Integrales: √ 1
dx = sen−1
+C
2 − x2
a
a
1
x
1
√ 1
dx = sen−1 −1 x+ C C
dx = tan a
+
2+ 2
a 2 − x2
a
a
1
11
−1 x
dx = tan−1
+C
√ 2
sec
2
a 2 + x2
a
a
x x −a
1
1
x
√
dx = sec−1
+C
2 − a2
a
a
x x

Dx (sinh x) = cosh x
Dx(cosh x) = cosh x
Dx (sinh x) = sinh x
Dx (sinh x) = cosh x
Dx (tanh x) = sinh 2 x
Dx (cosh x) = sech x
Dx (cosh x) = sinh x
Dx (sech x) = −sech
Dx (tanh x) = sech2 x x tanh x
Dx (tanh x) = sech2 x
Dx (csch x) = −csch x coth x
Dx (sech x) = −sech x tanh x
Dx (sech x) = −sech x tanh x
Dx (coth x) = −csch 2 coth x
Dx (csch x) = −csch xx
Dx (csch x) = −csch 2 coth x
x
Dx (coth x) =−csch 2x
Dx (coth x) = −csch x
sinh x dx = cosh x + C
sinh x dx = cosh x + C
cosh x dx = cosh x + C
sinh
sinh

Dx (sen−1 x) = √

Dx (sen−1 x) =
Dx (cos−1 x) =

x
FUNCIONES TRIGONOMÉTRICAS
loga x dx = x loga x −
+C
ln a
Derivadas:

Dx (cos x) = − sen x

Integrales:

FUNCIONES TRIGONOMÉTRICAS INVERSAS
´
Funciones Trigonometricas Inversas
Derivadas:

´
FuncionesTrigonometricas

Dx (sen x) = cos x

Derivadas:
Derivadas:

cos x dx = sen x + C

y Logar´
ıtmicas
Funciones Exponenciales

 
y Logar´
ıtmicas

FUNCIONES
Derivadas: EXPONENCIALES Y LOGARÍTMICAS
Funciones Exponenciales
Derivadas:
x
x
y Logar´ Dx (e ) = e
ıtmicas
x
D (ax = ex
Dxx (e )) = ax ln a
ivadas:
Dx (ax ) = 1 x ln a
a
Dx (ln x) =
x
x
x
1
Dx (e ) = e
Dx (ln x) =
x D(log x) = x 1
x
Dx (a ) = xa lnaa
x ln a
1
Dx (loga x) =
1
x ln a
Dx (ln x) =
x
1
Integrales:
Dx (loga x) =
x ln a
Integrales:
ex dx = ex + C
ex dx = ex + C
ax
grales:
ax dx = x + C
ln a
a
ax dx =
+C
ex dx = ex + C
ln a
ln x dx = x ln x − x + C
x
aln x dx = x ln x − x + C
x
ax dx =
+C
loga x dx = x loga x −
+C
ln a
lnx
a
loga x dx = x log x −
+C
ln x dx = xln x − x + C a
ln a

´
Funciones Hiperbolicas
Derivadas: FUNCIONES HIPERBÓLICAS
´
Funciones Hiperbolicas

Integrales:

cosh x dx = sinh x + C
tanh x dx = sinh x +x| + C
ln | cosh C
cosh
tanh x dx = ln | cosh x| + C
coth
sinh
tanh x dx = ln | cosh x| + C
coth x dx = ln | sinh x| + C

´
coth x dx = ln | sinh x| + C
Funciones Hiperbolicas Inversas

FUNCIONES HIPERBÓLICASINVERSAS
´
Funciones Hiperbolicas Inversas
Derivadas:
´

Funciones Hiperbolicas Inversas

Derivadas:
Derivadas:

Dx (sinh−1 x) = √

1

x2 + 1
1
Dx (sinh−1 x) = √ 1
Dx (cosh−1 x) = √x2 + 1
x (sinh
x2 + 1
1−
−1
√ 11
Dx (cosh −1 x) =
Dx (tanh x) = √x2 − 1
x (cosh
1 −2x2 1
x −
1
−1
Dx (tanh −1 x) =
1−1
−1
Dx (sech x) = 1 √ x2
x) = −
Dx (tanh
x 1−
1 −−1 x2
x2
Dx(sech−1 x) = √ −1
Dx (sech−1 x) = x √1 − x2
x 1 − x2

Integrales:
Integrales:

sici´n en fracciones parciales incluye las siguientes:
o

1
x
√ 1
dx = sinh−1 x + C
−1
2
2
a +C
Integrales: √x 2 + a 2 dx = sinh
a
x 1+ a
x
√ 1
dx = cosh−1 x + C
1 2 a2 dx = −1 −1 a + C
x
√ √x 2 −dx2 = sinhcosh
+C
x −
a ax
x 2 + a2 a
1
1
−1
1
1
x
1 a2 − x2 dx = a tanh −1 a + C
dx =...