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Ecuaciones DIferenciales
Integrales
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Cards (40)
∫
x
n
⋅
d
x
=
\int x^{n} \cdot dx=
∫
x
n
⋅
d
x
=
=
=
=
x
n
+
1
n
+
1
+
\frac{x^{n+1}}{n+1}+
n
+
1
x
n
+
1
+
C
C
C
∫
e
x
⋅
d
x
=
\int e^{x} \cdot dx=
∫
e
x
⋅
d
x
=
=
=
=
e
x
+
e^{x}+
e
x
+
C
C
C
∫
l
n
(
x
)
⋅
d
x
=
\int ln(x) \cdot dx=
∫
l
n
(
x
)
⋅
d
x
=
=
=
=
x
l
n
(
x
)
−
x
+
xln(x)-x+
x
l
n
(
x
)
−
x
+
C
C
C
∫
s
e
n
(
x
)
⋅
d
x
=
\int sen(x) \cdot dx=
∫
se
n
(
x
)
⋅
d
x
=
=
=
=
−
c
o
s
(
x
)
+
-cos(x)+
−
cos
(
x
)
+
C
C
C
∫
c
o
s
(
x
)
⋅
d
x
=
\int cos(x)\cdot dx=
∫
cos
(
x
)
⋅
d
x
=
=
=
=
s
e
n
(
x
)
+
sen(x)+
se
n
(
x
)
+
C
C
C
∫
t
a
n
(
x
)
⋅
d
x
=
\int tan(x) \cdot dx=
∫
t
an
(
x
)
⋅
d
x
=
=
=
=
−
l
n
∣
c
o
s
(
x
)
∣
+
-ln |cos(x)|+
−
l
n
∣
cos
(
x
)
∣
+
C
C
C
(alternativa)
∫
t
a
n
(
x
)
⋅
d
x
=
\int tan(x) \cdot dx=
∫
t
an
(
x
)
⋅
d
x
=
=
=
=
l
n
∣
s
e
c
(
x
)
∣
+
ln|sec(x)|+
l
n
∣
sec
(
x
)
∣
+
C
C
C
∫
c
o
t
(
x
)
⋅
d
x
=
\int cot(x) \cdot dx=
∫
co
t
(
x
)
⋅
d
x
=
=
=
=
l
n
∣
s
e
n
(
x
)
∣
+
ln|sen(x)|+
l
n
∣
se
n
(
x
)
∣
+
C
C
C
∫
s
e
c
(
x
)
⋅
d
x
=
\int sec(x) \cdot dx=
∫
sec
(
x
)
⋅
d
x
=
=
=
=
l
n
∣
s
e
c
(
x
)
+
ln|sec(x)+
l
n
∣
sec
(
x
)
+
t
a
n
(
x
)
∣
+
tan(x)|+
t
an
(
x
)
∣
+
C
C
C
∫
c
s
c
(
x
)
⋅
d
x
=
\int csc(x) \cdot dx=
∫
csc
(
x
)
⋅
d
x
=
=
=
=
l
n
∣
c
s
c
(
x
)
−
c
o
t
(
x
)
∣
+
ln|csc(x)-cot(x)|+
l
n
∣
csc
(
x
)
−
co
t
(
x
)
∣
+
C
C
C
∫
1
x
2
−
a
2
⋅
d
x
\int \frac{1}{x^{2}-a^{2}}\cdot dx
∫
x
2
−
a
2
1
⋅
d
x
=
=
=
1
2
a
l
n
∣
u
−
a
∣
∣
u
+
a
∣
+
\frac {1}{2a}ln\frac{|u-a|}{|u+a|}+
2
a
1
l
n
∣
u
+
a
∣
∣
u
−
a
∣
+
C
C
C
∫
b
x
⋅
d
x
=
\int b^{x} \cdot dx=
∫
b
x
⋅
d
x
=
=
=
=
b
x
l
n
(
b
)
+
\frac{b^{x}}{ln(b)}+
l
n
(
b
)
b
x
+
C
C
C
∫
d
x
1
−
x
2
=
\int \frac{dx}{\sqrt{1-x^{2}}}=
∫
1
−
x
2
d
x
=
=
=
=
a
n
g
s
e
n
(
x
)
+
angsen(x)+
an
g
se
n
(
x
)
+
C
C
C
∫
u
⋅
d
v
=
\int u \cdot dv=
∫
u
⋅
d
v
=
=
=
=
u
v
−
∫
v
d
u
uv-\int vdu
uv
−
∫
v
d
u
Prioridad integracion por partes
Trigonométricas Inversas
Logaritmicas
ALgebraicas
Trigonometricas
Exponenciales
Método D/I
(con trigonométricas y exponenciales) la algebraica siempre es la que se
deriva.
∫
c
s
c
2
(
x
)
⋅
d
x
=
\int csc^{2}(x) \cdot dx=
∫
cs
c
2
(
x
)
⋅
d
x
=
−
c
o
t
(
u
)
+
-cot(u)+
−
co
t
(
u
)
+
C
C
C
∫
t
a
n
h
(
x
)
⋅
d
x
=
\int tanh(x) \cdot dx=
∫
t
anh
(
x
)
⋅
d
x
=
l
n
(
c
o
s
h
x
)
+
ln(coshx)+
l
n
(
cos
h
x
)
+
C
C
C
∫
c
s
c
h
(
x
)
⋅
d
x
=
\int csch(x) \cdot dx=
∫
csc
h
(
x
)
⋅
d
x
=
=
=
=
l
n
∣
t
a
n
h
x
2
∣
+
ln|tanh \frac{x}{2}|+
l
n
∣
t
anh
2
x
∣
+
c
c
c
∫
s
e
c
h
(
x
)
t
a
n
h
(
x
)
⋅
d
x
=
\int sech(x)tanh(x)\cdot dx=
∫
sec
h
(
x
)
t
anh
(
x
)
⋅
d
x
=
=
=
=
−
s
e
c
h
(
x
)
+
-sech(x)+
−
sec
h
(
x
)
+
C
C
C
∫
s
e
c
(
x
)
t
a
n
(
x
)
⋅
d
x
=
\int sec(x)tan(x)\cdot dx=
∫
sec
(
x
)
t
an
(
x
)
⋅
d
x
=
=
=
=
s
e
c
(
x
)
+
sec(x)+
sec
(
x
)
+
C
C
C
∫
d
x
u
2
±
a
2
=
\int \frac{dx}{\sqrt{u^{2}\pm a^{2}}}=
∫
u
2
±
a
2
d
x
=
=
=
=
l
n
∣
u
+
ln|u+
l
n
∣
u
+
u
2
±
a
2
∣
+
\sqrt{u^{2}\pm a^{2}}|+
u
2
±
a
2
∣
+
C
C
C
∫
s
e
n
h
(
x
)
⋅
d
x
=
\int senh(x)\cdot dx=
∫
se
nh
(
x
)
⋅
d
x
=
=
=
=
c
o
s
h
(
x
)
+
cosh(x)+
cos
h
(
x
)
+
C
C
C
∫
c
o
t
h
(
x
)
⋅
d
x
=
\int coth(x)\cdot dx=
∫
co
t
h
(
x
)
⋅
d
x
=
l
n
∣
s
e
n
h
(
x
)
∣
+
ln|senh(x)|+
l
n
∣
se
nh
(
x
)
∣
+
C
C
C
∫
s
e
c
h
2
(
x
)
⋅
d
x
=
\int sech^{2}(x)\cdot dx=
∫
sec
h
2
(
x
)
⋅
d
x
=
=
=
=
t
a
n
h
(
x
)
+
tanh(x)+
t
anh
(
x
)
+
C
C
C
∫
c
s
c
h
(
x
)
c
o
t
h
(
x
)
⋅
d
x
=
\int csch(x)coth(x)\cdot dx=
∫
csc
h
(
x
)
co
t
h
(
x
)
⋅
d
x
=
−
c
s
c
h
(
x
)
+
-csch(x)+
−
csc
h
(
x
)
+
C
C
C
∫
s
e
c
2
(
x
)
⋅
d
x
=
\int sec^{2}(x)\cdot dx=
∫
se
c
2
(
x
)
⋅
d
x
=
=
=
=
t
a
n
(
x
)
+
tan(x)+
t
an
(
x
)
+
C
C
C
∫
c
s
c
(
x
)
c
o
t
(
x
)
⋅
d
x
=
\int csc(x)cot(x)\cdot dx=
∫
csc
(
x
)
co
t
(
x
)
⋅
d
x
=
−
c
s
c
(
x
)
+
-csc(x)+
−
csc
(
x
)
+
C
C
C
∫
d
x
u
u
2
−
a
2
=
\int \frac{dx}{u\sqrt{u^{2}-a^{2}}}=
∫
u
u
2
−
a
2
d
x
=
=
=
=
1
a
a
n
g
s
e
c
u
a
+
\frac {1}{a}angsec\frac{u}{a}+
a
1
an
g
sec
a
u
+
C
C
C
∫
c
o
s
h
(
x
)
⋅
d
x
=
\int cosh(x)\cdot dx=
∫
cos
h
(
x
)
⋅
d
x
=
s
e
n
h
(
x
)
+
senh(x)+
se
nh
(
x
)
+
C
C
C
∫
s
e
c
h
(
x
)
⋅
d
x
=
\int sech(x)\cdot dx=
∫
sec
h
(
x
)
⋅
d
x
=
=
=
=
a
n
g
t
a
n
∣
s
e
n
h
(
x
)
∣
+
angtan|senh(x)|+
an
g
t
an
∣
se
nh
(
x
)
∣
+
C
C
C
∫
c
s
c
2
(
x
)
⋅
d
x
=
\int csc^{2}(x)\cdot dx=
∫
cs
c
2
(
x
)
⋅
d
x
=
−
c
o
t
h
(
x
)
+
-coth(x)+
−
co
t
h
(
x
)
+
C
C
C
∫
d
x
x
=
\int \frac{dx}{x}=
∫
x
d
x
=
l
n
∣
x
∣
+
ln|x|+
l
n
∣
x
∣
+
C
C
C
∫
d
x
a
2
−
x
2
=
\int \frac {dx}{a^{2}-x^{2}}=
∫
a
2
−
x
2
d
x
=
=
=
=
1
2
a
l
n
∣
a
+
x
a
−
x
∣
+
\frac {1}{2a}ln|\frac{a+x}{a-x}|+
2
a
1
l
n
∣
a
−
x
a
+
x
∣
+
C
C
C
¿En que casos se aplica el conjugado en integración trigonométrica?
∫
d
x
1
±
s
i
n
(
x
)
\int \frac{dx}{1\pm sin(x)}
∫
1
±
s
in
(
x
)
d
x
∫
d
x
1
±
c
o
s
(
x
)
\int \frac{dx}{1\pm cos(x)}
∫
1
±
cos
(
x
)
d
x
Forma del factor
(
a
x
+
b
)
(ax+b)
(
a
x
+
b
)
La fracción parcial es:
=
=
=
A
a
x
+
b
\frac{A}{ax+b}
a
x
+
b
A
Forma del factor
(
a
x
+
b
)
n
(ax+b)^{n}
(
a
x
+
b
)
n
La fracción parcial es:
A
(
a
x
+
b
)
+
\frac{A}{(ax+b)}+
(
a
x
+
b
)
A
+
B
(
a
x
+
b
)
2
+
\frac{B}{(ax+b)^{2}}+
(
a
x
+
b
)
2
B
+
.
.
.
C
(
a
x
+
b
)
n
...\space\space\frac{C}{(ax+b)^{n}}
...
(
a
x
+
b
)
n
C
Forma del Factor
(
a
x
2
+
(ax^{2}+
(
a
x
2
+
b
x
+
bx+
b
x
+
c
)
c)
c
)
La fracción parcial es:
A
x
+
B
(
a
x
2
+
b
x
+
c
)
\frac{Ax+B}{(ax^2 +bx+c)}
(
a
x
2
+
b
x
+
c
)
A
x
+
B
Forma del Factor
(
a
x
2
+
b
x
+
c
)
n
(ax^2+bx+c)^n
(
a
x
2
+
b
x
+
c
)
n
La fracción parcial es:
(
A
x
+
B
)
(
a
x
2
+
b
x
+
c
)
+
\frac{(Ax+B)}{(ax^2+bx+c)}+
(
a
x
2
+
b
x
+
c
)
(
A
x
+
B
)
+
(
C
x
+
D
)
(
a
x
2
+
b
x
+
c
)
2
+
\frac{(Cx+D)}{(ax^2+bx+c)^2}+
(
a
x
2
+
b
x
+
c
)
2
(
C
x
+
D
)
+
.
.
.
(
E
x
+
F
)
(
a
x
2
+
b
x
+
c
)
n
...\frac{(Ex+F)}{(ax^2+bx+c)^n}
...
(
a
x
2
+
b
x
+
c
)
n
(
E
x
+
F
)
∫
1
a
2
+
x
2
d
x
\int \frac{1}{a^2+x^2}dx
∫
a
2
+
x
2
1
d
x
1
a
a
r
c
t
a
n
(
x
a
)
+
\frac{1}{a}arctan(\frac{x}{a})+
a
1
a
rc
t
an
(
a
x
)
+
c
c
c
