UNIVERSIDAD NACIONAL DE TUMBES
DEPARTAMENTO ACADÉMICO
DE MATEMÁTICA E INFORMÁTICA
Formulario integral indefinida
Semestre académico 2022−II
Docente: Mg. Oswaldo Rafael López Michelini
Curso: Matemática II
Derivadas Integrales
d
dx
( x ) = dx = x + k
d
dx
cos ( x ) = −sen ( x ) sen ( x ) dx = − cos ( x ) + k
d
dx
sen ( x ) = cos ( x ) cos ( x ) dx = sen ( x ) + k
d
tg ( x ) = sec2 ( x ) sec ( x ) dx = tg ( x ) + k
2
dx
d
ctg ( x ) = − csc2 ( x ) csc ( x ) dx = −ctg ( x ) + k
2
dx
d
dx
csc ( x ) = − csc ( x ) ctg ( x ) csc ( x ) ctg ( x ) dx = − csc ( x ) + k
d
dx
sec ( x ) = sec ( x ) tg ( x ) sec ( x ) tg ( x ) dx = sec ( x ) + k
d x
dx
( )e = ex e
x
dx = ex + k
d m+1 x m+1
dx
( x ) = ( m + 1) x m x dx =
m
m +1
+ k , m − −1
d 1 1
arc cos ( x ) = − dx = − arc cos ( x ) + k
dx 1 − x2 1 − x2
d 1 1
arc sen ( x ) = dx = arc sen ( x ) + k
dx 1 − x2 1 − x2
d 1 1
arc tg ( x ) = 1 + x2 dx = arc tg ( x ) + k
dx 1 + x2
d 1 1
arc ctg ( x ) = − 1 + x2 dx = −arc ctg ( x ) + k
dx 1 + x2
d 1 1
arc sec ( x ) = x x2 − 1 dx = arc sec ( x ) + k
dx x x2 − 1
Derivadas Integrales
d 1 1
arc csc ( x ) = − dx = − arc csc ( x ) + k
dx x x2 − 1 x x2 − 1
d 1 1
ln ( x ) = x dx = ln x +k
dx x
d
dx
ln sec ( x ) + tg ( x ) = sec ( x )
sec ( x ) dx = ln sec ( x ) + tg ( x ) +k
d
dx
ln csc ( x ) − ctg ( x ) = csc ( x )
csc ( x ) dx = ln csc ( x ) − ctg ( x ) + k
d
dx
ln sen ( x ) = ctg ( x )
ctg ( x ) dx = ln sen ( x ) +k
d
dx
ln sec ( x ) = tg ( x )
tg ( x ) dx = ln sec ( x ) +k
