TABLA DE DERIVADAS E INTEGRALES.
f(x)f0(x)Rf(x)dx
xααxα−1Rxαdx =xα+1
α+ 1 +C(si α6= 1)
exexRexdx =ex+C
ln x1
xRdx
x= ln |x|+C
ax(si a > 0) axln aRaxdx =ax
ln a+C
logax1
xln a
sen xcos xRsen x dx =−cos x+C
cos x−sen xRcos x dx = sen x+C
tan x1
cos2x
arc sen x1
√1−x2
arctan x1
1 + x2
REGLAS B ´
ASICAS DE DERIVACI ´
ON E INTEGRACI´
ON
Derivada del producto: (f·g)0(x) = f0(x)g(x) + f(x)g0(x)
Regla de la cadena: £f¡g(x)¢¤0=f0¡g(x)¢g0(x)
Integraci´on por partes: Zb
a
u(x)v0(x)dx =u(x)v(x)ix=b
x=a−Zb
a
v(x)u0(x)dx
Cambio de variables “x=g(t)”: Zb
a
f(x)dx =Zg−1(b)
g−1(a)
f¡g(t)¢g0(t)dt
1