Taula d’integrals
Quan la funci´o que volem integrar ´es la derivada d’una de les funcions b`asiques, diem que la integral ´es
una integral immediata. Les integrals quasi-immediates es calculen a partir de les integrals immediates i
la regla de la cadena
Zg0(f(x)) f0(x)dx =g(f(x)) + c, c ∈R
Integrals immediates Integrals quasi-immediates
Zdx =x+cZf0(x)dx =f(x) + c
Zxndx =xn+1
n+ 1 +c, n 6= 1 Zf0(x)(f(x))ndx =(f(x))n+1
n+ 1 +c, n 6= 1
Z1
xdx = ln |x|+cZf0(x)
f(x)dx = ln |f(x)|+c
Zexdx =ex+cZf0(x)ef(x)dx =ef(x)+c
Zaxdx =ex+cZf0(x)af(x)dx =af(x)
ln a+c
Zcos x dx = sin x+cZf0(x) cos(f(x)) dx = sin(f(x)) + c
Zsin x dx =−cos x+cZf0(x) sin(f(x)) dx =−cos(f(x)) + c
Z1
cos2xdx = tan x+cZf0(x)
cos2(f(x)) dx = tan(f(x)) + c
Z(1 + tan2x)dx = tan x+cZf0(x)(1 + tan2f(x)) dx = tan(f(x)) + c
Z1
sin2xdx =−cot x+cZf0(x)
sin2(f(x)) dx =−cot(f(x)) + c
Z(1 + cot2x)dx =−cot x+cZf0(x)(1 + cot2f(x)) dx =−cot(f(x)) + c
Z1
√a2−x2dx = arcsin x
a+c=Zf0(x)
pa2−(f(x))2dx = arcsin f(x)
a+c=
Z1
√a2−x2dx =−arccos x
a+cZf0(x)
pa2−(f(x))2dx =−arccos f(x)
a+c
Zdx
a2+x2=1
aarctan x
a+cZf0(x)
a2+ (f(x))2dx =1
aarctan f(x)
a+c