Exemples de recherche de primitives par des méthodes variées.

◦

◦
f
[a, b]
Zb
a
f(x)dx
f
I
F F (x) = Zx
a
f(t)dt
f I
a
F
f
f
Zb
a
f(x)dx
fx7→ xnx7→ √x
x7→ ln x x 7→ ex
u0
uu0eu
u0un

f
f F
(∀x∈I)F0(x) = f(x)

sin cos

(exp u)u0uαu0u0
u
◦ ◦
Rf g h
f(x) = tan x+ tan3x g(x) = 4x−2
px2−x+ 1 h(x) = (1 −x)(x2−2x+ 2)−3
◦ ◦
1
ln ]0,+∞[
◦
Rf g R
f(x) = cos4x
2sin2x g(x) = sin xcos 3x
◦ ◦
f]0,+∞[
f(x) = x3+x+ 1
x(x2+ 1)
a b c d
∀x∈]0,+∞[, f(x) = a+b
x+cx +d
x2+ 1.
f]0,+∞[
◦ ◦
Rf
f(x) = (x+px2+ 1)2
px2+ 1
u(x) = x+px2+ 1 u0
f