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∫ ln2 x
x
dx
= ∫ 1 x . ln2 x dx
1
2+1 ln3 x + c
1 3 ln3 x + c
∫ 1
x lnx dx
= ∫
1
x
lnx dx
= ln|ln x| + c
∫ x2
x 2 +1 dx
∫ (x2 +1)−1
dx
x 2 +1
∫ x2 +1
− 1
dx
x 2 +1 x 2 +1
∫ 1 − 1
dx x 2 +1
= x − arctan x + c
3. Primitives par partie :
I = ∫ u. v ′ dx
u ⟼ u′
⟹ I = u. v′ ∫ u ′ . v dx
v′ ⟼ v
Exemple :
1. I = ∫ xe x dx
u: x ⟼ u ′ = 1
v ′ : e x ⟼ v = e x
I = xe x − ∫ e x dx = xe x − e x + c