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PRIMITIVES USUELLES
f ou f(x)
xα (α ≠ –1)
Puissances Exponentielle
F ( primitive de f )
x
! +1
ln(|x|)
1/x
uα
...
π , π/2+k
...
π , π + k
...
π , π/2+k
...
π , π + k
...
ln
R
]– ∞ ,–1[ ou]–1,1[ ou ]1,+∞[
1+ x
2
1! x
Arcsin(x)
]–1,1[
2
x2 ! 1
1
(
±Argch(±x)= ln ±x +
x2 ! 1
)
]– ∞ ,–1[ ou ]1 , +∞[
±Argch(±x/a)
x 2 ! a2
1
(
Argsh(x) = ln x +
x +1
1
2
]– ∞ ,–a[ ou ]a , +∞[
(a > 0)
x2 + 1
)
R
Argsh(x/a)
R
x 2 + a2
dx
* (x ! " )
2
+#
2
=
1
#
$ x !"'
+K
% # )
(