Base Primitives
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Déterminez une fonction F qui soit une primitive de la fonction f.
5 4 3 2 x − x +1 3 4
1)
f ( x) =
3)
f ( x ) = ( x + 1)
5)
f ( x ) = (2 − x )
7)
f ( x ) = ( 2 x − 3) ( x 2 − 3x + 1)
9)
f ( x ) = (1 − 2 x )
2
12
11) f ( x ) =
5
4)
f ( x ) = ( 2 x + 1)
6)
f ( x ) = 6 x ( 3x 2 + 1)
8)
f ( x ) = 6 x (1 − x 2 )
12) f ( x ) = −
2
x3 − 3 13) f ( x ) = x2 15) f ( x ) =
f ( x ) = x 3 − 5 x 2 + 3x − 2
14) f ( x ) =
2 1 + 2 3 x 2x
17) f ( x ) = (16 x − 10 ) ( 4 x 2 − 5 x )
18) f ( x ) =
3 2
(x
2
+ x + 3)
1 x
22) f ( x ) = x −
25) f ( x ) = x 3 ax 2 + b , a ≠ 0 27) f ( x ) =
3x 2 9 + x3
29) f ( x ) = ( 3x 2 + 1) x 3 + x + 2
6
2x + 1
21) f ( x ) = x x 2 + 1
1 x
1 x2
(1 + 2 x )
20) f ( x ) =
3
3
3x 2
16) f ( x ) = ( 3x + 2 ) 2
3
1 x
24) f ( x) = 2 x + 2 x 26) f ( x ) = 28) f ( x ) =
(
2
4 1 3 − 3+ 5 4 x x x
19) f ( x ) = x x
23) f ( x ) = 3 x +
3
10) f ( x ) = 2 x + 1 −
2
1
( x − 1)
2)
2x + 1 x2 + x + 1 3x 2 5x 3 + 8
30) f ( x) = x + 2 x
)
2
2
31) f ( x) = cos ( x) ⋅ sin( x)
32) f ( x) = sin ( 3x )
33) f ( x) = 1 + tan 2 ( 2 x )
34) f ( x) = 2 sin ( x ) + 3cos ( x )
35) f ( x) = tan 2 ( x )
36) f ( x) =
37) f ( x) = sin5 ( x ) ⋅ cos ( x )
38) f ( x) = sin ( x ) ⋅ cos 4 ( x )
x x 39) f ( x) = cos 2 ⋅ sin 2 2
40) f ( x) = sin ( x ) (1 − cos ( x ) )
41) f ( x) =
43) f ( x) =
sin ( x )
(1 + cos ( x ) )
42) f ( x) = cos ( x ) − sin 2 ( x ) ⋅ cos ( x )
2
cos ( x )
( 4sin ( x ) − 1)
x −1 45) f ( x) = 2 x − 2x + 4
1 cos ( 4 x ) 2
3
44) f ( x) =
46)
1 2x − 5
( x + 1) f ( x) =
2
x
47) f ( x) =
3x x +1
48) f ( x) =
1 ln ( x ) x
49) f ( x) =
2x −1 x −x−2
50) f ( x) =
x x −4
51) f ( x) =
1 x ⋅ ln ( x )
52) f ( x) =
53) f ( x) =
4x + 2 x + x +1
54) f ( x) = x ⋅ e x
2
2
2
2
− sin ( x ) cos ( x ) 2
1
ex 55) f ( x) = 2 x 57) f ( x) =
e
2x
2x
56) f ( x) = x 2 ⋅ e x
3
5 4 3 2 x − x +1 3 4
1)
f ( x) =
3)
f ( x ) = ( x + 1)
5)
f ( x ) = (2 − x )
7)
f ( x ) = ( 2 x − 3) ( x 2 − 3x + 1)
9)
f ( x ) = (1 − 2 x )
2
12
11) f ( x ) =
5
4)
f ( x ) = ( 2 x + 1)
6)
f ( x ) = 6 x ( 3x 2 + 1)
8)
f ( x ) = 6 x (1 − x 2 )
12) f ( x ) = −
2
x3 − 3 13) f ( x ) = x2 15) f ( x ) =
f ( x ) = x 3 − 5 x 2 + 3x − 2
14) f ( x ) =
2 1 + 2 3 x 2x
17) f ( x ) = (16 x − 10 ) ( 4 x 2 − 5 x )
18) f ( x ) =
3 2
(x
2
+ x + 3)
1 x
22) f ( x ) = x −
25) f ( x ) = x 3 ax 2 + b , a ≠ 0 27) f ( x ) =
3x 2 9 + x3
29) f ( x ) = ( 3x 2 + 1) x 3 + x + 2
6
2x + 1
21) f ( x ) = x x 2 + 1
1 x
1 x2
(1 + 2 x )
20) f ( x ) =
3
3
3x 2
16) f ( x ) = ( 3x + 2 ) 2
3
1 x
24) f ( x) = 2 x + 2 x 26) f ( x ) = 28) f ( x ) =
(
2
4 1 3 − 3+ 5 4 x x x
19) f ( x ) = x x
23) f ( x ) = 3 x +
3
10) f ( x ) = 2 x + 1 −
2
1
( x − 1)
2)
2x + 1 x2 + x + 1 3x 2 5x 3 + 8
30) f ( x) = x + 2 x
)
2
2
31) f ( x) = cos ( x) ⋅ sin( x)
32) f ( x) = sin ( 3x )
33) f ( x) = 1 + tan 2 ( 2 x )
34) f ( x) = 2 sin ( x ) + 3cos ( x )
35) f ( x) = tan 2 ( x )
36) f ( x) =
37) f ( x) = sin5 ( x ) ⋅ cos ( x )
38) f ( x) = sin ( x ) ⋅ cos 4 ( x )
x x 39) f ( x) = cos 2 ⋅ sin 2 2
40) f ( x) = sin ( x ) (1 − cos ( x ) )
41) f ( x) =
43) f ( x) =
sin ( x )
(1 + cos ( x ) )
42) f ( x) = cos ( x ) − sin 2 ( x ) ⋅ cos ( x )
2
cos ( x )
( 4sin ( x ) − 1)
x −1 45) f ( x) = 2 x − 2x + 4
1 cos ( 4 x ) 2
3
44) f ( x) =
46)
1 2x − 5
( x + 1) f ( x) =
2
x
47) f ( x) =
3x x +1
48) f ( x) =
1 ln ( x ) x
49) f ( x) =
2x −1 x −x−2
50) f ( x) =
x x −4
51) f ( x) =
1 x ⋅ ln ( x )
52) f ( x) =
53) f ( x) =
4x + 2 x + x +1
54) f ( x) = x ⋅ e x
2
2
2
2
− sin ( x ) cos ( x ) 2
1
ex 55) f ( x) = 2 x 57) f ( x) =
e
2x
2x
56) f ( x) = x 2 ⋅ e x
3
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