BÀI TẬP NGUYÊN HÀM HỬU TỶ Dùng phương pháp hệ số bất định đưa về tổng 1... PTTH BÌNH MINH.
Trang 1BÀI TẬP NGUYÊN HÀM HỬU TỶ
(Dùng phương pháp hệ số bất định đưa về tổng )
1 ∫ −− ++ dx
x x
x x
6 5
9 5
2 2
2
∫ − +− −+ dx
x x
x
x x
12 11 2
9 41 2
2 3
2
x x x
∫ 3 −2 2 +
1 4
dx x
x x
x x
x
∫ 3−−66 2++1212 −+86
2 3
4
5 ∫ +− dx
x
x
1
1
6 4
6
(x ) (x ) dx
x x
∫ − +2 ++ 2
2
1 3
8 6 5
x x
x
∫ 24−5+11+6
8 ∫ (x2 + x+ )2dx
2 3 1
9 ∫ x4 −4x2 +3
dx
10 ∫ + dx x
x
1
6 3
11 ∫ ( + )
+ dx
xe x
x
x
1 1
12 ∫ + + dx
x
x x
2 sin 3
cos sin
13 ∫ + dx
x
x
9
sin 1 cot 14
x x x x
x
1 2 2
1
2 3 4
2
15 ∫ x4(1 x+ 2)
dx
16 ∫ ( −x ) dx
x
2 2
2
1
17 ∫ x(x10+1)
dx
18 ∫ +− dx x
x
1
1
6 4
HD:
1
1 1
1 ) 1 )(
1 (
) 1 (
1
1
6
2 2
2 4 2
2 2
4 6
4
−
−
−
= + +
−
− + +
=
−
+
x
x x
x x x
x x
x x
x
+
−
−
=
1 1
1 2
1 1
1
x
•
1
6
2
−
x
x
đặt t= x3
−
−
− +
= +
−
+
−
2
1 3
1 3 1 6 5
9 5
2
2
x x
x x
x x
3
4 3
1 12
11 2
9 41 2
2 3
2
−
+ +
+
−
= +
−
−
− +
x
C x
B x
A x
x x
x x
• 2x2 +41x−9= A(x+3)(x−4) (+B x−1)(x−4)+C(x−1)(x+3)
Gán x=1,x= -3 ,x=4 tìm A ,B ,C
Trang 24 3 2 ( )2 ( )2
1 1
1
1 2
1
+
+ + +
= +
= +
C x
B x
A x
x x x
( )3 2
3
2 3
4
2
6 8 8
12
6
6 12
6
−
+
− +
=
− +
−
+ +
−
x
x x x
x
x
x x
x
2 2
2
6 8
−
+
−
+
−
= +
−
x
C x
B x
A MS
x
tìm A,B,C
6
2
1 1
3 3
1 3
8 6
5
+
+ +
+
−
+
−
= +
−
+ +
X
D x
C x
B x
A x
x
x x
7
2 3
6
5
11
4
2 − + = − + −
+
x
B x
A x
x
x
8
2 2
1 1
1 2
3
1
+
− +
= +
x
9 − + = ( − )( − ) = − − −1
1 3
1 2
1 3 1
1 3
4
1
2 2
2 2 2
1
6 1 6
1
+
− +
−
=
x
x
11 ( ) x ( ( )x)
x
x e xe
x
x
+
+
= +
+
1
1 1
1
đặt t=1+xe x
t t
1 1
1 −
−
−
−
−
=
− +
−
= +
+
+
= +
+
4 sin
2 2
4 cos 2
4 cos
1 2
4 cos 2 cos
sin 2
cos sin
2
sin
3
cos
sin
2 2
π π
π
x
dx x
x
dx x
x x
dx x x
dx x
x x
đặt
−
=
4
sin x π
t
8 9
1 sin
1 sin
cos sin
1
cot
t
t t x x
xdx x
xdx
+
−
= +
=
x
x x
x
x dx
x x x
x
x
3
1 2 1
1 1 1
2 2
1
2
2 2
3
4
2
−
+ +
+
−
= + +
− +
−
x x
t= +1
Trang 315 4( 2) 4 2 1 2
1 1 1 1
1
x x
x x
16
2
1
1 1
1
x
−
−
−
=
−
1 1
1 2
1 1
1
x
• ( − ) = ( − ) (+ + ) (− −1)( +1)
2 1
1 1
1 4
1 1
1
2 2
2
x
17 ( 1) ( 1)
1
10 10
9
10 + = x x +
x x
10
1 x
t= +
18
1 1
1 1
1
6
2 2
6
4
−
−
−
=
−
+
x
x x
x
x
Nguyễn văn Phép
Gv PTTH BÌNH MINH