(一) 含有ax b +的积分()0a ≠ 1.
11ln dx ax b C ax b a =+++⎰ 2.()()
()()1111ax b dx ax b C a μμμμ++=++≠-+⎰ 3.()2
1ln x dx ax b b ax b C ax b a =+-+++⎰ 4.()()2223112ln 2x dx ax b b ax b b ax b C ax b a ⎡⎤=+-++++⎢⎥+⎣⎦
⎰ 5.()11ln ax b dx C x ax b b x
+=-++⎰ 6.
()2211ln a ax b dx C x ax b bx b x +=-+++⎰ 7.()
221ln x b dx ax b C a ax b ax b ⎛⎫=+++ ⎪+⎝⎭+⎰ 8.()
222312ln x b dx ax b b ax b C a ax b ax b ⎛⎫=+-+-+ ⎪++⎝⎭⎰ 9.()
()22111ln ax b dx C b ax b b x x ax b +=-+++⎰
(二)的积分
10.C =
11.(223215ax b C a =-⎰
12.(2223
215128105x a x abx b C a =-+⎰
13.(
2223ax b C a =-
14.(2222
3234815a x abx b C a =-+
15.
(
)
()
C b
C b
⎧
+>
=
<
16.
2
a
dx
b
=-
17.b
=
18.
2
a
=+
(三)含有22
x a
±的积分
19.
22
11
arctan
x
dx C
x a a a
=+
+
⎰
20.
()()()()()
11
2
2222222
1231
21
21
n n n
x n
dx dx
n a
x a n a x a x a
--
-
=+
-
+-++
⎰⎰
21.
22
11
ln
2
x a
dx C
x a a x a
-
=+
-+
⎰
(四)含有()
20
ax b a
+>的积分
22.
(
)
()
2
1
C b
dx
ax b
C b
⎧
+>
⎪
⎪
=⎨
+
+<
⎰
23.2
2
1
ln
2
指数函数积分
x
dx ax b C
ax b a
=++
+
⎰
24.
2
22
1
x x b
dx dx
ax b a a ax b
=-
++
⎰⎰
25.()22
2
11
ln
2
x
dx C
b ax b
x ax b
=+
+
+
⎰
26.()2
22
111
a
dx dx
bx b ax b
x ax b
=--
+
+
⎰⎰
27.()
22223211ln 22ax b a dx C b x bx x ax b +=-++⎰ 28.()()22221
1122x dx dx b ax b
b ax b ax b =++++⎰⎰ (五)含有()2
0ax bx c a ++>的积分
29.(
)()222414C b ac dx ax bx c C b ac ⎧<⎪⎪=⎨++>⎰ 30.22211ln 22x b dx ax bx c dx ax bx c a a ax bx c
=++-++++⎰⎰ (六)
含有)0a >的积分
31.(1arsh ln x C x C a =+=++ 32.
C =+
33.C =
34.
C =+
35.(22ln 2a x C =+
36.
(2
ln x C =++
37.1ln C a =+
38.2C a x =-+
39.(2ln 2a x C =++
40.
(
(224325ln 88x x a a x C =+++
41.
C =
⎰
42.(
(4222ln 88x a x x a x C =+++⎰
43.ln a a C x x
=+⎰
44.(ln x C =++ (
七)含有)0a >的积分
45.1arch ln x x C x C x a =+= 46.
C =+
47.C =
48.
C =
49.2
2ln 2a x C =+ 50.
2
ln x C =++
51.1arccos a C a x
=+
52.C =+
53.2ln 2a x C =+
54.
(
224325ln 88
x x a a x C =-+
55.
C =⎰
56.(
4222ln 88x a x x a x C =-+⎰
57.arccos a a C x
=+
58.ln x C =++ (
八)含有)0a >的积分
59.arcsin x C a
=+ 60.
C =
61.C =
62.
C =+
63.2
2arcsin 2a x C a =+
64.
2
arcsin x C a =-+
65.1C a =
66.2C a x =-+
67.
2arcsin 2a x C a =+
68.
(224352arcsin 88x x a
x a C a =-
+
69.C =-⎰

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