§ 1.2 基本积分公式
CxFdxxf )()(
F?(x)=f(x)
例如,
)1(
1
x
x?
Cxdxx
1
1
(1)
基本积分表
Cxdx)2(
Cxdxx
1)3(
1
Cdx 0)1(
(1)
Cxdxx ||ln1)4(
( x? 0)
Cedxe xx)5(
Caadxa
xx
ln)6(
(a >0,a? 1)
Cxx d x s inc o s)7(
Cxx d x c o ss in)8(
Cxdx
x
x d x t a n
co s
1s e c)9(
2
2
Cxdx
x
xdx co t
s i n
1cs c)10(
2
2
Cxxdxx s e ct a ns e c)11(
Cxxdxx c s cc o tc s c)12(
Cxdx
x
a r c s in
1
1)13(
2=?arccosx+C?
Cxdx
x
a rct a n
1
1)14(
2=?arccotx+C?
例 1 求积分?
dxxx 2
解,? dxxx 2 dxx 25
Cxdxx
1
1
根据积分公式
dxxx 2 Cx?
1
2
5
1
2
5
Cx 2
7
7
2
CxFdxxf )()(
F?(x)=f(x)
例如,
)1(
1
x
x?
Cxdxx
1
1
(1)
基本积分表
Cxdx)2(
Cxdxx
1)3(
1
Cdx 0)1(
(1)
Cxdxx ||ln1)4(
( x? 0)
Cedxe xx)5(
Caadxa
xx
ln)6(
(a >0,a? 1)
Cxx d x s inc o s)7(
Cxx d x c o ss in)8(
Cxdx
x
x d x t a n
co s
1s e c)9(
2
2
Cxdx
x
xdx co t
s i n
1cs c)10(
2
2
Cxxdxx s e ct a ns e c)11(
Cxxdxx c s cc o tc s c)12(
Cxdx
x
a r c s in
1
1)13(
2=?arccosx+C?
Cxdx
x
a rct a n
1
1)14(
2=?arccotx+C?
例 1 求积分?
dxxx 2
解,? dxxx 2 dxx 25
Cxdxx
1
1
根据积分公式
dxxx 2 Cx?
1
2
5
1
2
5
Cx 2
7
7
2