← 导数表
微积分学
积分表
目录
1 运算法则
2 幂函数
3 三角函数
3.1 基本三角函数
3.2 倒數三角函数
3.3 降阶公式
3.4 显形式
3.5 反三角函数
4 指数和对数函数
4.1 降阶公式
5 反三角函数
6 双曲函数
6.1 基本双曲函数
6.2 倒数双曲函数
6.3 反双曲函数
7 杂项
8 定积分
运算法则
编辑
∫
c
⋅
f
(
x
)
d
x
=
c
⋅
∫
f
(
x
)
d
x
{\displaystyle \int c\cdot f(x)\mathrm {d} x=c\cdot \int f(x)\mathrm {d} x}
∫
(
f
(
x
)
±
g
(
x
)
)
d
x
=
∫
f
(
x
)
d
x
±
∫
g
(
x
)
d
x
{\displaystyle \int {\big (}f(x)\pm g(x){\big )}\mathrm {d} x=\int f(x)\mathrm {d} x\pm \int g(x)\mathrm {d} x}
∫
u
d
v
=
u
v
−
∫
v
d
u
{\displaystyle \int u\,dv=uv-\int v\,du}
幂函数
编辑
∫
d
x
=
x
+
C
{\displaystyle \int \mathrm {d} x=x+C}
∫
a
d
x
=
a
x
+
C
{\displaystyle \int a\,\mathrm {d} x=ax+C}
∫
x
n
d
x
=
x
n
+
1
n
+
1
+
C
(
n
≠
−
1
)
{\displaystyle \int x^{n}\mathrm {d} x={\frac {x^{n+1}}{n+1}}+C\qquad (n\neq -1)}
∫
d
x
x
=
ln
|
x
|
+
C
{\displaystyle \int {\frac {\mathrm {d} x}{x}}=\ln |x|+C}
∫
d
x
a
x
+
b
=
ln
|
a
x
+
b
|
a
+
C
(
a
≠
0
)
{\displaystyle \int {\frac {\mathrm {d} x}{ax+b}}={\frac {\ln |ax+b|}{a}}+C\qquad (a\neq 0)}
三角函数
编辑
基本三角函数
编辑
∫
sin
(
x
)
d
x
=
−
cos
(
x
)
+
C
{\displaystyle \int \sin(x)\mathrm {d} x=-\cos(x)+C}
∫
cos
(
x
)
d
x
=
sin
(
x
)
+
C
{\displaystyle \int \cos(x)\mathrm {d} x=\sin(x)+C}
∫
tan
(
x
)
d
x
=
−
ln
|
cos
(
x
)
|
+
C
{\displaystyle \int \tan(x)\mathrm {d} x=-\ln |\cos(x)|+C}
∫
sin
2
(
x
)
d
x
=
∫
1
−
cos
(
2
x
)
2
d
x
=
x
2
−
sin
(
2
x
)
4
+
C
{\displaystyle \int \sin ^{2}(x)\mathrm {d} x=\int {\frac {1-\cos(2x)}{2}}\mathrm {d} x={\frac {x}{2}}-{\frac {\sin(2x)}{4}}+C}
∫
cos
2
(
x
)
d
x
=
∫
1
+
cos
(
2
x
)
2
d
x
=
x
2
+
sin
(
2
x
)
4
+
C
{\displaystyle \int \cos ^{2}(x)\mathrm {d} x=\int {\frac {1+\cos(2x)}{2}}\mathrm {d} x={\frac {x}{2}}+{\frac {\sin(2x)}{4}}+C}
∫
tan
2
(
x
)
d
x
=
tan
(
x
)
−
x
+
C
{\displaystyle \int \tan ^{2}(x)\mathrm {d} x=\tan(x)-x+C}
倒數三角函数
编辑
∫
sec
(
x
)
d
x
=
ln
|
sec
(
x
)
+
tan
(
x
)
|
+
C
=
ln
|
tan
(
x
2
+
π
4
)
|
+
C
=
2
a
r
t
a
n
h
(
tan
(
x
2
)
)
+
C
{\displaystyle \int \sec(x)\mathrm {d} x=\ln {\Big |}\sec(x)+\tan(x){\Big |}+C=\ln \left|\tan \left({\frac {x}{2}}+{\frac {\pi }{4}}\right)\right|+C=2\mathrm {artanh} \left(\tan \left({\frac {x}{2}}\right)\right)+C}
∫
csc
(
x
)
d
x
=
−
ln
|
csc
(
x
)
+
cot
(
x
)
|
+
C
=
ln
|
tan
(
x
2
)
|
+
C
{\displaystyle \int \csc(x)\mathrm {d} x=-\ln {\Big |}\csc(x)+\cot(x){\Big |}+C=\ln \left|\tan \left({\frac {x}{2}}\right)\right|+C}
∫
cot
(
x
)
d
x
=
ln
|
sin
(
x
)
|
+
C
{\displaystyle \int \cot(x)\mathrm {d} x=\ln |\sin(x)|+C}
∫
sec
2
(
a
x
)
d
x
=
tan
(
a
x
)
a
+
C
{\displaystyle \int \sec ^{2}(ax)\mathrm {d} x={\frac {\tan(ax)}{a}}+C}
∫
csc
2
(
a
x
)
d
x
=
−
cot
(
a
x
)
a
+
C
{\displaystyle \int \csc ^{2}(ax)\mathrm {d} x=-{\frac {\cot(ax)}{a}}+C}
∫
cot
2
(
a
x
)
d
x
=
−
x
−
cot
(
a
x
)
a
+
C
{\displaystyle \int \cot ^{2}(ax)\mathrm {d} x=-x-{\frac {\cot(ax)}{a}}+C}
∫
sec
(
x
)
tan
(
x
)
d
x
=
sec
(
x
)
+
C
{\displaystyle \int \sec(x)\tan(x)\mathrm {d} x=\sec(x)+C}
∫
sec
(
x
)
csc
(
x
)
d
x
=
ln
|
tan
(
x
)
|
+
C
{\displaystyle \int \sec(x)\csc(x)\mathrm {d} x=\ln |\tan(x)|+C}
降阶公式
编辑
∫
sin
n
(
x
)
d
x
=
−
sin
n
−
1
(
x
)
cos
(
x
)
n
+
n
−
1
n
∫
sin
n
−
2
(
x
)
d
x
+
C
(
n
>
0
)
{\displaystyle \int \sin ^{n}(x)\mathrm {d} x=-{\frac {\sin ^{n-1}(x)\cos(x)}{n}}+{\frac {n-1}{n}}\int \sin ^{n-2}(x)\mathrm {d} x+C\qquad (n>0)}
∫
cos
n
(
x
)
d
x
=
−
cos
n
−
1
(
x
)
sin
(
x
)
n
+
n
−
1
n
∫
cos
n
−
2
(
x
)
d
x
+
C
(
n
>
0
)
{\displaystyle \int \cos ^{n}(x)\mathrm {d} x=-{\frac {\cos ^{n-1}(x)\sin(x)}{n}}+{\frac {n-1}{n}}\int \cos ^{n-2}(x)\mathrm {d} x+C\qquad (n>0)}
∫
tan
n
(
x
)
d
x
=
tan
n
−
1
(
x
)
(
n
−
1
)
−
∫
tan
n
−
2
(
x
)
d
x
+
C
(
n
≠
1
)
{\displaystyle \int \tan ^{n}(x)\mathrm {d} x={\frac {\tan ^{n-1}(x)}{(n-1)}}-\int \tan ^{n-2}(x)\mathrm {d} x+C\qquad (n\neq 1)}
∫
sec
n
(
x
)
d
x
=
sec
n
−
1
(
x
)
sin
(
x
)
n
−
1
+
n
−
2
n
−
1
∫
sec
n
−
2
(
x
)
d
x
+
C
(
n
≠
1
)
{\displaystyle \int \sec ^{n}(x)\mathrm {d} x={\frac {\sec ^{n-1}(x)\sin(x)}{n-1}}+{\frac {n-2}{n-1}}\int \sec ^{n-2}(x)\mathrm {d} x+C\qquad (n\neq 1)}
∫
csc
n
(
x
)
d
x
=
−
csc
n
−
1
(
x
)
cos
(
x
)
n
−
1
+
n
−
2
n
−
1
∫
csc
n
−
2
(
x
)
d
x
+
C
(
n
≠
1
)
{\displaystyle \int \csc ^{n}(x)\mathrm {d} x=-{\frac {\csc ^{n-1}(x)\cos(x)}{n-1}}+{\frac {n-2}{n-1}}\int \csc ^{n-2}(x)\mathrm {d} x+C\qquad (n\neq 1)}
∫
cot
n
(
x
)
d
x
=
−
cot
n
−
1
(
x
)
n
−
1
−
∫
cot
n
−
2
(
x
)
d
x
+
C
(
n
≠
1
)
{\displaystyle \int \cot ^{n}(x)\mathrm {d} x=-{\frac {\cot ^{n-1}(x)}{n-1}}-\int \cot ^{n-2}(x)\mathrm {d} x+C\qquad (n\neq 1)}
a
2
∫
x
n
sin
(
a
x
)
d
x
=
n
x
n
−
1
sin
(
a
x
)
−
a
x
n
cos
(
a
x
)
−
n
(
n
−
1
)
∫
x
n
−
2
sin
(
a
x
)
d
x
{\displaystyle a^{2}\int x^{n}\sin(ax)\mathrm {d} x=nx^{n-1}\sin(ax)-ax^{n}\cos(ax)-n(n-1)\int x^{n-2}\sin(ax)\mathrm {d} x}
a
2
∫
x
n
cos
(
a
x
)
d
x
=
a
x
n
sin
(
a
x
)
+
n
x
n
−
1
cos
(
a
x
)
−
n
(
n
−
1
)
∫
x
n
−
2
cos
(
a
x
)
d
x
{\displaystyle a^{2}\int x^{n}\cos(ax)\mathrm {d} x=ax^{n}\sin(ax)+nx^{n-1}\cos(ax)-n(n-1)\int x^{n-2}\cos(ax)\mathrm {d} x}
显形式
编辑
∫
sin
n
(
x
)
d
x
=
−
cos
(
x
)
2
F
1
(
1
2
,
1
−
n
2
;
3
2
;
cos
2
(
x
)
)
+
C
{\displaystyle \int \sin ^{n}(x)\mathrm {d} x=-\cos(x)_{2}F_{1}\left({\frac {1}{2}},{\frac {1-n}{2}};{\frac {3}{2}};\cos ^{2}(x)\right)+C}
∫
cos
n
(
x
)
d
x
=
−
1
n
+
1
s
g
n
(
sin
(
x
)
)
cos
n
+
1
(
x
)
2
F
1
(
1
2
,
n
+
1
2
;
n
+
3
2
;
cos
2
(
x
)
)
+
C
(
n
≠
−
1
)
{\displaystyle \int \cos ^{n}(x)\mathrm {d} x=-{\frac {1}{n+1}}\mathrm {sgn} (\sin(x))\cos ^{n+1}(x)_{2}F_{1}\left({\frac {1}{2}},{\frac {n+1}{2}};{\frac {n+3}{2}};\cos ^{2}(x)\right)+C\qquad (n\neq -1)}
∫
tan
n
(
x
)
d
x
=
1
n
+
1
tan
n
+
1
(
x
)
2
F
1
(
1
,
n
+
1
2
;
n
+
3
2
;
−
tan
2
(
x
)
)
+
C
(
n
≠
−
1
)
{\displaystyle \int \tan ^{n}(x)\mathrm {d} x={\frac {1}{n+1}}\tan ^{n+1}(x)_{2}F_{1}\left(1,{\frac {n+1}{2}};{\frac {n+3}{2}};-\tan ^{2}(x)\right)+C\qquad (n\neq -1)}
∫
csc
n
(
x
)
d
x
=
−
cos
(
x
)
2
F
1
(
1
2
,
n
+
1
2
;
3
2
;
cos
2
(
x
)
)
+
C
{\displaystyle \int \csc ^{n}(x)\mathrm {d} x=-\cos(x)_{2}F_{1}\left({\frac {1}{2}},{\frac {n+1}{2}};{\frac {3}{2}};\cos ^{2}(x)\right)+C}
∫
sec
n
(
x
)
d
x
=
sin
(
x
)
2
F
1
(
1
2
,
n
+
1
2
;
3
2
;
sin
2
(
x
)
)
+
C
{\displaystyle \int \sec ^{n}(x)\mathrm {d} x=\sin(x)_{2}F_{1}\left({\frac {1}{2}},{\frac {n+1}{2}};{\frac {3}{2}};\sin ^{2}(x)\right)+C}
∫
cot
n
(
x
)
d
x
=
−
1
n
+
1
cot
n
+
1
(
x
)
2
F
1
(
1
,
n
+
1
2
;
n
+
3
2
;
−
cot
2
(
x
)
)
+
C
(
n
≠
−
1
)
{\displaystyle \int \cot ^{n}(x)\mathrm {d} x=-{\frac {1}{n+1}}\cot ^{n+1}(x)_{2}F_{1}\left(1,{\frac {n+1}{2}};{\frac {n+3}{2}};-\cot ^{2}(x)\right)+C\qquad (n\neq -1)}
其中
2
F
1
{\displaystyle {}_{2}F_{1}}
为超几何函数，
s
g
n
{\displaystyle \mathrm {sgn} }
为符号函数。
反三角函数
编辑
∫
d
x
1
−
x
2
=
arcsin
(
x
)
+
C
{\displaystyle \int {\frac {\mathrm {d} x}{\sqrt {1-x^{2}}}}=\arcsin(x)+C}
∫
d
x
a
2
−
x
2
=
arcsin
(
x
a
)
+
C
(
a
≠
0
)
{\displaystyle \int {\frac {\mathrm {d} x}{\sqrt {a^{2}-x^{2}}}}=\arcsin \left({\tfrac {x}{a}}\right)+C\qquad (a\neq 0)}
∫
d
x
1
+
x
2
=
arctan
(
x
)
+
C
{\displaystyle \int {\frac {\mathrm {d} x}{1+x^{2}}}=\arctan(x)+C}
∫
d
x
a
2
+
x
2
=
arctan
(
x
a
)
a
+
C
(
a
≠
0
)
{\displaystyle \int {\frac {\mathrm {d} x}{a^{2}+x^{2}}}={\frac {\arctan \left({\tfrac {x}{a}}\right)}{a}}+C\qquad (a\neq 0)}
指数和对数函数
编辑
∫
e
x
d
x
=
e
x
+
C
{\displaystyle \int e^{x}\mathrm {d} x=e^{x}+C}
∫
e
a
x
d
x
=
e
a
x
a
+
C
(
a
≠
0
)
{\displaystyle \int e^{ax}\mathrm {d} x={\frac {e^{ax}}{a}}+C\qquad (a\neq 0)}
∫
a
x
d
x
=
a
x
ln
(
a
)
+
C
(
a
>
0
,
a
≠
1
)
{\displaystyle \int a^{x}\mathrm {d} x={\frac {a^{x}}{\ln(a)}}+C\qquad (a>0,a\neq 1)}
∫
ln
(
x
)
d
x
=
x
ln
(
x
)
−
x
+
C
{\displaystyle \int \ln(x)\mathrm {d} x=x\ln(x)-x+C}
∫
e
x
sin
(
x
)
d
x
=
e
x
2
(
sin
(
x
)
−
cos
(
x
)
)
+
C
{\displaystyle \int e^{x}\sin(x)\mathrm {d} x={\frac {e^{x}}{2}}(\sin(x)-\cos(x))+C}
∫
e
x
cos
(
x
)
d
x
=
e
x
2
(
sin
(
x
)
+
cos
(
x
)
)
+
C
{\displaystyle \int e^{x}\cos(x)\mathrm {d} x={\frac {e^{x}}{2}}(\sin(x)+\cos(x))+C}
降阶公式
编辑
∫
x
n
e
a
x
d
x
=
1
a
x
n
e
a
x
−
n
a
∫
x
n
−
1
e
a
x
d
x
{\displaystyle \int x^{n}e^{ax}\mathrm {d} x={\frac {1}{a}}x^{n}e^{ax}-{\frac {n}{a}}\int x^{n-1}e^{ax}\mathrm {d} x}
反三角函数
编辑
∫
arcsin
(
x
)
d
x
=
x
arcsin
(
x
)
+
1
−
x
2
+
C
{\displaystyle \int \arcsin(x)\mathrm {d} x=x\arcsin(x)+{\sqrt {1-x^{2}}}+C}
∫
arccos
(
x
)
d
x
=
x
arccos
(
x
)
−
1
−
x
2
+
C
{\displaystyle \int \arccos(x)\mathrm {d} x=x\arccos(x)-{\sqrt {1-x^{2}}}+C}
∫
arctan
(
x
)
d
x
=
x
arctan
(
x
)
−
1
2
ln
|
1
+
x
2
|
+
C
{\displaystyle \int \arctan(x)\mathrm {d} x=x\arctan(x)-{\frac {1}{2}}\ln |1+x^{2}|+C}
∫
arccsc
(
x
)
d
x
=
x
arccsc
(
x
)
+
ln
|
x
+
x
1
−
1
x
2
|
+
C
{\displaystyle \int \operatorname {arccsc}(x)\mathrm {d} x=x\operatorname {arccsc}(x)+\ln \left|x+x{\sqrt {1-{\frac {1}{x^{2}}}}}\right|+C}
∫
arcsec
(
x
)
d
x
=
x
arcsec
(
x
)
−
ln
|
x
+
x
1
−
1
x
2
|
+
C
{\displaystyle \int \operatorname {arcsec}(x)\mathrm {d} x=x\operatorname {arcsec}(x)-\ln \left|x+x{\sqrt {1-{\frac {1}{x^{2}}}}}\right|+C}
∫
arccot
(
x
)
d
x
=
x
arccot
(
x
)
+
1
2
ln
|
1
+
x
2
|
+
C
{\displaystyle \int \operatorname {arccot}(x)\mathrm {d} x=x\operatorname {arccot}(x)+{\frac {1}{2}}\ln |1+x^{2}|+C}
双曲函数
编辑
基本双曲函数
编辑
∫
sinh
(
x
)
d
x
=
−
i
∫
sin
(
i
x
)
d
x
=
cos
(
i
x
)
+
C
=
cosh
(
x
)
+
C
{\displaystyle \int \sinh(x)\mathrm {d} x=-i\int \sin(ix)\mathrm {d} x=\cos(ix)+C=\cosh(x)+C}
∫
cosh
(
x
)
d
x
=
∫
cos
(
i
x
)
d
x
=
−
i
sin
(
i
x
)
+
C
=
sinh
(
x
)
+
C
{\displaystyle \int \cosh(x)\mathrm {d} x=\int \cos(ix)\mathrm {d} x=-i\sin(ix)+C=\sinh(x)+C}
∫
tanh
(
x
)
d
x
=
−
i
∫
tan
(
i
x
)
d
x
=
ln
|
cos
(
i
x
)
|
+
C
=
ln
|
cosh
(
x
)
|
+
C
{\displaystyle \int \tanh(x)\mathrm {d} x=-i\int \tan(ix)\mathrm {d} x=\ln \left|\cos(ix)\right|+C=\ln \left|\cosh(x)\right|+C}
倒数双曲函数
编辑
∫
c
s
c
h
(
x
)
d
x
=
i
∫
csc
(
i
x
)
d
x
=
log
|
−
i
tan
(
i
x
2
)
|
+
C
=
log
|
tanh
(
x
2
)
|
+
C
{\displaystyle \int \mathrm {csch} (x)\mathrm {d} x=i\int \csc(ix)\mathrm {d} x=\log \left|-i\tan \left({\frac {ix}{2}}\right)\right|+C=\log \left|\tanh \left({\frac {x}{2}}\right)\right|+C}
∫
s
e
c
h
(
x
)
d
x
=
∫
sec
(
i
x
)
d
x
=
2
a
r
t
a
n
h
(
−
i
tan
(
x
2
i
)
)
+
C
=
2
arctan
(
tanh
(
x
2
)
)
+
C
{\displaystyle \int \mathrm {sech} (x)\mathrm {d} x=\int \sec(ix)\mathrm {d} x=2\mathrm {artanh} \left(-i\tan \left({\frac {x}{2}}i\right)\right)+C=2\arctan \left(\tanh \left({\frac {x}{2}}\right)\right)+C}
∫
c
o
t
h
(
x
)
d
x
=
i
∫
cot
(
i
x
)
d
x
=
log
|
−
i
sin
(
i
x
)
|
+
C
=
log
|
sinh
(
x
)
|
+
C
{\displaystyle \int \mathrm {coth} (x)\mathrm {d} x=i\int \cot(ix)\mathrm {d} x=\log \left|-i\sin(ix)\right|+C=\log \left|\sinh(x)\right|+C}
反双曲函数
编辑
∫
a
r
s
i
n
h
(
x
)
d
x
=
x
a
r
s
i
n
h
(
x
)
−
x
2
+
1
+
C
{\displaystyle \int \mathrm {arsinh} (x)\mathrm {d} x=x\mathrm {arsinh} (x)-{\sqrt {x^{2}+1}}+C}
∫
a
r
c
o
s
h
(
x
)
d
x
=
x
a
r
c
o
s
h
(
x
)
−
x
2
−
1
+
C
{\displaystyle \int \mathrm {arcosh} (x)\mathrm {d} x=x\mathrm {arcosh} (x)-{\sqrt {x^{2}-1}}+C}
∫
a
r
t
a
n
h
(
x
)
d
x
=
x
a
r
t
a
n
h
(
x
)
+
1
2
ln
(
1
−
x
2
)
+
C
{\displaystyle \int \mathrm {artanh} (x)\mathrm {d} x=x\mathrm {artanh} (x)+{\frac {1}{2}}\ln(1-x^{2})+C}
∫
a
r
c
s
c
h
(
x
)
d
x
=
x
a
r
c
s
c
h
(
x
)
+
|
a
r
s
i
n
h
(
x
)
|
+
C
{\displaystyle \int \mathrm {arcsch} (x)\mathrm {d} x=x\mathrm {arcsch} (x)+|\mathrm {arsinh} (x)|+C}
∫
a
r
s
e
c
h
(
x
)
d
x
=
x
a
r
s
e
c
h
(
x
)
+
arcsin
(
x
)
+
C
{\displaystyle \int \mathrm {arsech} (x)\mathrm {d} x=x\mathrm {arsech} (x)+\arcsin(x)+C}
∫
a
r
t
a
n
h
(
x
)
d
x
=
x
a
r
c
o
t
h
(
x
)
+
1
2
ln
(
x
2
−
1
)
+
C
{\displaystyle \int \mathrm {artanh} (x)\mathrm {d} x=x\mathrm {arcoth} (x)+{\frac {1}{2}}\ln(x^{2}-1)+C}
杂项
编辑
∫
|
f
(
x
)
|
d
x
=
s
g
n
(
f
(
x
)
)
∫
f
(
x
)
d
x
{\displaystyle \int |f(x)|\mathrm {d} x=\mathrm {sgn} (f(x))\int f(x)\mathrm {d} x}
，其中
s
g
n
{\displaystyle \mathrm {sgn} }
为符号函数。
定积分
编辑
∫
[
0
,
1
]
n
∏
i
=
1
n
d
x
i
1
−
∏
i
=
1
n
x
i
=
ζ
(
n
)
{\displaystyle \int _{[0,1]^{n}}{\frac {\prod _{i=1}^{n}\mathrm {d} x_{i}}{1-\prod _{i=1}^{n}x_{i}}}=\zeta (n)}
，其中整数
n
>
1
{\displaystyle n>1}
，
ζ
{\displaystyle \zeta }
为黎曼ζ函數。
∫
−
∞
∞
e
−
x
2
d
x
=
π
{\displaystyle \int _{-\infty }^{\infty }e^{-x^{2}}\mathrm {d} x={\sqrt {\pi }}}
∫
0
1
t
u
−
1
(
1
−
t
)
v
−
1
d
t
=
β
(
u
,
v
)
=
Γ
(
u
)
Γ
(
v
)
Γ
(
u
+
v
)
{\displaystyle \int _{0}^{1}t^{u-1}(1-t)^{v-1}\mathrm {d} t=\beta (u,v)={\frac {\Gamma (u)\Gamma (v)}{\Gamma (u+v)}}}
，其中
Γ
{\displaystyle \Gamma }
为Γ函数。
∫
0
∞
t
s
−
1
e
−
t
d
t
=
Γ
(
s
)
{\displaystyle \int _{0}^{\infty }t^{s-1}e^{-t}\mathrm {d} t=\Gamma (s)}
∫
0
2
π
e
u
cos
θ
d
θ
=
2
π
I
0
(
u
)
{\displaystyle \int _{0}^{2\pi }e^{u\cos \theta }\mathrm {d} \theta =2\pi I_{0}(u)}
，其中
I
0
{\displaystyle I_{0}}
为第一类修正贝塞尔函数。
∫
0
∞
sin
(
x
)
x
d
x
=
π
2
{\displaystyle \int _{0}^{\infty }{\frac {\sin(x)}{x}}\mathrm {d} x={\frac {\pi }{2}}}
← 导数表
微积分学
积分表
章节导航:
目录 ·
预备知识 ·
极限 ·
导数 ·
积分 ·
极坐标方程与参数方程 ·
数列和级数 ·
多元函数微积分 ·
扩展知识 ·
附录