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2024年3月21日发(作者：oracle minus)
_x0001_
微积分公式
D
x
sin x=cos x
cos x = -sin x
tan x = sec
2
x
cot x = -csc
2
x
sec x = sec x tan x
C
csc x = -csc x cot x
C
1
x
D
x
sin
-1
()=
22
a
ax
sin x dx = -cos x + C
cos x dx = sin x + C
tan x dx = ln |sec x | + C
cot x dx = ln |sin x | + C
sin
-1
(-x) = -sin
-1
x
cos
-1
(-x) = - cos
-1
x
tan
-1
(-x) = -tan
-1
x
cot
-1
(-x) = - cot
-1
x
- sec
-1
x sec x dx = ln |sec x + tan x | + sec
-1
(-x) =
csc
-1
(-x) = - csc
-1
x
csc x dx = ln |csc x – cot x | +
sin
-1
x dx = x sin
-1
x+
1x
2
+C
cos
-1
x dx = x cos
-1
x-
1x
2
+C
sinh
-1
(
x
)= ln (x+
a
2
x
2
) x
R
a
cos
-1
(
1
x
)=
22
a
ax
tan
-1
x dx = x tan
-1
x-½ln (1+x
2
)+C
x
-1
cosh ()=ln (x+
x
2
a
2
) x≧1
-1-12
cot x dx = x cot x+½ln (1+x)+C
a
sec
-1
x dx = x sec
-1
x- ln
|x+
x
2
1
|+C
csc
-1
x dx = x csc
-1
x+ ln
|x+
x
2
1
|+C
coth
-1
(
tanh
-1
(
x1ax
)=ln () |x| <1
a2aax
x1xa
)=ln () |x| >1
a2axa
tan
-1
(
a
x
)=
2
a
ax
2
a
x
)=
2
2
a
ax
x
)=
a
x
cot
-1
(
sec
-1
(
a
xa
22
x1
1x
2
sech()=ln(+)0≦x
2
ax
x
≦1
-1
csc
-1
(
x
)=
a
x
a
xa
22
x1
1x
2
csch ()=ln(+) |x| >0
2
ax
x
-1
页脚内容1
_x0001_
D
x
sinh x = cosh x
cosh x = sinh x
tanh x = sech
2
x
coth x = -csch
2
x
sinh x dx = cosh x + C
cosh x dx = sinh x + C
tanh x dx = ln | cosh x |+ C
coth x dx = ln | sinh x | + C
→
d
uv
=
u
d
v
+
v
d
u
d
uv
=
uv
=
u
d
v
=
uv
-
u
d
v
+
v
d
u
v
d
u
cos
2
θ-sin
2
θ=cos2θ
sech x = -sech x tanh sech x dx = -2tan
-1
(
e
-x
) + C cos
2
θ+ sin
2
θ=1
x
cosh
2
θ-sinh
2
θ=1
1e
x
csch x dx = 2 ln || + C
2x
csch x = -csch x coth
1e
cosh
2
θ+sinh
2
θ=cosh2θ
x
1
x
D
x
sinh()=
22
a
ax
-1
3
sin 3θ=3sinθ-4sinθ
-1-1
2
sinh x dx = x sinh x-
1x
+ C
cos3θ=4cos
3
θ-3cosθ
cosh
-1
(
1
x
)=
22
a
xa
3
cosh
-1
x dx = x cosh
-1
x-
x
2
1
+ C
→sinθ= ¼ (3sinθ-sin3θ)
tanh
-1
(
a
x
)=
2
2
a
ax
a
x
)=
2
a
ax
2
coth
-1
(
sech
-1
(
a
xax
2
x
)=
a
2
→cos
3
θ=¼(3cosθ+cos3θ)
tanh x dx = x tanh x+ ½ ln |
1-x
2
|+ C
e
jx
e
jx
sin x = cos x =
2j
coth
-1
x dx = x coth
-1
x- ½ ln |
jxjx
2
ee
1-x|+ C
2
-1-1
β
sech
-1
x dx = x sech x- sin x +
xx
ee
C
sinh x = cosh x =
2
csch
-1
x dx = x csch
-1
x+ sinh
-1
x +
e
x
e
x
C
2
-1-1
csch
-1
(
x
a
)=
a
xa
2
x
2
a
R
c
γ
b
α
正弦定理:
b
c
a
= ==2R
sin
sin
sin
余弦定理: a
2
=b
2
+c
2
-2bc cosα
b
2
=a
2
+c
2
-2ac cosβ
c
2
=a
2
+b
2
-2ab cosγ
页脚内容2
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