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统计数据
常见 微积分 问题
integral of (x+2)/(sqrt(x^2+4x))
∫
x
+
2
√
x
2
+
4
x
dx
integral of 1/(1+sqrt(3x))
∫
1
1
+
√
3
x
dx
derivative y=sin(tan(3x))
derivative
y
=
sin
(
tan
(
3
x
)
)
integral of x^2e^{-14x}
∫
x
2
e
−
1
4
x
dx
integral from 5 to 8 of 1
∫
5
8
1
(\partial)/(\partial x)(cos^7(x^6y^6))
∂
∂
x
(
cos
7
(
x
6
y
6
)
)
derivative of 2sin(2x-ln(3x+1))
d
dx
(
2
sin
(
2
x
)
−
ln
(
3
x
+
1
)
)
integral of (8ln(x))/(x^2)
∫
8
ln
(
x
)
x
2
dx
derivative of ((40x^5)/(e^x))
d
dx
(
(
4
0
x
5
)
e
x
)
t^2(dy)/(dt)-t=1+y+ty,y(1)=4
t
2
dy
dt
−
t
=
1
+
y
+
ty
,
y
(
1
)
=
4
(\partial)/(\partial x)(xln(xy))
∂
∂
x
(
x
ln
(
xy
)
)
integral of 4/(x^2+9)
∫
4
x
2
+
9
dx
y^{''}-4y^'+4y=6t^2e^{2t}
y
′
′
−
4
y
′
+
4
y
=
6
t
2
e
2
t
derivative f(x)=ln(ex)
derivative
f
(
x
)
=
ln
(
ex
)
limit as x approaches-3 of (2x+8)/(x+3)
lim
x
→
−
3
(
2
x
+
8
x
+
3
)
derivative of (x^4-12x^2/((x^2-4)^2))
d
dx
(
x
4
−
1
2
x
2
(
x
2
−
4
)
2
)
(\partial)/(\partial x)(arcsin(a/b sin(x)))
∂
∂
x
(
arcsin
(
a
b
sin
(
x
)
)
)
inverse拉普拉斯 (48)/(s^5)
inverselaplace
4
8
s
5
integral of e^{2x^3-1}x^2
∫
e
2
x
3
−
1
x
2
dx
integral of 3cos^4(x)
∫
3
cos
4
(
x
)
dx
limit as x approaches 0 of (x^2-1)/(x+1)
lim
x
→
0
(
x
2
−
1
x
+
1
)
integral of 8/(3cos(2x)+1)
∫
8
3
cos
(
2
x
)
+
1
dx
limit as x approaches 2+of 1/(x^2-4)
lim
x
→
2
+
(
1
x
2
−
4
)
integral of (ln(sin(x)))/(tan(x))
∫
ln
(
sin
(
x
)
)
tan
(
x
)
dx
derivative x/9-9/x
derivative
x
9
−
9
x
f(x)=e^{cos(x)}
f
(
x
)
=
e
cos
(
x
)
tangent x^2+2y^2=3,(1,1)
tangent
x
2
+
2
y
2
=
3
,
(
1
,
1
)
integral of (5-4e^x+3/(x^2))
∫
(
5
−
4
e
x
+
3
x
2
)
dx
limit as h approaches 0 of ((2h^2+6h))/h
lim
h
→
0
(
(
2
h
2
+
6
h
)
h
)
limit as x approaches 0 of f(x)*g(x)
lim
x
→
0
(
f
(
x
)
·
g
(
x
)
)
derivative of (-x^2/4)
d
dx
(
−
x
2
4
)
derivative f(x)=(4z^4+2z^2+1)(2z^3-z)
derivative
f
(
x
)
=
(
4
z
4
+
2
z
2
+
1
)
(
2
z
3
−
z
)
integral of-1/(2x+1)
∫
−
1
2
x
+
1
dx
derivative of-(2x/((-3+x^2)^2))
d
dx
(
−
2
x
(
−
3
+
x
2
)
2
)
integral of (sec^2(x)+x)
∫
(
sec
2
(
x
)
+
x
)
dx
integral from b to a of f(x)
∫
b
a
f
(
x
)
dx
integral of (x^3+x+1)/(x^2-x)
∫
x
3
+
x
+
1
x
2
−
x
dx
limit as x approaches 0 of e^{x^2}
lim
x
→
0
(
e
x
2
)
integral from 1 to 2 of x^3ln(x)
∫
1
2
x
3
ln
(
x
)
dx
integral of 2sin(x)+1
∫
2
sin
(
x
)
+
1
dx
integral from 0 to pi/3 of (sec^2(x))
∫
0
π
3
(
sec
2
(
x
)
)
dx
derivative y=sin(xcos(x))
derivative
y
=
sin
(
x
cos
(
x
)
)
derivative of sqrt(x)(x-1^2)
d
dx
(
√
x
(
x
−
1
)
2
)
(\partial)/(\partial x)((4x)/(5+y))
∂
∂
x
(
4
x
5
+
y
)
derivative 1/(c+ke^c)
derivative
1
c
+
ke
c
y^{''}-8y^'+16y=((10.5e^{4t}))/((t^2+1))
y
′
′
−
8
y
′
+
1
6
y
=
(
1
0
.
5
e
4
t
)
(
t
2
+
1
)
derivative 55.6-22.1v^{0.16}
derivative
5
5
.
6
−
2
2
.
1
v
0
.
1
6
((t^3)/3)^'
(
t
3
3
)
′
limit as x approaches 4 of (x^3+8)/(x+2)
lim
x
→
4
(
x
3
+
8
x
+
2
)
面积 x=-2,x=2,y=5x,y=x^2-6
area
x
=
−
2
,
x
=
2
,
y
=
5
x
,
y
=
x
2
−
6
limit as x approaches 0 of (e^{2x}-1)/(sin(x))
lim
x
→
0
(
e
2
x
−
1
sin
(
x
)
)
(\partial)/(\partial y)(xy+x/y)
∂
∂
y
(
xy
+
x
y
)
integral from-2 to 3 of 6/(x^4)
∫
−
2
3
6
x
4
dx
integral of (sqrt(x)ln(2x))
∫
(
√
x
ln
(
2
x
)
)
dx
limit as x approaches 3 of 3x-1
lim
x
→
3
(
3
x
−
1
)
integral of cos^2(a)x
∫
cos
2
(
a
)
xdx
integral from 1 to infinity of x/(x^2+3)
∫
1
∞
x
x
2
+
3
dx
integral of sqrt(1-16x^2)
∫
√
1
−
1
6
x
2
dx
derivative arcsin(x/2)
derivative
arcsin
(
x
2
)
(dy)/(dx)=(2x)/(x+2)
dy
dx
=
2
x
x
+
2
integral of (12)/(x^5)
∫
1
2
x
5
dx
limit as n approaches infinity of e^{3n^2}
lim
n
→
∞
(
e
3
n
2
)
(\partial)/(\partial y)(sqrt(17-x^2-4y^2))
∂
∂
y
(
√
1
7
−
x
2
−
4
y
2
)
derivative of ae^{x/2}+be^{-x}
d
dx
(
ae
x
2
+
be
−
x
)
integral of 1/2 (1-cos(x))^2
∫
1
2
(
1
−
cos
(
x
)
)
2
dx
integral from 0 to 1 of xsqrt(4+5x)
∫
0
1
x
√
4
+
5
x
dx
derivative of cos(xln(x^2+1)-ln(x^4+1))
d
dx
(
cos
(
x
)
ln
(
x
2
+
1
)
−
ln
(
x
4
+
1
)
)
y^'=-y^3,y(0)=a
y
′
=
−
y
3
,
y
(
0
)
=
a
泰勒 1+x^2
taylor
1
+
x
2
derivative of (e^x/(9x^2))
d
dx
(
e
x
9
x
2
)
limit as x approaches-1 of (x+1)/(x^2+x)
lim
x
→
−
1
(
x
+
1
x
2
+
x
)
sum from n=0 to infinity}((-1)^{n+1}(x-1)^{n+1 of)/(n+1)
∑
n
=
0
∞
(
−
1
)
n
+
1
(
x
−
1
)
n
+
1
n
+
1
tangent (sin(t))/(4+4cos(t))
tangent
sin
(
t
)
4
+
4
cos
(
t
)
integral of (x^4)/((sqrt(1-x^2))^3)
∫
x
4
(
√
1
−
x
2
)
3
dx
derivative x^2ln(3x)
derivative
x
2
ln
(
3
x
)
integral of sqrt(x)sin(sqrt(x)y)
∫
√
x
sin
(
√
x
y
)
dy
limit as x approaches-1 of 2x-3
lim
x
→
−
1
(
2
x
−
3
)
limit as x approaches infinity of (1+8/x)^{x/9}
lim
x
→
∞
(
(
1
+
8
x
)
x
9
)
limit as x approaches 0 of ln(1/x)
lim
x
→
0
(
ln
(
1
x
)
)
inverse拉普拉斯 (4se^{-s})/(2s^2+32)
inverselaplace
4
se
−
s
2
s
2
+
3
2
integral of (x^2-x+12)/(x^3+2x)
∫
x
2
−
x
+
1
2
x
3
+
2
x
dx
integral of (x+5)/x
∫
x
+
5
x
dx
derivative of 1/3 sin(x)
d
dx
(
1
3
sin
(
x
)
)
derivative f(x)=(3/5 x)^9
derivative
f
(
x
)
=
(
3
5
x
)
9
derivative of (21/(64x^{11/4)})
d
dx
(
2
1
6
4
x
1
1
4
)
integral from 0 to 1 of x^2((2(x+1))/3)
∫
0
1
x
2
(
2
(
x
+
1
)
3
)
dx
limit as x approaches pi-of ln(x)
lim
x
→
π
−
(
ln
(
x
)
)
integral from 0 to 4 of 2pix(4x-x^2)
∫
0
4
2
π
x
(
4
x
−
x
2
)
dx
斜率 y^4-4y^2=x^4-9x^2,(3,-2)
slope
y
4
−
4
y
2
=
x
4
−
9
x
2
,
(
3
,
−
2
)
integral of x^2(1-x)^6
∫
x
2
(
1
−
x
)
6
dx
derivative of-1/(x^{7.7})
d
dx
(
−
1
x
7
.
7
)
derivative of (|x|/x)
d
dx
(
|
x
|
x
)
integral of (x^3-8x+1)/((2x)^4)
∫
x
3
−
8
x
+
1
(
2
x
)
4
dx
xy^'+y=-2xy^2,y(1)=-5
xy
′
+
y
=
−
2
xy
2
,
y
(
1
)
=
−
5
derivative of tanh(sqrt(x))
d
dx
(
tanh
(
√
x
)
)
integral of 1/(3-5x)
∫
1
3
−
5
x
dx
tangent 7x-x^2(1.6)
tangent
7
x
−
x
2
(
1
.
6
)
面积 y=x^2-1,y=3
area
y
=
x
2
−
1
,
y
=
3
(\partial)/(\partial x)(0.4x-4)
∂
∂
x
(
0
.
4
x
−
4
)
(d^2y)/(dx^2)-4y=0
d
2
y
dx
2
−
4
y
=
0
1
..
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1220
1221
1222
1223
..
2459