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统计数据
常见 微积分 问题
derivative of 4-e^{2x}
d
dx
(
4
−
e
2
x
)
integral of (1-cos(2t))(cos(t))t
∫
(
1
−
cos
(
2
t
)
)
(
cos
(
t
)
)
tdt
sum from n=0 to infinity of n^2e^{-7n}
∑
n
=
0
∞
n
2
e
−
7
n
integral of cos^3(X)sin^2(X)DX
∫
cos
3
(
X
)
sin
2
(
X
)
DXdX
integral of 2cos(x)-2sin(x)
∫
2
cos
(
x
)
−
2
sin
(
x
)
dx
integral of-2xcos(8x)
∫
−
2
x
cos
(
8
x
)
dx
derivative sqrt(3x-5)
derivative
√
3
x
−
5
inverse拉普拉斯 5/(s(4s^2+4s+1))
inverselaplace
5
s
(
4
s
2
+
4
s
+
1
)
limit as x approaches 3 of-xsqrt(6x-8)
lim
x
→
3
(
−
x
√
6
x
−
8
)
integral from-infinity to 1 of 3^x
∫
−
∞
1
3
x
dx
derivative of 3pi^8
d
dx
(
3
π
8
)
tangent f(x)=-4x^{1/2}-10,\at x=9
tangent
f
(
x
)
=
−
4
x
1
2
−
1
0
,
at
x
=
9
tangent 8x+7cos(x)
tangent
8
x
+
7
cos
(
x
)
tangent f(x)=2x^2-5x+3,\at x=2
tangent
f
(
x
)
=
2
x
2
−
5
x
+
3
,
at
x
=
2
d/(dt)((8t)/(8+sqrt(t)))
d
dt
(
8
t
8
+
√
t
)
integral of 1/(sqrt(t^2-8t+20))
∫
1
√
t
2
−
8
t
+
2
0
dt
limit as x approaches 0 of 1/(cos(3x))
lim
x
→
0
(
1
cos
(
3
x
)
)
y^{''}+7y^'-8y=0
y
′
′
+
7
y
′
−
8
y
=
0
(dy)/(dx)=6x^5e^{-y}
dy
dx
=
6
x
5
e
−
y
derivative of sin(sqrt(1+x^2))
d
dx
(
sin
(
√
1
+
x
2
)
)
derivative y=(2x^2+6x+4)/(sqrt(x))
derivative
y
=
2
x
2
+
6
x
+
4
√
x
limit as x approaches 1 of (x-3)^2
lim
x
→
1
(
(
x
−
3
)
2
)
(\partial)/(\partial u)(2ucos(v))
∂
∂
u
(
2
u
cos
(
v
)
)
y^'+y-4cos(x)=0
y
′
+
y
−
4
cos
(
x
)
=
0
inverse拉普拉斯 s/((s+2)(s+3))
inverselaplace
s
(
s
+
2
)
(
s
+
3
)
derivative of ((3x-1/(x^2+3))^2)
d
dx
(
(
3
x
−
1
x
2
+
3
)
2
)
limit as x approaches 0 of (1-cos(x))/(5x^2)
lim
x
→
0
(
1
−
cos
(
x
)
5
x
2
)
y^'-y=10te^{2t}
y
′
−
y
=
1
0
te
2
t
integral of 1/(y^2+1)
∫
1
y
2
+
1
dy
derivative of e^y+y/x
d
dx
(
e
y
+
y
x
)
limit as x approaches-2 of (2x^2+3x)/(x-3)
lim
x
→
−
2
(
2
x
2
+
3
x
x
−
3
)
derivative of arcsin(8x+arccos(8x))
d
dx
(
arcsin
(
8
x
)
+
arccos
(
8
x
)
)
y^{''}-6y^'-16y=0
y
′
′
−
6
y
′
−
1
6
y
=
0
derivative of 4x^{0.75}*(240-2x^{0.5})
d
dx
(
4
x
0
.
7
5
·
(
2
4
0
−
2
x
)
0
.
5
)
integral from-3 to-1 of 5/(x^4)
∫
−
3
−
1
5
x
4
dx
normal f(x)=(27)/(5x^2)-3/2 ,\at x=1
normal
f
(
x
)
=
2
7
5
x
2
−
3
2
,
at
x
=
1
integral from 1 to 5 of (x^2+5)/(6x-x^2)
∫
1
5
x
2
+
5
6
x
−
x
2
dx
(dy}{dx}=\frac{(xy+x))/y
dy
dx
=
(
xy
+
x
)
y
y^{''}+2piy^'+pi^2y=0
y
′
′
+
2
π
y
′
+
π
2
y
=
0
(dy)/(dx)=(x^2-2)/(3y)
dy
dx
=
x
2
−
2
3
y
integral of ((x^4+2))/(x^3+9x)
∫
(
x
4
+
2
)
x
3
+
9
x
dx
integral of (θ^8+sec^2(θ))
∫
(
θ
8
+
sec
2
(
θ
)
)
d
θ
泰勒 sin(x),(2pi)/3
taylor
sin
(
x
)
,
2
π
3
integral of (4x-sin(x))
∫
(
4
x
−
sin
(
x
)
)
dx
integral from 5 to 1 of (-4x+1)
∫
5
1
(
−
4
x
+
1
)
dx
limit as x approaches 3-of 2
lim
x
→
3
−
(
2
)
f^'=f^3
f
′
=
f
3
derivative of x^{-2}ln(x)
d
dx
(
x
−
2
ln
(
x
)
)
integral from 1 to 4 of x/(x^2+6x+13)
∫
1
4
x
x
2
+
6
x
+
1
3
dx
(\partial)/(\partial x)(arctan(3x))
∂
∂
x
(
arctan
(
3
x
)
)
limit as x approaches infinity of (sqrt(4x^6-x))/(x^3+2)
lim
x
→
∞
(
√
4
x
6
−
x
x
3
+
2
)
limit as x approaches infinity of 2xe^{-2x}
lim
x
→
∞
(
2
xe
−
2
x
)
derivative g(x)=x(x-4)^3
derivative
g
(
x
)
=
x
(
x
−
4
)
3
limit as x approaches 0 of (7x^4-x^3)/x
lim
x
→
0
(
7
x
4
−
x
3
x
)
integral of e^{tx}
∫
e
tx
dx
integral of 4e^{3x}
∫
4
e
3
x
dx
4y^{''}-y^'+1=0
4
y
′
′
−
y
′
+
1
=
0
limit as t approaches infinity of sin(t)
lim
t
→
∞
(
sin
(
t
)
)
integral of (z^2)/(\sqrt[3]{1+z^3)}
∫
z
2
3
√
1
+
z
3
dz
integral of x^4ln(x^2)
∫
x
4
ln
(
x
2
)
dx
derivative f(x)=(3x-1)/(x+2)
derivative
f
(
x
)
=
3
x
−
1
x
+
2
derivative 4/t
derivative
4
t
integral from 0 to 6 of 1/(sqrt(x-3))
∫
0
6
1
√
x
−
3
dx
partialfraction (x^2)/(3x+1)
partialfraction
x
2
3
x
+
1
integral of cos((npix)/(2pi))
∫
cos
(
n
π
x
2
π
)
dx
limit as x approaches 2-of 3/(2-x)
lim
x
→
2
−
(
3
2
−
x
)
f^'(x)=2x^2+x-1
f
′
(
x
)
=
2
x
2
+
x
−
1
integral of sqrt(64-x^2)
∫
√
6
4
−
x
2
dx
derivative of 5/(sqrt(x+8))
d
dx
(
5
√
x
+
8
)
derivative of ln(4sin^2(x))
d
dx
(
ln
(
4
sin
2
(
x
)
)
)
derivative of 3^x-2^x
d
dx
(
3
x
−
2
x
)
derivative of xsqrt(6-x^2)
d
dx
(
x
√
6
−
x
2
)
integral of-sqrt(2)sin(t)
∫
−
√
2
sin
(
t
)
dt
sum from n=2 to infinity of 7/(2^n)
∑
n
=
2
∞
7
2
n
integral from 0 to 1 of (32)/(x^2-64)
∫
0
1
3
2
x
2
−
6
4
dx
inverse拉普拉斯 1/(s^2*(s+1))
inverselaplace
1
s
2
·
(
s
+
1
)
derivative f(x)= 7/2 x^{2/7}
derivative
f
(
x
)
=
7
2
x
2
7
limit as x approaches 8 of (x^2-64)/(x^2-8x)
lim
x
→
8
(
x
2
−
6
4
x
2
−
8
x
)
(\partial)/(\partial x)(sqrt(2x+1))
∂
∂
x
(
√
2
x
+
1
)
integral of (8/(x^3))
∫
(
8
x
3
)
dx
tangent f(x)=2x^3-3x^2-16x+3,\at x=-4
tangent
f
(
x
)
=
2
x
3
−
3
x
2
−
1
6
x
+
3
,
at
x
=
−
4
derivative of (e^x^{sin(x)})
d
dx
(
(
e
x
)
sin
(
x
)
)
tangent y=x^3-7x^2+16x+7
tangent
y
=
x
3
−
7
x
2
+
1
6
x
+
7
斜率 (0,-2),(5,-4)
slope
(
0
,
−
2
)
,
(
5
,
−
4
)
integral from 0 to 3 of 2e^{-3x}
∫
0
3
2
e
−
3
x
dx
integral of x^3sin(x^2)
∫
x
3
sin
(
x
2
)
dx
(\partial)/(\partial x)(cos^9(x^4y^8))
∂
∂
x
(
cos
9
(
x
4
y
8
)
)
integral from 1 to 3 of sqrt(x+2)
∫
1
3
√
x
+
2
dx
d/(dt)((t^2)/2)
d
dt
(
t
2
2
)
derivative of e^{(x^2-x})
d
dx
(
e
(
x
2
−
x
)
)
integral from 0 to 3 of x-(x^2-2x)
∫
0
3
x
−
(
x
2
−
2
x
)
dx
integral of sqrt(7+6x-x^2)
∫
√
7
+
6
x
−
x
2
dx
(dy)/(dx)=2e^x
dy
dx
=
2
e
x
limit as x approaches-3 of ((x+2))/(x+3)
lim
x
→
−
3
(
(
x
+
2
)
x
+
3
)
(\partial)/(\partial x)(x^2y+2xz+2y^2+6z+9)
∂
∂
x
(
x
2
y
+
2
xz
+
2
y
2
+
6
z
+
9
)
(\partial)/(\partial t)(xzt^2sqrt(y+1))
∂
∂
t
(
xzt
2
√
y
+
1
)
integral of e^xsqrt(1+e^x)
∫
e
x
√
1
+
e
x
dx
derivative A/(y^{10)}+Be^y
derivative
A
y
1
0
+
Be
y
面积 y=x+1,y=x^2-1
area
y
=
x
+
1
,
y
=
x
2
−
1
integral of (x^2-x+30)/(x^3+5x)
∫
x
2
−
x
+
3
0
x
3
+
5
x
dx
1
..
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..
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