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统计数据
常见 微积分 问题
integral of (3x-4)e^{-x}
∫
(
3
x
−
4
)
e
−
x
dx
integral of 8x+4
∫
8
x
+
4
dx
integral of 2x*e^{-2x}
∫
2
x
·
e
−
2
x
dx
integral of (x^3-6x^2+4x-10)/(x^2-1)
∫
x
3
−
6
x
2
+
4
x
−
1
0
x
2
−
1
dx
integral of cos(4x)cos(7x)
∫
cos
(
4
x
)
cos
(
7
x
)
dx
f(x)=-6/(x^4)
f
(
x
)
=
−
6
x
4
limit as x approaches pi/4 of cos(x)
lim
x
→
π
4
(
cos
(
x
)
)
limit as n approaches infinity of \sqrt[n]{10n}
lim
n
→
∞
(
n
√
1
0
n
)
3y^'+y=0
3
y
′
+
y
=
0
(\partial)/(\partial z)(x^2+2y^2+3z^2)
∂
∂
z
(
x
2
+
2
y
2
+
3
z
2
)
(\partial)/(\partial x)(e^{-5x^2-y^2})
∂
∂
x
(
e
−
5
x
2
−
y
2
)
integral from 0 to 2 of (e^t+e^{-t})
∫
0
2
(
e
t
+
e
−
t
)
dt
integral from e to e^2 of ln(x)
∫
e
e
2
ln
(
x
)
dx
limit as x approaches 3 of ((9-x^2))/(cos(pi/2 x))
lim
x
→
3
(
(
9
−
x
2
)
cos
(
π
2
x
)
)
sum from n=0 to infinity of (-1)^{2n+1}
∑
n
=
0
∞
(
−
1
)
2
n
+
1
integral of sin^2(θ)cos^2(θ)
∫
sin
2
(
θ
)
cos
2
(
θ
)
d
θ
integral of 1/(1+6x)
∫
1
1
+
6
x
dx
derivative of (x^2+2^2(x^4+4)^4)
d
dx
(
(
x
2
+
2
)
2
(
x
4
+
4
)
4
)
5sqrt(xy)(dy)/(dx)=3
5
√
xy
dy
dx
=
3
y^{'''}-6y^{''}=6-cos(x)
y
′
′
′
−
6
y
′
′
=
6
−
cos
(
x
)
limit as x approaches 0 of x*cos(7/x)
lim
x
→
0
(
x
·
cos
(
7
x
)
)
y^'= x/y+(2y)/x
y
′
=
x
y
+
2
y
x
integral of 1/(4x^2+25)
∫
1
4
x
2
+
2
5
dx
integral of e^{-r^2}r
∫
e
−
r
2
rdr
derivative of csc((3x^4/(5x)))
d
dx
(
csc
(
3
x
4
5
x
)
)
integral from 0 to pi/8 of 3cos^5(4x)
∫
0
π
8
3
cos
5
(
4
x
)
dx
integral of (x^2-2x+1)/(sqrt(x^2-2x+37))
∫
x
2
−
2
x
+
1
√
x
2
−
2
x
+
3
7
dx
sum from n=0 to infinity}(x^{2n of)/(2n!)
∑
n
=
0
∞
x
2
n
2
n
!
integral of 2+60x-5x^2
∫
2
+
6
0
x
−
5
x
2
dx
inverse拉普拉斯 e^{-5s} 1/(1+s)
inverselaplace
e
−
5
s
1
1
+
s
xy^'-y= 1/2 xln(x)
xy
′
−
y
=
1
2
x
ln
(
x
)
integral of (e^{ax}+b)/(e^{ax)-b}
∫
e
ax
+
b
e
ax
−
b
dx
integral of 10x^4-2x-6
∫
1
0
x
4
−
2
x
−
6
dx
integral of xsqrt(x+6)
∫
x
√
x
+
6
dx
derivative of (x^2/(1+x^3))
d
dx
(
x
2
1
+
x
3
)
(tan^3(x))^'
(
tan
3
(
x
)
)
′
laplace变换 4te^{-2t}
laplacetransform
4
te
−
2
t
derivative of ln((x^2-5^2/(x^2+5^2)))
d
dx
(
ln
(
x
2
−
5
2
x
2
+
5
2
)
)
integral of 8x^{13}e^{-x^7}
∫
8
x
1
3
e
−
x
7
dx
integral of (7^{x-2})
∫
(
7
x
−
2
)
dx
inverse拉普拉斯 (10s)/(s^2+16)
inverselaplace
1
0
s
s
2
+
1
6
integral of (sec^2(x)+8)
∫
(
sec
2
(
x
)
+
8
)
dx
integral of 2xsqrt(x^2+9)
∫
2
x
√
x
2
+
9
dx
derivative of (2x^2-4x^2)
d
dx
(
(
2
x
2
−
4
x
)
2
)
inverse拉普拉斯 3/(ss^2+8ss+18s)
inverselaplace
3
ss
2
+
8
ss
+
1
8
s
d/(d{x)}(4{x}-3{x}^2-{y}^2-({z}-1)^2)
d
d
x
(
4
x
−
3
x
2
−
y
2
−
(
z
−
1
)
2
)
derivative sqrt(3/x)-e^4
derivative
√
3
x
−
e
4
derivative of-5x(2x-3^4)
d
dx
(
−
5
x
(
2
x
−
3
)
4
)
(\partial)/(\partial v)({u}(v,w)+v*e^w)
∂
∂
v
(
u
(
v
,
w
)
+
v
·
e
w
)
integral of sin(2x)e^x
∫
sin
(
2
x
)
e
x
dx
derivative p(x)=x^4-3x^3+10x^2-6x-20
derivative
p
(
x
)
=
x
4
−
3
x
3
+
1
0
x
2
−
6
x
−
2
0
integral of 1/((3-x)^2)
∫
1
(
3
−
x
)
2
dx
tangent f(x)=9e^x+x,\at x=0
tangent
f
(
x
)
=
9
e
x
+
x
,
at
x
=
0
integral of-e^{-2t}
∫
−
e
−
2
t
dt
(\partial)/(\partial x)(1/(sqrt(2pit))e^{-((x-y)^2)/(2t)})
∂
∂
x
(
1
√
2
π
t
e
−
(
x
−
y
)
2
2
t
)
limit as x approaches 1 of x^2-2
lim
x
→
1
(
x
2
−
2
)
泰勒 e^{2x},3
taylor
e
2
x
,
3
integral of (4x^2+6)/((x^2-2x+2)^2)
∫
4
x
2
+
6
(
x
2
−
2
x
+
2
)
2
dx
integral of sin^5(θ)cos^5(θ)
∫
sin
5
(
θ
)
cos
5
(
θ
)
d
θ
面积 sqrt(x)+2,-3x+6,0,1
area
√
x
+
2
,
−
3
x
+
6
,
0
,
1
derivative of-9cos(x)
d
dx
(
−
9
cos
(
x
)
)
(\partial)/(\partial x)(sqrt(x^2+y^2)+xy)
∂
∂
x
(
√
x
2
+
y
2
+
xy
)
derivative f(x)=cos(x)+7
derivative
f
(
x
)
=
cos
(
x
)
+
7
derivative of arctan(2^x)
d
dx
(
arctan
(
2
x
)
)
integral from-infinity to 0 of e^{6x}
∫
−
∞
0
e
6
x
dx
(\partial)/(\partial y)(2xy^2+x/(y^2))
∂
∂
y
(
2
xy
2
+
x
y
2
)
derivative of ln(5^x)
d
dx
(
ln
(
5
x
)
)
(\partial)/(\partial x)((-4)/(x+y))
∂
∂
x
(
−
4
x
+
y
)
derivative y= 1/(7x^{6/7)}
derivative
y
=
1
7
x
6
7
limit as x approaches 0 of (6x)/(sin(x))
lim
x
→
0
(
6
x
sin
(
x
)
)
tangent f(x)=x^2-7,(4,9)
tangent
f
(
x
)
=
x
2
−
7
,
(
4
,
9
)
inverse拉普拉斯 ((s+1))/((s^2+4s+20))
inverselaplace
(
s
+
1
)
(
s
2
+
4
s
+
2
0
)
limit as x approaches-infinity of (4+5e^{4x})/(5-6e^{5x)}
lim
x
→
−
∞
(
4
+
5
e
4
x
5
−
6
e
5
x
)
integral of-2xsqrt(1-x^2)
∫
−
2
x
√
1
−
x
2
dx
derivative of y-1/(cos(x))=0
d
dx
y
−
1
cos
(
x
)
=
0
f(x)=ln(x+sqrt(1+x^2))
f
(
x
)
=
ln
(
x
+
√
1
+
x
2
)
limit as x approaches 8-of 4/(x-8)
lim
x
→
8
−
(
4
x
−
8
)
f(x)=-1/(2x^2)
f
(
x
)
=
−
1
2
x
2
integral of e^x(cos(x)+sin(x))
∫
e
x
(
cos
(
x
)
+
sin
(
x
)
)
dx
sum from k=2 to infinity of 3/(9^{k-1)}
∑
k
=
2
∞
3
9
k
−
1
(dy)/(dx)= y/(x^2)
dy
dx
=
y
x
2
derivative of 1/(1-e^{-x})
d
dx
(
1
1
−
e
−
x
)
integral of ecos(x)
∫
e
cos
(
x
)
dx
d/(dy)((ax+by)/(cx+dy))
d
dy
(
ax
+
by
cx
+
dy
)
derivative of (2x^{3/2}/3)
d
dx
(
2
x
3
2
3
)
integral of (x^2)/(sqrt(7-x))
∫
x
2
√
7
−
x
dx
sum from n=0 to infinity of (x/7)^n
∑
n
=
0
∞
(
x
7
)
n
斜率intercept (3,-2),(-5,0)
slopeintercept
(
3
,
−
2
)
,
(
−
5
,
0
)
limit as x approaches 0 of x*3^{1/x}
lim
x
→
0
(
x
·
3
1
x
)
derivative f(x)=tan^5(x)
derivative
f
(
x
)
=
tan
5
(
x
)
integral of ((x^2-2x+1))/(x^2+x)
∫
(
x
2
−
2
x
+
1
)
x
2
+
x
dx
derivative of (e^{-x}-e^2(e^x+e^{-5}))
d
dx
(
(
e
−
x
−
e
2
)
(
e
x
+
e
−
5
)
)
(\partial)/(\partial x)(y-8/(x^2))
∂
∂
x
(
y
−
8
x
2
)
integral of sin^5(2t)
∫
sin
5
(
2
t
)
dt
(\partial)/(\partial x)(3sin(xcos(y)))
∂
∂
x
(
3
sin
(
x
cos
(
y
)
)
)
limit as x approaches 0 of xsin(1/x)
lim
x
→
0
(
x
sin
(
1
x
)
)
integral of 1/(1-2x)
∫
1
1
−
2
x
dx
(\partial)/(\partial x)(xy(1-xy))
∂
∂
x
(
xy
(
1
−
xy
)
)
(\partial)/(\partial y)(xe^{2y})
∂
∂
y
(
xe
2
y
)
d/(dt)(te^{t^3})
d
dt
(
te
t
3
)
1
..
1403
1404
1405
1406
1407
..
2459