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统计数据
常见 微积分 问题
integral from 1 to 5 of sqrt(37)
∫
1
5
√
3
7
dx
integral from-infinity to 0 of x5^{-x^2}
∫
−
∞
0
x
5
−
x
2
dx
integral of sqrt(16+y^2)
∫
√
1
6
+
y
2
dy
(\partial)/(\partial x)(54x^8y^5-40x^7y^4)
∂
∂
x
(
5
4
x
8
y
5
−
4
0
x
7
y
4
)
integral of (ln(x))/x
∫
ln
(
x
)
x
dx
derivative f(x)=(3)e-5x
derivative
f
(
x
)
=
(
3
)
e
−
5
x
derivative of (x^2+4^2)
d
dx
(
(
x
2
+
4
)
2
)
derivative xe^x+e^x
derivative
xe
x
+
e
x
(dy)/(dx)=(-x^2y)/(1+x^3)
dy
dx
=
−
x
2
y
1
+
x
3
d/(dt)(1+(t-y)^2)
d
dt
(
1
+
(
t
−
y
)
2
)
derivative of 1/((3+x^3))
d
dx
(
1
(
3
+
x
)
3
)
limit as x approaches 6 of (x^2-3)/(x-6)
lim
x
→
6
(
x
2
−
3
x
−
6
)
limit as x approaches-2 of sqrt(2x)
lim
x
→
−
2
(
√
2
x
)
(\partial)/(\partial x)(2/(x-3))
∂
∂
x
(
2
x
−
3
)
derivative 2arcsin(x^4)
derivative
2
arcsin
(
x
4
)
limit as x approaches infinity of 6(1+1/x)^{x^2}
lim
x
→
∞
(
6
(
1
+
1
x
)
x
2
)
derivative (5x^4)/(e^x)
derivative
5
x
4
e
x
(\partial)/(\partial y)(x-sqrt(y^2+z^2))
∂
∂
y
(
x
−
√
y
2
+
z
2
)
integral from 2 to 4 of sqrt(16-x^2)
∫
2
4
√
1
6
−
x
2
dx
derivative 6e^{2t}
derivative
6
e
2
t
derivative of sin^2(cos(x))
d
dx
(
sin
2
(
cos
(
x
)
)
)
(\partial)/(\partial y)(6y)
∂
∂
y
(
6
y
)
integral of z/(z+1)
∫
z
z
+
1
dz
derivative 12(2x-3)^5
derivative
1
2
(
2
x
−
3
)
5
integral of 1-cos(t)
∫
1
−
cos
(
t
)
dt
4x^2y^'=y^'+4xe^{-y}
4
x
2
y
′
=
y
′
+
4
xe
−
y
2sec(2t)2t*y^'=1
2
sec
(
2
t
)
2
t
·
y
′
=
1
面积 y=3x^3,y=75x
area
y
=
3
x
3
,
y
=
7
5
x
derivative sqrt(x-3)
derivative
√
x
−
3
derivative 7pir^2
derivative
7
π
r
2
tangent x^2-7
tangent
x
2
−
7
(y^')/(sqrt(y))=6x^2
y
′
√
y
=
6
x
2
implicit (dy)/(dx),y*cos(x)=2x^2+5y^2
implicit
dy
dx
,
y
·
cos
(
x
)
=
2
x
2
+
5
y
2
integral from 5 to 8 of x/(x^2+6x+13)
∫
5
8
x
x
2
+
6
x
+
1
3
dx
integral from 1/7 to 5 of 14xln(7x)
∫
1
7
5
1
4
x
ln
(
7
x
)
dx
f(x)=(x+1)(x^3+x-2)
f
(
x
)
=
(
x
+
1
)
(
x
3
+
x
−
2
)
integral from 1 to 4 of (x^2+6)/(5x-x^2)
∫
1
4
x
2
+
6
5
x
−
x
2
dx
integral of cos^2(pi)x
∫
cos
2
(
π
)
xdx
derivative of x^3+x^2+x+5
d
dx
(
x
3
+
x
2
+
x
+
5
)
integral of sqrt(x^7)sin(1+x^{9/2})
∫
√
x
7
sin
(
1
+
x
9
2
)
dx
limit as x approaches 3 of 7/((x-3)^2)
lim
x
→
3
(
7
(
x
−
3
)
2
)
tangent f(x)=(x^2)/(x+6)
tangent
f
(
x
)
=
x
2
x
+
6
limit as x approaches-infinity of 2^x+3
lim
x
→
−
∞
(
2
x
+
3
)
y^{''}-y^'+1/4 y=5+e^{x/2}
y
′
′
−
y
′
+
1
4
y
=
5
+
e
x
2
derivative x^2(1-8x)
derivative
x
2
(
1
−
8
x
)
(dN)/(dt)+N=Nte^{t+8}
dN
dt
+
N
=
Nte
t
+
8
derivative of (1+x^3/(1-x^3))
d
dx
(
1
+
x
3
1
−
x
3
)
integral of 1+2sin(θ)+sin^2(θ)
∫
1
+
2
sin
(
θ
)
+
sin
2
(
θ
)
d
θ
泰勒 sin(3x)
taylor
sin
(
3
x
)
integral of 4e^{cos(x)}sin(x)
∫
4
e
cos
(
x
)
sin
(
x
)
dx
integral of (2sin(x))/(cos(x))
∫
2
sin
(
x
)
cos
(
x
)
dx
f(x)=tan(8x)
f
(
x
)
=
tan
(
8
x
)
integral of 1/((x^2+4)(x+2))
∫
1
(
x
2
+
4
)
(
x
+
2
)
dx
limit as t approaches 0 of tan(7t)
lim
t
→
0
(
tan
(
7
t
)
)
(\partial)/(\partial x)(10x^5y^4e^{-x})
∂
∂
x
(
1
0
x
5
y
4
e
−
x
)
derivative of e^{log_{3}(x})
d
dx
(
e
log
3
(
x
)
)
(\partial)/(\partial x)(r^2cos^2(x))
∂
∂
x
(
r
2
cos
2
(
x
)
)
integral from-6 to 6 of (6-|x|)
∫
−
6
6
(
6
−
|
x
|
)
dx
f(x)=sqrt(tan(x^2))
f
(
x
)
=
√
tan
(
x
2
)
derivative of (2x-1^2ln(3x+4))
d
dx
(
(
2
x
−
1
)
2
ln
(
3
x
+
4
)
)
integral of 20e^{5x}
∫
2
0
e
5
x
dx
integral of nx
∫
nxdx
derivative of 2/((1-2x^2))
d
dx
(
2
(
1
−
2
x
)
2
)
integral of (2x^4+1)/(5x^3)
∫
2
x
4
+
1
5
x
3
dx
derivative of (xsinh(x+cos(x))^5)
d
dx
(
(
x
sinh
(
x
)
+
cos
(
x
)
)
5
)
integral of xsin(1/10)x
∫
x
sin
(
1
1
0
)
xdx
integral from 0 to 1 of 2pi(x+9)x^2
∫
0
1
2
π
(
x
+
9
)
x
2
dx
(1+y)dx-(1-x)dy=0
(
1
+
y
)
dx
−
(
1
−
x
)
dy
=
0
limit as x approaches 10 of x/2
lim
x
→
1
0
(
x
2
)
derivative y=e^{7x+1}
derivative
y
=
e
7
x
+
1
integral of x^2*(1+2x^3)^5
∫
x
2
·
(
1
+
2
x
3
)
5
dx
derivative of 9sqrt(x)-1/x
d
dx
(
9
√
x
−
1
x
)
derivative f(x)=4x^5ln(x)
derivative
f
(
x
)
=
4
x
5
ln
(
x
)
laplace变换 e^{20t}
laplacetransform
e
2
0
t
y^'=((xy^2))/((1+x^2))
y
′
=
(
xy
2
)
(
1
+
x
2
)
y^{''}-16y^'+64y=0,y(0)=1,y(1)=0
y
′
′
−
1
6
y
′
+
6
4
y
=
0
,
y
(
0
)
=
1
,
y
(
1
)
=
0
limit as x approaches 0 of (1-2x)^{3/x}
lim
x
→
0
(
(
1
−
2
x
)
3
x
)
derivative ln(361sin^2(x))
derivative
ln
(
3
6
1
sin
2
(
x
)
)
(\partial)/(\partial y)(sin(-2x)cos(8y))
∂
∂
y
(
sin
(
−
2
x
)
cos
(
8
y
)
)
(x+y)dx+xdy=0
(
x
+
y
)
dx
+
xdy
=
0
integral of 1/5 cos(5x)
∫
1
5
cos
(
5
x
)
dx
limit as x approaches infinity of coth(x)
lim
x
→
∞
(
coth
(
x
)
)
integral of (2x+1)y^2sin(2xy)
∫
(
2
x
+
1
)
y
2
sin
(
2
xy
)
dx
(\partial)/(\partial x)(xysin(x)+ye^{xy})
∂
∂
x
(
xy
sin
(
x
)
+
ye
xy
)
derivative f(x)=(5x-7)/(6x-9)
derivative
f
(
x
)
=
5
x
−
7
6
x
−
9
integral of e^xsqrt(29+e^x)
∫
e
x
√
2
9
+
e
x
dx
integral of xe^{tx}
∫
xe
tx
dx
(dy)/(dt)=7te^{-y},y(0)=3
dy
dt
=
7
te
−
y
,
y
(
0
)
=
3
d/(dy)(7y)
d
dy
(
7
y
)
integral of ((ln(x))^8)/x
∫
(
ln
(
x
)
)
8
x
dx
integral of (x^2+x+1)sin(x)
∫
(
x
2
+
x
+
1
)
sin
(
x
)
dx
limit as x approaches-1 of 1+x
lim
x
→
−
1
(
1
+
x
)
derivative of (-12x/((x^2+3)^2))
d
dx
(
−
1
2
x
(
x
2
+
3
)
2
)
derivative 2x^2-6x+3
derivative
2
x
2
−
6
x
+
3
(\partial)/(\partial x)(arccos(xy))
∂
∂
x
(
arccos
(
xy
)
)
integral of e^{-3x}tan(e^{-3x})
∫
e
−
3
x
tan
(
e
−
3
x
)
dx
integral from 2 to 3 of (27)/(sqrt(3-x))
∫
2
3
2
7
√
3
−
x
dx
integral of (5e^x)/(e^x+4)
∫
5
e
x
e
x
+
4
dx
limit as x approaches 8-of (6x)/(x-8)
lim
x
→
8
−
(
6
x
x
−
8
)
f(t)=t^2+1
f
(
t
)
=
t
2
+
1
1
..
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