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统计数据
常见 微积分 问题
derivative of-ke^{l(x-m}+ne^{-p(x-m)}+q)
d
dx
(
−
ke
l
(
x
−
m
)
+
ne
−
p
(
x
−
m
)
+
q
)
inverse拉普拉斯 1/((s-2)^2+9)
inverselaplace
1
(
s
−
2
)
2
+
9
d/(dj)(6i+10j)
d
dj
(
6
i
+
1
0
j
)
(x+y)dx-(x+y-2)dy=0
(
x
+
y
)
dx
−
(
x
+
y
−
2
)
dy
=
0
derivative of (x^2-1(x^2+1))
d
dx
(
(
x
2
−
1
)
(
x
2
+
1
)
)
derivative sin^2(2x)
derivative
sin
2
(
2
x
)
integral of (1-x)/(e^x)
∫
1
−
x
e
x
dx
integral of tsec^2(2t)
∫
t
sec
2
(
2
t
)
dt
(\partial)/(\partial y)(y/((x+y)^2))
∂
∂
y
(
y
(
x
+
y
)
2
)
derivative of (3x^2+ln(x)(5x^3)^x)
d
dx
(
(
3
x
2
+
ln
(
x
)
)
(
5
x
3
)
x
)
derivative f(t)=t^{5/3}e^t
derivative
f
(
t
)
=
t
5
3
e
t
integral from 0 to infinity of e^{-x}cos(x)
∫
0
∞
e
−
x
cos
(
x
)
dx
(\partial)/(\partial x)(e^{-2t}cos(pix))
∂
∂
x
(
e
−
2
t
cos
(
π
x
)
)
(dy)/(dt)= t/(ye^{y+t^2)}
dy
dt
=
t
ye
y
+
t
2
derivative of sin^4(3xtan^3(4x))
d
dx
(
sin
4
(
3
x
)
tan
3
(
4
x
)
)
integral of (x^2)/(sqrt(a^2+(x-b)^2))
∫
x
2
√
a
2
+
(
x
−
b
)
2
dx
integral of 5xcos(8x)
∫
5
x
cos
(
8
x
)
dx
derivative of 2pisqrt((0.5/(9.8)))
d
dx
(
2
π
√
0
.
5
9
.
8
)
sqrt(2xy)(dy)/(dx)=1
√
2
xy
dy
dx
=
1
derivative f(x)=x^3(x-4)^2
derivative
f
(
x
)
=
x
3
(
x
−
4
)
2
derivative of-2x(e^{-2x})
d
dx
(
−
2
x
(
e
−
2
x
)
)
derivative of (1-e^{2x}/(1+e^{2x)})
d
dx
(
1
−
e
2
x
1
+
e
2
x
)
integral of (cos(x))/(1-sin^2(x))
∫
cos
(
x
)
1
−
sin
2
(
x
)
dx
integral of ((x-2))/1
∫
(
x
−
2
)
1
dx
derivative of 9arctan(x+sqrt(1+x^2))
d
dx
(
9
arctan
(
x
+
√
1
+
x
2
)
)
limit as x approaches 4 of (4x)/(x-4)
lim
x
→
4
(
4
x
x
−
4
)
integral of (sin(x))/(x^2)
∫
sin
(
x
)
x
2
dx
integral of (x+1)/(2x^2+4x+5)
∫
x
+
1
2
x
2
+
4
x
+
5
dx
y^'=ysin(2x),y(0)=1.6
y
′
=
y
sin
(
2
x
)
,
y
(
0
)
=
1
.
6
integral of (16)/(x^2)
∫
1
6
x
2
dx
derivative 2e^x+4/(\sqrt[3]{x)}
derivative
2
e
x
+
4
3
√
x
integral from 0 to 4 of x^2sqrt(16-x^2)
∫
0
4
x
2
√
1
6
−
x
2
dx
(dy)/(dx)-xy^2=2xy
dy
dx
−
xy
2
=
2
xy
sum from n=0 to infinity of 1/(2^{2n)}
∑
n
=
0
∞
1
2
2
n
integral of 1/6 e^{6x}
∫
1
6
e
6
x
dx
limit as x approaches 3 of x^2-3x-10
lim
x
→
3
(
x
2
−
3
x
−
1
0
)
integral of (x^2-16x+9)/(x^4+10x^2+9)
∫
x
2
−
1
6
x
+
9
x
4
+
1
0
x
2
+
9
dx
derivative y= 3/2 x
derivative
y
=
3
2
x
limit as x approaches 0 of (2^x)/x
lim
x
→
0
(
2
x
x
)
limit as x approaches 0+of 9sin(x)ln(x)
lim
x
→
0
+
(
9
sin
(
x
)
ln
(
x
)
)
limit as x approaches 0-of-1/(3x^3)
lim
x
→
0
−
(
−
1
3
x
3
)
integral from 0 to pi/9 of 7-7cos(3x)
∫
0
π
9
7
−
7
cos
(
3
x
)
dx
limit as x approaches 1 of-x/(x^2-x)
lim
x
→
1
(
−
x
x
2
−
x
)
derivative f(x)=(csc(3x-1))^{2/3}
derivative
f
(
x
)
=
(
csc
(
3
x
−
1
)
)
2
3
integral of (sqrt(15y^2-2))/(y^2)
∫
√
1
5
y
2
−
2
y
2
dy
derivative f(x)=6tan(x)
derivative
f
(
x
)
=
6
tan
(
x
)
integral of sqrt(x^2+2x)
∫
√
x
2
+
2
x
dx
(d^2)/(dx^2)(1/(x^7))
d
2
dx
2
(
1
x
7
)
sum from n=1 to infinity of 5/(sqrt(n))
∑
n
=
1
∞
5
√
n
integral of (4(sec(θ))^2-sin(θ))
∫
(
4
(
sec
(
θ
)
)
2
−
sin
(
θ
)
)
d
θ
limit as x approaches 3 of (x+4)/(x+7)
lim
x
→
3
(
x
+
4
x
+
7
)
integral from 0 to 1 of (x^2+3x+4)
∫
0
1
(
x
2
+
3
x
+
4
)
dx
limit as x approaches-3 of (3-x)/(3+x)
lim
x
→
−
3
(
3
−
x
3
+
x
)
derivative 2(ln(x)+1)
derivative
2
(
ln
(
x
)
+
1
)
integral of 1/(x^e)
∫
1
x
e
dx
derivative y=6log_{5}(x^2-6)
derivative
y
=
6
log
5
(
x
2
−
6
)
derivative y=(5-2x^3)^3
derivative
y
=
(
5
−
2
x
3
)
3
integral of 2^xx^2
∫
2
x
x
2
dx
integral of x^5sqrt(x^6+3)
∫
x
5
√
x
6
+
3
dx
derivative f(x)=(e^x)/(-8x^7)
derivative
f
(
x
)
=
e
x
−
8
x
7
y^'+y=te^{-t}+e^t
y
′
+
y
=
te
−
t
+
e
t
limit as x approaches 0 of ln(x/(x-1))
lim
x
→
0
(
ln
(
x
x
−
1
)
)
inverse拉普拉斯 (e^{-s})/(s-8)
inverselaplace
e
−
s
s
−
8
integral of sqrt(4-2x)
∫
√
4
−
2
x
dx
2x-y(dy)/(dx)=3
2
x
−
y
dy
dx
=
3
integral of (sqrt(x^2+1))/(x^4)
∫
√
x
2
+
1
x
4
dx
derivative 500-500t^{-1}
derivative
5
0
0
−
5
0
0
t
−
1
泰勒 sqrt(2+x),-1
taylor
√
2
+
x
,
−
1
integral of ((8x^2-5x+1))/(x^2+x)
∫
(
8
x
2
−
5
x
+
1
)
x
2
+
x
dx
integral of (11)/(x^3-27)
∫
1
1
x
3
−
2
7
dx
integral of x^2(5x^3-1)^{3/2}
∫
x
2
(
5
x
3
−
1
)
3
2
dx
derivative of (-3x^5-x^4-x^3+4x^2/(x^2))
d
dx
(
−
3
x
5
−
x
4
−
x
3
+
4
x
2
x
2
)
y^{''}+4y^'+4y=0,y(0)=-1,y^'(0)=0
y
′
′
+
4
y
′
+
4
y
=
0
,
y
(
0
)
=
−
1
,
y
′
(
0
)
=
0
limit as x approaches-4 of sqrt(-2x+3)
lim
x
→
−
4
(
√
−
2
x
+
3
)
(\partial)/(\partial x)((4x-2y)/(2x^2+3y))
∂
∂
x
(
4
x
−
2
y
2
x
2
+
3
y
)
derivative of 5/(x^2+25)
d
dx
(
5
x
2
+
2
5
)
integral of 5sin(x)sqrt(5-cos(x))
∫
5
sin
(
x
)
√
5
−
cos
(
x
)
dx
integral from 0 to 4 of 1/(x^2+x-6)
∫
0
4
1
x
2
+
x
−
6
dx
integral from 1 to 4 of (4x^2+sqrt(x))
∫
1
4
(
4
x
2
+
√
x
)
dx
integral of 1/(1-5t)
∫
1
1
−
5
t
dt
(\partial)/(\partial x)(x^3*4x+5y)
∂
∂
x
(
x
3
·
4
x
+
5
y
)
derivative y=x(x-4)
derivative
y
=
x
(
x
−
4
)
derivative of sin(x+cos(2x))
d
dx
(
sin
(
x
)
+
cos
(
2
x
)
)
integral from 0 to 2 of |x-1|
∫
0
2
|
x
−
1
|
dx
integral from 0 to infinity of 5/(x^2+4)
∫
0
∞
5
x
2
+
4
dx
integral of cos(8x^2)
∫
cos
(
8
x
2
)
dx
(\partial)/(\partial x)(-sqrt(x))
∂
∂
x
(
−
√
x
)
integral from 0 to 4 of 2x
∫
0
4
2
xdx
y^{''}-4y^'=7x+1
y
′
′
−
4
y
′
=
7
x
+
1
(\partial)/(\partial x)(e^{4x}cos(7y))
∂
∂
x
(
e
4
x
cos
(
7
y
)
)
d/(dy)(y^{-1})
d
dy
(
y
−
1
)
derivative of x^2e^x-3
d
dx
(
x
2
e
x
−
3
)
limit as x approaches 0 of x*arctan(1/x)
lim
x
→
0
(
x
·
arctan
(
1
x
)
)
integral of (2x^3+3x+1)^4(6x^2+3)
∫
(
2
x
3
+
3
x
+
1
)
4
(
6
x
2
+
3
)
dx
integral of 1/(x(1+x^2))
∫
1
x
(
1
+
x
2
)
dx
(ln(1-x^2))^'
(
ln
(
1
−
x
2
)
)
′
derivative of cos(ysqrt(x^2+1))
d
dx
(
cos
(
y
√
x
2
+
1
)
)
xy^2y^'=y^3-2x^3
xy
2
y
′
=
y
3
−
2
x
3
derivative of sqrt(20-25sin^2(x))
d
dx
(
√
2
0
−
2
5
sin
2
(
x
)
)
derivative of 1/(4+3x)
d
dx
(
1
4
+
3
x
)
1
..
332
333
334
335
336
..
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