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统计数据
常见 微积分 问题
integral of 2x(x^2+1)^9
∫
2
x
(
x
2
+
1
)
9
dx
derivative of-(x+1sin((x^2)/2))
d
dx
(
−
(
x
+
1
)
sin
(
x
2
2
)
)
斜率 y=6sin(pix-y),(1,0)
slope
y
=
6
sin
(
π
x
−
y
)
,
(
1
,
0
)
integral of 2cos(2x)-1
∫
2
cos
(
2
x
)
−
1
dx
laplace变换 cos^2(2t)
laplacetransform
cos
2
(
2
t
)
inverse拉普拉斯 (((s+1)^2+1))/s
inverselaplace
(
(
s
+
1
)
2
+
1
)
s
integral of 2x(x^2+3)^7
∫
2
x
(
x
2
+
3
)
7
dx
麦克劳林 x-e^{3x}
maclaurin
x
−
e
3
x
derivative (\sqrt[3]{t})/(t-9)
derivative
3
√
t
t
−
9
integral of 3/(8+6x)
∫
3
8
+
6
x
dx
面积 y= 1/x ,y= 1/4 x
area
y
=
1
x
,
y
=
1
4
x
limit as x approaches 1 of (x+2)/(x^3+8)
lim
x
→
1
(
x
+
2
x
3
+
8
)
integral of 2/(xln^3(x))
∫
2
x
ln
3
(
x
)
dx
(\partial)/(\partial x)(x^4ln(yz))
∂
∂
x
(
x
4
ln
(
yz
)
)
sum from n=1 to infinity of 1/(10^n)
∑
n
=
1
∞
1
1
0
n
sum from n=1 to infinity of (2/7)*n
∑
n
=
1
∞
(
2
7
)
·
n
integral of sin^4(x/2)cos^2(x/2)
∫
sin
4
(
x
2
)
cos
2
(
x
2
)
dx
integral of 2t+2
∫
2
t
+
2
dt
sum from n=0 to infinity of (-14)/8
∑
n
=
0
∞
−
1
4
8
derivative of \sqrt[5]{ln(x})
d
dx
(
5
√
ln
(
x
)
)
derivative of 3sin(x+2cos(x)tan(x))
d
dx
(
3
sin
(
x
)
+
2
cos
(
x
)
tan
(
x
)
)
面积 2x+1,x^3-5x^2+6x+1
area
2
x
+
1
,
x
3
−
5
x
2
+
6
x
+
1
integral of-30x^{2/3}
∫
−
3
0
x
2
3
dx
(dy)/(dx)=((e^{x-y}))/(1+e^x)
dy
dx
=
(
e
x
−
y
)
1
+
e
x
integral from 0 to 2 of 30000e^{0.03x}
∫
0
2
3
0
0
0
0
e
0
.
0
3
x
dx
integral of 36t^8e^{-t^9}
∫
3
6
t
8
e
−
t
9
dt
limit as x approaches-1 of sqrt(5-11x)
lim
x
→
−
1
(
√
5
−
1
1
x
)
(\partial)/(\partial x)(x/(y^2)+xy+2)
∂
∂
x
(
x
y
2
+
xy
+
2
)
tangent x^2+5
tangent
x
2
+
5
derivative of (x^3/3+7x^2+50x)
d
dx
(
x
3
3
+
7
x
2
+
5
0
x
)
(\partial)/(\partial x)(5arccot(x))
∂
∂
x
(
5
arccot
(
x
)
)
derivative of (2x-8^4(x^2+x+1)^5)
d
dx
(
(
2
x
−
8
)
4
(
x
2
+
x
+
1
)
5
)
integral of (e^{x-y})/(1+e^x)
∫
e
x
−
y
1
+
e
x
derivative of log_{3}(3x-7)
d
dx
(
log
3
(
3
x
−
7
)
)
integral of 8xe^{15x}
∫
8
xe
1
5
x
dx
derivative of (-x^2+y^2/((x^2+y^2)^2))
d
dx
(
−
x
2
+
y
2
(
x
2
+
y
2
)
2
)
(dy)/(dt)=-y/t+2
dy
dt
=
−
y
t
+
2
implicit (dy)/(dx),xy+x=2
implicit
dy
dx
,
xy
+
x
=
2
integral of (sqrt(a^2+x^2))/(x^2)
∫
√
a
2
+
x
2
x
2
dx
面积 y=6x-x^2,y=x
area
y
=
6
x
−
x
2
,
y
=
x
integral from 5 to 8 of 5/(sqrt(x-5))
∫
5
8
5
√
x
−
5
dx
(\partial)/(\partial x)(u/(1+2.4(x/y)))
∂
∂
x
(
u
1
+
2
.
4
(
x
y
)
)
(\partial)/(\partial x)(6x^5y^6+5x^4y^7)
∂
∂
x
(
6
x
5
y
6
+
5
x
4
y
7
)
integral from 0 to 3 of 15x
∫
0
3
1
5
xdx
limit as x approaches 0 of x(x)
lim
x
→
0
(
x
(
x
)
)
limit as x approaches-2 of (x^2-6)/(2-x)
lim
x
→
−
2
(
x
2
−
6
2
−
x
)
inverse拉普拉斯 1/(s^3+s^2)
inverselaplace
1
s
3
+
s
2
derivative 3^{1-2n}
derivative
3
1
−
2
n
(\partial)/(\partial x)(3xy-x^2y^2+23)
∂
∂
x
(
3
xy
−
x
2
y
2
+
2
3
)
(dy)/(dx)=(sqrt(x))/(e^y)
dy
dx
=
√
x
e
y
derivative sqrt(3x^2-2)
derivative
√
3
x
2
−
2
derivative f(x)=-9.8x^2+2x+1
derivative
f
(
x
)
=
−
9
.
8
x
2
+
2
x
+
1
integral of 1/(arcsin(x)sqrt(1-x^2))
∫
1
arcsin
(
x
)
√
1
−
x
2
dx
(\partial)/(\partial x)(x^2+xy+y^2+2x-y)
∂
∂
x
(
x
2
+
xy
+
y
2
+
2
x
−
y
)
d/(dt)(-cos(2t))
d
dt
(
−
cos
(
2
t
)
)
tangent y=x^8e^{-x},(1, 1/e)
tangent
y
=
x
8
e
−
x
,
(
1
,
1
e
)
integral of (2x^4-8x^3)*e^{-3x}
∫
(
2
x
4
−
8
x
3
)
·
e
−
3
x
dx
derivative of (2cos(x)/(sec(x)))
d
dx
(
2
cos
(
x
)
sec
(
x
)
)
y^{''}+y^'+6y=0,y(0)=0,y^'(0)=0
y
′
′
+
y
′
+
6
y
=
0
,
y
(
0
)
=
0
,
y
′
(
0
)
=
0
(2xy)dy+(x^2+y^2)dx=0
(
2
xy
)
dy
+
(
x
2
+
y
2
)
dx
=
0
y^{''}-6y^'+25y=0,y(0)=3,y^'(0)=1
y
′
′
−
6
y
′
+
2
5
y
=
0
,
y
(
0
)
=
3
,
y
′
(
0
)
=
1
derivative y=(tan(x))^{9/x}
derivative
y
=
(
tan
(
x
)
)
9
x
integral of (x^2sqrt(x))
∫
(
x
2
√
x
)
dx
derivative 6x^{1/4}
derivative
6
x
1
4
integral of (3x)/((1-x^2)^3)
∫
3
x
(
1
−
x
2
)
3
dx
e^ydx+xe^ydy=0
e
y
dx
+
xe
y
dy
=
0
(\partial)/(\partial x)(cos^2(x))
∂
∂
x
(
cos
2
(
x
)
)
derivative (x^2(x^2+9x))^6
derivative
(
x
2
(
x
2
+
9
x
)
)
6
(\partial)/(\partial x)(ln(x+y^2))
∂
∂
x
(
ln
(
x
+
y
2
)
)
(\partial)/(\partial x)((2xy)/(x+y))
∂
∂
x
(
2
xy
x
+
y
)
integral of wsqrt(w^2-ln(3))
∫
w
√
w
2
−
ln
(
3
)
dw
limit as x approaches 0 of (3x)/(xe^x)
lim
x
→
0
(
3
x
xe
x
)
integral of (3x^2-2x+5)/(x^2)
∫
3
x
2
−
2
x
+
5
x
2
dx
x^3(dy)/(dx)+y^2=x^2y
x
3
dy
dx
+
y
2
=
x
2
y
longdivision (3x^2+1)/(2x^2-5)
longdivision
3
x
2
+
1
2
x
2
−
5
derivative f(x)=x^3sqrt(x)
derivative
f
(
x
)
=
x
3
√
x
limit as x approaches-3+of sqrt(x^3+27)
lim
x
→
−
3
+
(
√
x
3
+
2
7
)
integral from 0 to 8 of e^xsin(x)
∫
0
8
e
x
sin
(
x
)
dx
(\partial)/(\partial u)(u^2+v)
∂
∂
u
(
u
2
+
v
)
limit as x approaches 0+of x^{x^5}
lim
x
→
0
+
(
x
x
5
)
derivative (ln(6x))/(6x)
derivative
ln
(
6
x
)
6
x
integral of ((3+ln(x))^3+12)/(4x)
∫
(
3
+
ln
(
x
)
)
3
+
1
2
4
x
dx
derivative of 2cos(x+sin(2x))
d
dx
(
2
cos
(
x
)
+
sin
(
2
x
)
)
derivative of ax+b/x
d
dx
(
ax
+
b
x
)
derivative of (e^x/(x^2-1))
d
dx
(
e
x
x
2
−
1
)
laplace变换 e^{-7t}
laplacetransform
e
−
7
t
integral of x*sin(x)cos(x)
∫
x
·
sin
(
x
)
cos
(
x
)
dx
sum from n=7 to infinity of 1/(nln(n))
∑
n
=
7
∞
1
n
ln
(
n
)
integral from 0 to 3 of |x^2-9|
∫
0
3
|
x
2
−
9
|
dx
integral of-e^{-2x}
∫
−
e
−
2
x
dx
derivative (64)/(x^2+16)
derivative
6
4
x
2
+
1
6
tangent f(x)=x^2-4x,\at x=1
tangent
f
(
x
)
=
x
2
−
4
x
,
at
x
=
1
derivative of-5sin(x)
d
dx
(
−
5
sin
(
x
)
)
(\partial)/(\partial x)(sqrt(2-x^2-y^2))
∂
∂
x
(
√
2
−
x
2
−
y
2
)
derivative of-e^{-4x}
d
dx
(
−
e
−
4
x
)
integral from 3 to infinity of (e^{-1/x})/(x^2)
∫
3
∞
e
−
1
x
x
2
dx
(cos(x))^'
(
cos
(
x
)
)
′
(\partial)/(\partial x)(y/(1+x))
∂
∂
x
(
y
1
+
x
)
integral of (sqrt(x)+1)
∫
(
√
x
+
1
)
dx
integral of (2^x+4e^x+x^3+5)
∫
(
2
x
+
4
e
x
+
x
3
+
5
)
dx
1
..
211
212
213
214
215
..
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