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常见 微积分 问题
integral of (x^2)/(9+x^6)
∫
x
2
9
+
x
6
dx
limit as x approaches 0 of (x^3+6x)/x
lim
x
→
0
(
x
3
+
6
x
x
)
integral of cos^2(ax)
∫
cos
2
(
ax
)
dx
sum from n=7 to infinity of 1/((n-4)^4)
∑
n
=
7
∞
1
(
n
−
4
)
4
integral of ((x-1))/(x^2+5x+6)
∫
(
x
−
1
)
x
2
+
5
x
+
6
dx
y^{''}-5/t y^'+(25)/(t^2)y=0
y
′
′
−
5
t
y
′
+
2
5
t
2
y
=
0
integral of 12sqrt(x)
∫
1
2
√
x
dx
integral of (1-3x)^{1/3}
∫
(
1
−
3
x
)
1
3
dx
limit as x approaches pi of tan(2/3 x)
lim
x
→
π
(
tan
(
2
3
x
)
)
derivative f(x)=(x^2)/(2+sqrt(x))
derivative
f
(
x
)
=
x
2
2
+
√
x
limit as n approaches infinity of n/1
lim
n
→
∞
(
n
1
)
integral of e^{3x}cos(4x)
∫
e
3
x
cos
(
4
x
)
dx
derivative of x^{(ln(2)/(1+ln(x))})
d
dx
(
x
ln
(
2
)
1
+
ln
(
x
)
)
integral of 7/((t-1)sqrt(t^2-2t-48))
∫
7
(
t
−
1
)
√
t
2
−
2
t
−
4
8
dt
sum from n=0 to infinity of 3^{n-1}
∑
n
=
0
∞
3
n
−
1
y^'+x/(x^2-9)y=2x
y
′
+
x
x
2
−
9
y
=
2
x
sum from n=3 to infinity}((ln(x))^{n-1 of)/(2^n)
∑
n
=
3
∞
(
ln
(
x
)
)
n
−
1
2
n
limit as x approaches-9 of (x^2-4)/(x-9)
lim
x
→
−
9
(
x
2
−
4
x
−
9
)
limit as x approaches infinity of x^4e^{-x^3}
lim
x
→
∞
(
x
4
e
−
x
3
)
sum from n=0 to infinity of 1/(n+1)
∑
n
=
0
∞
1
n
+
1
integral of (sqrt(x^2-16))/(x^3)
∫
√
x
2
−
1
6
x
3
dx
tangent f(x)=(2ln(x))/x ,\at x=1
tangent
f
(
x
)
=
2
ln
(
x
)
x
,
at
x
=
1
derivative of (sin(8x)/(e^{4x)})
d
dx
(
sin
(
8
x
)
e
4
x
)
(\partial)/(\partial x)(ln(3y^2-x^3-3))
∂
∂
x
(
ln
(
3
y
2
−
x
3
−
3
)
)
limit as x approaches 0 of (5^x-13^x)/x
lim
x
→
0
(
5
x
−
1
3
x
x
)
limit as x approaches 0 of x*sin(1/x)
lim
x
→
0
(
x
·
sin
(
1
x
)
)
(\partial)/(\partial x)(ln(x)-4)
∂
∂
x
(
ln
(
x
)
−
4
)
derivative of y^5sin(5x)
d
dx
(
y
5
sin
(
5
x
)
)
(\partial)/(\partial x)(4sin(4x)e^{3x})
∂
∂
x
(
4
sin
(
4
x
)
e
3
x
)
sum from n=1 to infinity of 5/(4^{n-1)}
∑
n
=
1
∞
5
4
n
−
1
(\partial)/(\partial y)(e^{x^2+y^2})
∂
∂
y
(
e
x
2
+
y
2
)
sum from k=1 to infinity of e^{-k}
∑
k
=
1
∞
e
−
k
(\partial)/(\partial x)(4xyarcsin(yz))
∂
∂
x
(
4
xy
arcsin
(
yz
)
)
integral of 8/(9tsqrt(81t^2-64))
∫
8
9
t
√
8
1
t
2
−
6
4
dt
integral of ((tan(x))/(cot(x)))^3
∫
(
tan
(
x
)
cot
(
x
)
)
3
dx
(sin(sin(x)))^'
(
sin
(
sin
(
x
)
)
)
′
derivative f(x)=x^2e^x
derivative
f
(
x
)
=
x
2
e
x
integral of (10)/(x^2+8x+15)
∫
1
0
x
2
+
8
x
+
1
5
dx
(\partial)/(\partial x)(ye^y-xe^x)
∂
∂
x
(
ye
y
−
xe
x
)
limit as x approaches 3 of x^2-5x+6
lim
x
→
3
(
x
2
−
5
x
+
6
)
(y^3-2x^2y)dx+(2x^3)dy=0
(
y
3
−
2
x
2
y
)
dx
+
(
2
x
3
)
dy
=
0
inverse拉普拉斯 (6s+3)/(s^4+5s^2+4)
inverselaplace
6
s
+
3
s
4
+
5
s
2
+
4
limit as x approaches-6 of ((4x+3)^{2/3}-9)/(x^2-36)
lim
x
→
−
6
(
(
4
x
+
3
)
2
3
−
9
x
2
−
3
6
)
integral of pi/3
∫
π
3
yy^'=xy^2-x-y^2+1
yy
′
=
xy
2
−
x
−
y
2
+
1
integral of (11x+20)/(x^2+4x+5)
∫
1
1
x
+
2
0
x
2
+
4
x
+
5
dx
f(x)= x/(4+x^2)
f
(
x
)
=
x
4
+
x
2
derivative f(t)=7t-2t^2
derivative
f
(
t
)
=
7
t
−
2
t
2
(\partial)/(\partial z)(e^{9xz})
∂
∂
z
(
e
9
xz
)
integral of 2sin(npix)
∫
2
sin
(
n
π
x
)
dx
sum from n=0 to infinity of (6n)/(2n-1)
∑
n
=
0
∞
6
n
2
n
−
1
derivative of (x^2-x^{7/3}^4)
d
dx
(
(
x
2
−
x
7
3
)
4
)
10y^'+5y=8e^{6x},y(0)=9
1
0
y
′
+
5
y
=
8
e
6
x
,
y
(
0
)
=
9
limit as x approaches 3 of (|x|-x)/(3-x)
lim
x
→
3
(
|
x
|
−
x
3
−
x
)
y^{''}+(y^')^2+1=0
y
′
′
+
(
y
′
)
2
+
1
=
0
integral from-40 to 0 of 1/(sqrt(9-x))
∫
−
4
0
0
1
√
9
−
x
dx
derivative y=30e^{-0.0000323x}
derivative
y
=
3
0
e
−
0
.
0
0
0
0
3
2
3
x
面积 1/8 x,8x, 2/x
area
1
8
x
,
8
x
,
2
x
integral from 2 to 8 of 5/(4-3x)
∫
2
8
5
4
−
3
x
dx
integral of (sqrt(1-x^2))
∫
(
√
1
−
x
2
)
dx
(x^2+y)dx-(x)dy=0
(
x
2
+
y
)
dx
−
(
x
)
dy
=
0
limit as x approaches 1 of (3x^2+5x-8)/(x^2-1)
lim
x
→
1
(
3
x
2
+
5
x
−
8
x
2
−
1
)
integral of (-2/(sqrt(7-7x^2)))
∫
(
−
2
√
7
−
7
x
2
)
dx
integral of 1/((2x+6)^2)
∫
1
(
2
x
+
6
)
2
dx
integral of (x+1)sqrt(2x-1)
∫
(
x
+
1
)
√
2
x
−
1
dx
(dx)/(dt)=x^2,x(0)=1
dx
dt
=
x
2
,
x
(
0
)
=
1
integral of-6x^{-7}
∫
−
6
x
−
7
dx
(dy)/(dx)+((1-y^2)/(1-x^2))^{1/2}=0
dy
dx
+
(
1
−
y
2
1
−
x
2
)
1
2
=
0
(dy)/(dx)=9y
dy
dx
=
9
y
derivative G(t)=(1-3t)/(4+t)
derivative
G
(
t
)
=
1
−
3
t
4
+
t
integral of (x^2)/(5x^3+8)
∫
x
2
5
x
3
+
8
dx
tangent f(x)=3e^x+x,(0,3)
tangent
f
(
x
)
=
3
e
x
+
x
,
(
0
,
3
)
integral of (7x(x^6-1/7))
∫
(
7
x
(
x
6
−
1
7
)
)
dx
inverse拉普拉斯 1/((s^2+5))
inverselaplace
1
(
s
2
+
5
)
derivative f(x)=(1-4x)/(1+4x)
derivative
f
(
x
)
=
1
−
4
x
1
+
4
x
(\partial)/(\partial y)(4x^3y^3+2)
∂
∂
y
(
4
x
3
y
3
+
2
)
xdy-ydx=(xy)^{1/2}
xdy
−
ydx
=
(
xy
)
1
2
(\partial)/(\partial x)(6e^{x^5y})
∂
∂
x
(
6
e
x
5
y
)
integral from 0 to 1 of (x-1)/(sqrt(x))
∫
0
1
x
−
1
√
x
dx
tangent g(x)=-3x^2+5x-6
tangent
g
(
x
)
=
−
3
x
2
+
5
x
−
6
derivative sqrt(6x)
derivative
√
6
x
integral of ((x-1))/2
∫
(
x
−
1
)
2
dx
(8+x)y^'=7y
(
8
+
x
)
y
′
=
7
y
(\partial)/(\partial x)(ln(x^2+y^4)-z)
∂
∂
x
(
ln
(
x
2
+
y
4
)
−
z
)
(\partial)/(\partial x)((2y)/(9x^2+y^2+9))
∂
∂
x
(
2
y
9
x
2
+
y
2
+
9
)
derivative ln(x^2+9)
derivative
ln
(
x
2
+
9
)
derivative of 2e^{-x^2}
d
dx
(
2
e
−
x
2
)
integral of 6cos(3x)
∫
6
cos
(
3
x
)
dx
integral of 1/(x(1-0.0004x))
∫
1
x
(
1
−
0
.
0
0
0
4
x
)
dx
derivative of acos(2x+bsin(2x))
d
dx
(
a
cos
(
2
x
)
+
b
sin
(
2
x
)
)
derivative of asin(x)
d
dx
(
a
sin
(
x
)
)
y^{''}+4y^'+4y=0,y(0)=1,y^'(0)=-4
y
′
′
+
4
y
′
+
4
y
=
0
,
y
(
0
)
=
1
,
y
′
(
0
)
=
−
4
integral of tan(2xse)c^22x
∫
tan
(
2
xse
)
c
2
2
xdx
tangent y=3x-2x^2,(-3,-27)
tangent
y
=
3
x
−
2
x
2
,
(
−
3
,
−
2
7
)
limit as x approaches 0+of x+1
lim
x
→
0
+
(
x
+
1
)
(dy)/(dx)=e^{2y}sin(x)
dy
dx
=
e
2
y
sin
(
x
)
integral of sqrt(x)-6cos(x)
∫
√
x
−
6
cos
(
x
)
dx
sum from n=1 to infinity of (x^n)/(10^n)
∑
n
=
1
∞
x
n
1
0
n
integral from 0 to 1 of sqrt(36t^2+9t^4)
∫
0
1
√
3
6
t
2
+
9
t
4
dt
y^'=(sin(2x))/(e^y)
y
′
=
sin
(
2
x
)
e
y
1
..
1389
1390
1391
1392
1393
..
2459