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常见 微积分 问题
integral of sin((npix)/L)
∫
sin
(
n
π
x
L
)
dx
derivative f(t)=(t+1)^{2/3}(2t^2-1)^3
derivative
f
(
t
)
=
(
t
+
1
)
2
3
(
2
t
2
−
1
)
3
integral of 1/(sec(x)tan(x))
∫
1
sec
(
x
)
tan
(
x
)
dx
d/(dt)((2t+5)/(2t))
d
dt
(
2
t
+
5
2
t
)
integral of x^2arctan(5x)
∫
x
2
arctan
(
5
x
)
dx
integral of 4^{-2x}
∫
4
−
2
x
dx
derivative (4x+1)^2
derivative
(
4
x
+
1
)
2
tangent f(x)=(x^3-25x)^{14},(5,0)
tangent
f
(
x
)
=
(
x
3
−
2
5
x
)
1
4
,
(
5
,
0
)
limit as t approaches 0 of ln(sin(4t))
lim
t
→
0
(
ln
(
sin
(
4
t
)
)
)
(\partial)/(\partial x)(e^{(2x+3y)/(3y)})
∂
∂
x
(
e
2
x
+
3
y
3
y
)
derivative of 5(e^x^{-4})
d
dx
(
5
(
e
x
)
−
4
)
limit as x approaches 2 of 12x^2
lim
x
→
2
(
1
2
x
2
)
limit as x approaches-2 of (|x+2|)/(x+2)
lim
x
→
−
2
(
|
x
+
2
|
x
+
2
)
integral of (sech(1/x)tanh(1/x))/(x^2)
∫
sech
(
1
x
)
tanh
(
1
x
)
x
2
dx
integral of 1/(sqrt(9+t^2))
∫
1
√
9
+
t
2
dt
integral of 9csc(x)
∫
9
csc
(
x
)
dx
laplace变换 e^{-t}(t-1)
laplacetransform
e
−
t
(
t
−
1
)
integral of x/(6x-5)
∫
x
6
x
−
5
dx
y^'=3y^{2/3}
y
′
=
3
y
2
3
d/(dy)(e^{-x}+e^{-2y})
d
dy
(
e
−
x
+
e
−
2
y
)
derivative f(x)=sin^4(x)
derivative
f
(
x
)
=
sin
4
(
x
)
derivative of 100x^2
d
dx
(
1
0
0
x
2
)
y^'=(x+y-2)2
y
′
=
(
x
+
y
−
2
)
2
(\partial)/(\partial x)(xln(yz))
∂
∂
x
(
x
ln
(
yz
)
)
integral of xe^{ax}
∫
xe
ax
dx
2y^{''}-3y^'+y=0,y(0)=2,y^'(0)= 1/2
2
y
′
′
−
3
y
′
+
y
=
0
,
y
(
0
)
=
2
,
y
′
(
0
)
=
1
2
integral of t^2sqrt(t+8)
∫
t
2
√
t
+
8
dt
derivative y=(2x)/(x-1)
derivative
y
=
2
x
x
−
1
limit as x approaches 0 of ((2arccos(x))/pi)^{1/x}
lim
x
→
0
(
(
2
arccos
(
x
)
π
)
1
x
)
integral of (2+x+x^2)/(sqrt(x))
∫
2
+
x
+
x
2
√
x
dx
derivative f(t)=(sin(t))/t
derivative
f
(
t
)
=
sin
(
t
)
t
integral of y/(e^{-y)}
∫
y
e
−
y
dy
f(x)=(xcos(x)-2pi)/(x-2pi)
f
(
x
)
=
x
cos
(
x
)
−
2
π
x
−
2
π
定义域 f(x)=(sqrt(x)-x^2)/(x^3+2)
domain
f
(
x
)
=
√
x
−
x
2
x
3
+
2
((m^2+2)/(sqrt(2m^3+4)))^'
(
m
2
+
2
√
2
m
3
+
4
)
′
y^{''}+9y=4cos(2x)
y
′
′
+
9
y
=
4
cos
(
2
x
)
(\partial)/(\partial x)(2e^y)
∂
∂
x
(
2
e
y
)
derivative of (x-1/(2x+1))
d
dx
(
x
−
1
2
x
+
1
)
limit as x approaches 0 of (1)^{1/x}
lim
x
→
0
(
(
1
)
1
x
)
y^{''}-4y=9e^t,y(0)=0,y^'(0)=0
y
′
′
−
4
y
=
9
e
t
,
y
(
0
)
=
0
,
y
′
(
0
)
=
0
limit as x approaches-1 of 5-2x-x^2
lim
x
→
−
1
(
5
−
2
x
−
x
2
)
integral of (2^x-3^x)^0
∫
(
2
x
−
3
x
)
0
dx
derivative of 7sec(x-2x)
d
dx
(
7
sec
(
x
)
−
2
x
)
(dy)/(dt)=-3(1-y)(1-2y)
dy
dt
=
−
3
(
1
−
y
)
(
1
−
2
y
)
d/(dy)((100y)/(x+y))=0
d
dy
(
1
0
0
y
x
+
y
)
=
0
derivative 1/(13x^2)
derivative
1
1
3
x
2
(\partial)/(\partial x)((11)/((9+x^2+y^2)))
∂
∂
x
(
1
1
(
9
+
x
2
+
y
2
)
)
inverse拉普拉斯-4e^{(-3s)}*1/(s-3)
inverselaplace
−
4
e
(
−
3
s
)
·
1
s
−
3
derivative of 2+cos(e^x-2-e^x)
d
dx
(
2
+
cos
(
e
x
−
2
)
−
e
x
)
(\partial)/(\partial x)(2^{90})
∂
∂
x
(
2
9
0
)
integral from 1 to 5 of x^4ln(5x)
∫
1
5
x
4
ln
(
5
x
)
dx
tangent y=x^{3-3x+1}
tangent
y
=
x
3
−
3
x
+
1
integral of sqrt(4x-y^2)
∫
√
4
x
−
y
2
dy
integral from 1 to 3 of 1/(x^2)
∫
1
3
1
x
2
dx
integral of (1/z-x/(y^2))
∫
(
1
z
−
x
y
2
)
dy
derivative of arctan(sqrt(x-3))
d
dx
(
arctan
(
√
x
−
3
)
)
derivative (2q^2-3)^6(5q+4)^3
derivative
(
2
q
2
−
3
)
6
(
5
q
+
4
)
3
inverse拉普拉斯 2/(s*(s^2+4s+8))
inverselaplace
2
s
·
(
s
2
+
4
s
+
8
)
integral from 2 to 3 of pi(4-1/2 x)^2
∫
2
3
π
(
4
−
1
2
x
)
2
dx
integral of-4x^3e^{-2x^2}
∫
−
4
x
3
e
−
2
x
2
dx
inverse拉普拉斯 ((s+2))/(s+1)
inverselaplace
(
s
+
2
)
s
+
1
(2y+2t-3)dt+(4y+2t-1)dy=0
(
2
y
+
2
t
−
3
)
dt
+
(
4
y
+
2
t
−
1
)
dy
=
0
(\partial)/(\partial x)(7e^{x^{10}y})
∂
∂
x
(
7
e
x
1
0
y
)
limit as x approaches 5 of x^2+2x-3
lim
x
→
5
(
x
2
+
2
x
−
3
)
derivative f(x)=ln(4x+7)
derivative
f
(
x
)
=
ln
(
4
x
+
7
)
d/(dt)(sin(3t))
d
dt
(
sin
(
3
t
)
)
d/(d{x)}({y}{z}(x))
d
d
x
(
y
z
(
x
)
)
integral of 4x^3+2xy^2
∫
4
x
3
+
2
xy
2
dx
(\partial)/(\partial x)(x^{1/2}y^{1/3})
∂
∂
x
(
x
1
2
y
1
3
)
derivative 4^x
derivative
4
x
integral from 0 to 4 of xe^{-3x}
∫
0
4
xe
−
3
x
dx
integral of (sqrt(x)-1/2 x+2/(sqrt(x)))
∫
(
√
x
−
1
2
x
+
2
√
x
)
dx
derivative x^{-3/5}+x^{3/5}
derivative
x
−
3
5
+
x
3
5
(\partial)/(\partial x)(vsin(x))
∂
∂
x
(
v
sin
(
x
)
)
integral from 1/2 to 7 of 16xln(2x)
∫
1
2
7
1
6
x
ln
(
2
x
)
dx
derivative f(x)=sqrt(2+x)
derivative
f
(
x
)
=
√
2
+
x
limit as x approaches 2 of (2x-3)/(x-2)
lim
x
→
2
(
2
x
−
3
x
−
2
)
(\partial)/(\partial x)(e^{mx})
∂
∂
x
(
e
mx
)
derivative xsin(2x)
derivative
x
sin
(
2
x
)
tangent 8/(sqrt(x))
tangent
8
√
x
integral of e^{-5x^2}
∫
e
−
5
x
2
dx
integral from 0 to a of 1/(x^2+a^2)
∫
0
a
1
x
2
+
a
2
dx
(\partial)/(\partial x)(1-x/y)
∂
∂
x
(
1
−
x
y
)
integral from 1 to 2 of xe^{2x^2-3}
∫
1
2
xe
2
x
2
−
3
dx
integral from 0 to pi of 10tsin(3t)
∫
0
π
1
0
t
sin
(
3
t
)
dt
tangent f(x)=x^4+9x^2-x,(1,9)
tangent
f
(
x
)
=
x
4
+
9
x
2
−
x
,
(
1
,
9
)
limit as x approaches infinity of (x*(x+1)^{x+1})/((x+1)^{x+2)}
lim
x
→
∞
(
x
·
(
x
+
1
)
x
+
1
(
x
+
1
)
x
+
2
)
laplace变换 1/((8^2+1)+(8^2+4))
laplacetransform
1
(
8
2
+
1
)
+
(
8
2
+
4
)
integral of 2e^{-0.4x}
∫
2
e
−
0
.
4
x
dx
derivative of sqrt(144+x^2)
d
dx
(
√
1
4
4
+
x
2
)
integral of (sin(x))^2(cos(x))^2
∫
(
sin
(
x
)
)
2
(
cos
(
x
)
)
2
dx
斜率intercept (2005,54),(2010,58)
slopeintercept
(
2
0
0
5
,
5
4
)
,
(
2
0
1
0
,
5
8
)
derivative 3x^{-1}
derivative
3
x
−
1
(d^2)/(dx^2)((x^2+9)^7)
d
2
dx
2
(
(
x
2
+
9
)
7
)
tangent f(x)=sqrt(2x+3)
tangent
f
(
x
)
=
√
2
x
+
3
integral of u^2+1
∫
u
2
+
1
du
derivative ln(1-9x)
derivative
ln
(
1
−
9
x
)
limit as x approaches 1 of-3/(x-1)
lim
x
→
1
(
−
3
x
−
1
)
y^'=y^3-6x^2y^3
y
′
=
y
3
−
6
x
2
y
3
integral of e^{5θ}sin(6θ)
∫
e
5
θ
sin
(
6
θ
)
d
θ
1
..
1374
1375
1376
1377
1378
..
2459