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常见 微积分 问题
integral of 3/(x^4)sqrt(8-1/(x^3))
∫
3
x
4
√
8
−
1
x
3
dx
derivative of \sqrt[3]{2x+1}
d
dx
(
3
√
2
x
+
1
)
integral of 2cos^2(x)tan^2(x)
∫
2
cos
2
(
x
)
tan
2
(
x
)
dx
f(x)=(ln(x))^4
f
(
x
)
=
(
ln
(
x
)
)
4
(d^2)/(dx^2)(cos(2x))
d
2
dx
2
(
cos
(
2
x
)
)
integral of (x^2)/(sqrt(3-x^2))
∫
x
2
√
3
−
x
2
dx
derivative 5y^2(4y^2+7)^{6/5}
derivative
5
y
2
(
4
y
2
+
7
)
6
5
integral of sqrt(-x^2+1)
∫
√
−
x
2
+
1
dx
(\partial)/(\partial x)(10sin(x))
∂
∂
x
(
1
0
sin
(
x
)
)
integral of (2sech^2(t))/(tanh(t))
∫
2
sech
2
(
t
)
tanh
(
t
)
dt
sum from n=1 to infinity of n/(4(n+1)!)
∑
n
=
1
∞
n
4
(
n
+
1
)
!
derivative ln((x^2(x+1))/(sqrt(x+2)))
derivative
ln
(
x
2
(
x
+
1
)
√
x
+
2
)
integral of (5+4x)/(1+x^2)
∫
5
+
4
x
1
+
x
2
dx
integral of e^{-x/8}
∫
e
−
x
8
dx
x^{''}+2x^'+2=0,x(0)=0,x^'(0)=1
x
′
′
+
2
x
′
+
2
=
0
,
x
(
0
)
=
0
,
x
′
(
0
)
=
1
limit as x approaches 0 of 1/(x^3-7x)
lim
x
→
0
(
1
x
3
−
7
x
)
面积 f(x)=2x^3+3x^2-5x,-4,3
area
f
(
x
)
=
2
x
3
+
3
x
2
−
5
x
,
−
4
,
3
(\partial)/(\partial x)(x^3ln(yz))
∂
∂
x
(
x
3
ln
(
yz
)
)
integral of xsqrt(x-12)
∫
x
√
x
−
1
2
dx
x(dv)/(dx)= 2/v+v
x
dv
dx
=
2
v
+
v
(dy)/(dx)=2y+x(e^{3x}-e^{2x})
dy
dx
=
2
y
+
x
(
e
3
x
−
e
2
x
)
integral from 0 to pi of pi(sin(x))^2
∫
0
π
π
(
sin
(
x
)
)
2
dx
laplace变换 e^{-t}-e^{-2t}
laplacetransform
e
−
t
−
e
−
2
t
sum from n=0 to infinity of 5(2/3)^{n-1}
∑
n
=
0
∞
5
(
2
3
)
n
−
1
limit as x approaches 0 of xcot(3x)
lim
x
→
0
(
x
cot
(
3
x
)
)
integral of (3x^2+4)/(x^3+4x)
∫
3
x
2
+
4
x
3
+
4
x
dx
integral of log_{e}(x)
∫
log
e
(
x
)
dx
derivative of c_{1}e^{-4x}
d
dx
(
c
1
e
−
4
x
)
inverse拉普拉斯 e^{-s}
inverselaplace
e
−
s
y^'-0.4y=29sin(x)
y
′
−
0
.
4
y
=
2
9
sin
(
x
)
泰勒 1/((1-x)^2),0
taylor
1
(
1
−
x
)
2
,
0
derivative h(t)=-16t^2+144t
derivative
h
(
t
)
=
−
1
6
t
2
+
1
4
4
t
derivative 30e^{-0.0000323h}
derivative
3
0
e
−
0
.
0
0
0
0
3
2
3
h
limit as x approaches 0 of-2xsin(1/x)
lim
x
→
0
(
−
2
x
sin
(
1
x
)
)
(\partial)/(\partial y)(xy^2-6x^2-3y^2)
∂
∂
y
(
xy
2
−
6
x
2
−
3
y
2
)
derivative y=(8x^3+5)^{3/2}
derivative
y
=
(
8
x
3
+
5
)
3
2
面积 y=e^x,y=e^{-2x},x=ln(6)
area
y
=
e
x
,
y
=
e
−
2
x
,
x
=
ln
(
6
)
derivative of-1/(x^2-1)
d
dx
(
−
1
x
2
−
1
)
derivative (480x)/((x^2+5)^3)
derivative
4
8
0
x
(
x
2
+
5
)
3
derivative of ln(sqrt(x^2-5))
d
dx
(
ln
(
√
x
2
−
5
)
)
derivative f(x)=(x^2-8)^2
derivative
f
(
x
)
=
(
x
2
−
8
)
2
derivative of x^2Inx
d
dx
(
x
2
Inx
)
limit as n approaches infinity of-1/n
lim
n
→
∞
(
−
1
n
)
integral of (3x^2+1)/(x(x-1)^3)
∫
3
x
2
+
1
x
(
x
−
1
)
3
dx
integral of x(x+5)^4
∫
x
(
x
+
5
)
4
dx
integral of cos^{(3)}(5x)sin^{-2}(5x)
∫
cos
(
3
)
(
5
x
)
sin
−
2
(
5
x
)
dx
(\partial)/(\partial x)(e^{x^5})
∂
∂
x
(
e
x
5
)
(\partial)/(\partial x)(x/((1-x)^2))
∂
∂
x
(
x
(
1
−
x
)
2
)
(\partial)/(\partial y)(1/(x^3-y^2))
∂
∂
y
(
1
x
3
−
y
2
)
tangent f(x)=x^2+3,\at x=1
tangent
f
(
x
)
=
x
2
+
3
,
at
x
=
1
limit as x approaches-10-of (x+9)/(x+10)
lim
x
→
−
1
0
−
(
x
+
9
x
+
1
0
)
(\partial)/(\partial x)(2e^{-y}x)
∂
∂
x
(
2
e
−
y
x
)
integral of (sin(2x))/(37+cos^2(x))
∫
sin
(
2
x
)
3
7
+
cos
2
(
x
)
dx
integral of x*log_{10}(x)
∫
x
·
log
1
0
(
x
)
dx
limit as m approaches 4 of (3m^2-8m-16)/(2m^2-9m+4)
lim
m
→
4
(
3
m
2
−
8
m
−
1
6
2
m
2
−
9
m
+
4
)
integral of 8y-24
∫
8
y
−
2
4
dy
limit as x approaches 5+of (-1)/(x^2-25)
lim
x
→
5
+
(
−
1
x
2
−
2
5
)
integral of 9θcos(θ)
∫
9
θ
cos
(
θ
)
d
θ
面积 x^2-3,2x
area
x
2
−
3
,
2
x
derivative e^x+3xe^x
derivative
e
x
+
3
xe
x
limit as x approaches 0+of x^{4sin(x)}
lim
x
→
0
+
(
x
4
sin
(
x
)
)
normal y=x^2-9x,(3,-18)
normal
y
=
x
2
−
9
x
,
(
3
,
−
1
8
)
derivative of 4(cos(x^2-2x^2sin(x^2)))
d
dx
(
4
(
cos
(
x
2
)
−
2
x
2
sin
(
x
2
)
)
)
integral of sqrt(tan^3(x))sec^4(x)
∫
√
tan
3
(
x
)
sec
4
(
x
)
dx
integral of x^{-5}
∫
x
−
5
dx
integral of (2x+1)/(x^2+6x+10)
∫
2
x
+
1
x
2
+
6
x
+
1
0
dx
limit as t approaches infinity of 1/(4t)
lim
t
→
∞
(
1
4
t
)
derivative f(x)=(sqrt(x))/(x+6)
derivative
f
(
x
)
=
√
x
x
+
6
化简 ln(xy)
simplify
ln
(
xy
)
(\partial)/(\partial x)(y^2-e^{xy}y)
∂
∂
x
(
y
2
−
e
xy
y
)
integral of (x+1)^4
∫
(
x
+
1
)
4
dx
integral of 1/(sqrt(4x^2-49))
∫
1
√
4
x
2
−
4
9
dx
integral of 2cos(4x)
∫
2
cos
(
4
x
)
dx
limit as x approaches 2+of (2-x)/(x^2-4)
lim
x
→
2
+
(
2
−
x
x
2
−
4
)
derivative of ln(2x+4)
d
dx
(
ln
(
2
x
+
4
)
)
integral of ln(u)
∫
ln
(
u
)
du
limit as x approaches infinity of (sqrt(x^2+3))/(sqrt(3x^2+1))
lim
x
→
∞
(
√
x
2
+
3
√
3
x
2
+
1
)
integral of (2x^3+x^2-5)/(x-1)
∫
2
x
3
+
x
2
−
5
x
−
1
dx
(x^2+1)y^'+5x(y-1)=0,y(0)=9
(
x
2
+
1
)
y
′
+
5
x
(
y
−
1
)
=
0
,
y
(
0
)
=
9
sum from n=0 to infinity of q^n
∑
n
=
0
∞
q
n
integral of (1+8v)/(-16v^2)
∫
1
+
8
v
−
1
6
v
2
dv
x(dy)/(dx)=x^2+3y
x
dy
dx
=
x
2
+
3
y
integral of ((x-2))/(sqrt(4x-x^2))
∫
(
x
−
2
)
√
4
x
−
x
2
dx
derivative of (x-5/(x+5))
d
dx
(
x
−
5
x
+
5
)
斜率 (4,-2),(-5,4)
slope
(
4
,
−
2
)
,
(
−
5
,
4
)
derivative of-((x^3+x-1/2))
d
dx
(
−
(
x
3
+
x
−
1
2
)
)
derivative f(x)= 7/x-sqrt(x)
derivative
f
(
x
)
=
7
x
−
√
x
derivative of 1+2sqrt(x)
d
dx
(
1
+
2
√
x
)
(\partial)/(\partial x)(log_{10}(x))
∂
∂
x
(
log
1
0
(
x
)
)
derivative ((5x-1)/(4x+2))^{-5}
derivative
(
5
x
−
1
4
x
+
2
)
−
5
limit as x approaches 0-of 1-e^x
lim
x
→
0
−
(
1
−
e
x
)
integral from 0 to 3 of (10x-6x^2+9)
∫
0
3
(
1
0
x
−
6
x
2
+
9
)
dx
integral of cos(t)sin^7(t)
∫
cos
(
t
)
sin
7
(
t
)
dt
(dy)/(dx)-y=e^{2x}
dy
dx
−
y
=
e
2
x
integral of 2x(x^2+3)^3
∫
2
x
(
x
2
+
3
)
3
dx
derivative of (x^2/(3+4x))
d
dx
(
x
2
3
+
4
x
)
derivative x^{log_{5}(x)}
derivative
x
log
5
(
x
)
(\partial)/(\partial x)(8/(x^2+y^2))
∂
∂
x
(
8
x
2
+
y
2
)
derivative of 1/(x+x^{-1})
d
dx
(
1
x
+
x
−
1
)
tangent sqrt(x)-1
tangent
√
x
−
1
1
..
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1207
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