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常见 微积分 问题
integral of sin(h)(x)
∫
sin
(
h
)
(
x
)
dx
integral of x/(sqrt(x+15))
∫
x
√
x
+
1
5
dx
integral of (e^{x+y})
∫
(
e
x
+
y
)
dy
integral of 10x^9-9/(x^9)
∫
1
0
x
9
−
9
x
9
dx
integral of 22sin^2(xco)s^2x
∫
2
2
sin
2
(
xco
)
s
2
xdx
integral of x^2+y^2
∫
x
2
+
y
2
dx
integral from 0 to infinity of x/(1+x^2)
∫
0
∞
x
1
+
x
2
dx
sum from n=1 to infinity of (6^n)/(7^n)
∑
n
=
1
∞
6
n
7
n
derivative 6e^t
derivative
6
e
t
derivative of ln(tanh(x/2))
d
dx
(
ln
(
tanh
(
x
2
)
)
)
integral of 7(1+tan^2(x))
∫
7
(
1
+
tan
2
(
x
)
)
dx
derivative of e^{-ax}
d
dx
(
e
−
ax
)
integral of (56)/(1-cos(7x))
∫
5
6
1
−
cos
(
7
x
)
dx
derivative of (\sqrt[3]{x^2+3}/x)
d
dx
(
3
√
x
2
+
3
x
)
integral of (t^3)/(\sqrt[4]{3+t^4)}
∫
t
3
4
√
3
+
t
4
dt
integral from 0 to 1 of e^{-st}(t)
∫
0
1
e
−
st
(
t
)
dt
49y^{''}-70y^'+25y=0,y(0)=2,y^'(0)=3
4
9
y
′
′
−
7
0
y
′
+
2
5
y
=
0
,
y
(
0
)
=
2
,
y
′
(
0
)
=
3
sum from k=1 to infinity of (sin(100))^k
∑
k
=
1
∞
(
sin
(
1
0
0
)
)
k
integral of ln(x)*sqrt(x)
∫
ln
(
x
)
·
√
x
dx
limit as x approaches 0 of (e^x-1)/(19x)
lim
x
→
0
(
e
x
−
1
1
9
x
)
limit as x approaches-2 of 3x
lim
x
→
−
2
(
3
x
)
(dy)/(dx)=7xe^y,y(0)=0
dy
dx
=
7
xe
y
,
y
(
0
)
=
0
derivative of-3cos^2(xsin(x))
d
dx
(
−
3
cos
2
(
x
)
sin
(
x
)
)
integral of 1/(x(x^2-9)^{3/2)}
∫
1
x
(
x
2
−
9
)
3
2
dx
(dy)/(dx)=2(y^2+1)
dy
dx
=
2
(
y
2
+
1
)
(dy)/(dx)+e^xy=x^2y^2
dy
dx
+
e
x
y
=
x
2
y
2
limit as x approaches-2 of 3x^3-4x+2
lim
x
→
−
2
(
3
x
3
−
4
x
+
2
)
integral of 2/((x^2+1)^2x^2)
∫
2
(
x
2
+
1
)
2
x
2
dx
derivative of x^3(5.4^x)
d
dx
(
x
3
(
5
.
4
)
x
)
derivative of xe^{2y}
d
dx
(
xe
2
y
)
sum from n=0 to infinity of (-3x+1)^n
∑
n
=
0
∞
(
−
3
x
+
1
)
n
integral from 0 to pi/9 of cos(3x)
∫
0
π
9
cos
(
3
x
)
dx
derivative of 1/2 cos(2x)
d
dx
(
1
2
cos
(
2
x
)
)
integral of (10)
∫
(
1
0
)
dx
derivative of 5/((4-7x^3))
d
dx
(
5
(
4
−
7
x
)
3
)
derivative of sqrt(cos^2(x))
d
dx
(
√
cos
2
(
x
)
)
derivative 2x^2-8x+11
derivative
2
x
2
−
8
x
+
1
1
derivative of x^2(x+sin(x)^5)
d
dx
(
x
2
(
x
+
sin
(
x
)
)
5
)
derivative 2tsin(pit)
derivative
2
t
sin
(
π
t
)
tangent f(x)=x^2+3x+2,\at x=3
tangent
f
(
x
)
=
x
2
+
3
x
+
2
,
at
x
=
3
(dx)/(dt)=(x^3-xt^2)/(t^3)
dx
dt
=
x
3
−
xt
2
t
3
derivative h(x)=arcsec(2x)
derivative
h
(
x
)
=
arcsec
(
2
x
)
(\partial)/(\partial x)(xy^2-e^y)
∂
∂
x
(
xy
2
−
e
y
)
limit as x approaches 0 of x^2e^{-x}
lim
x
→
0
(
x
2
e
−
x
)
integral of (3x-1)/(x^2+10x+29)
∫
3
x
−
1
x
2
+
1
0
x
+
2
9
dx
limit as x approaches-2 of (x-4)/(x+2)
lim
x
→
−
2
(
x
−
4
x
+
2
)
derivative (5x+6)/(4x+2)
derivative
5
x
+
6
4
x
+
2
derivative of cos^6(x)
d
dx
(
cos
6
(
x
)
)
integral of (sec^2(θ)+6)
∫
(
sec
2
(
θ
)
+
6
)
d
θ
derivative 1-2sin^2(x)
derivative
1
−
2
sin
2
(
x
)
tangent y=((x+3)/(x-1))^2,(5,4)
tangent
y
=
(
x
+
3
x
−
1
)
2
,
(
5
,
4
)
f(x)=sin(x)+arcsin(x)
f
(
x
)
=
sin
(
x
)
+
arcsin
(
x
)
derivative of log_{2}(5x)
d
dx
(
log
2
(
5
x
)
)
integral of (3+2x^2)/(x^2)
∫
3
+
2
x
2
x
2
dx
derivative of (10/(x^3))
d
dx
(
1
0
x
3
)
inverse拉普拉斯 7/(4s-12)
inverselaplace
7
4
s
−
1
2
integral of sin^2(x)cos^2(x)
∫
sin
2
(
x
)
cos
2
(
x
)
dx
derivative of pi/(x^{18})
d
dx
(
π
x
1
8
)
tangent f(x)=2x^3-6x,\at x=-3
tangent
f
(
x
)
=
2
x
3
−
6
x
,
at
x
=
−
3
integral of ((2x^2-5x+2))/(x^3+x)
∫
(
2
x
2
−
5
x
+
2
)
x
3
+
x
dx
integral of 1/(sqrt(3-x^2+4x))
∫
1
√
3
−
x
2
+
4
x
dx
f(t)=cos(t)+tsin(t)
f
(
t
)
=
cos
(
t
)
+
t
sin
(
t
)
derivative of 1/((x+k^3))
d
dx
(
1
(
x
+
k
)
3
)
integral of (x^5+x-1)/(x^3+1)
∫
x
5
+
x
−
1
x
3
+
1
dx
integral of sin(2x)sqrt(2-cos(2x))
∫
sin
(
2
x
)
√
2
−
cos
(
2
x
)
dx
inverse拉普拉斯 2/(s^2-s)
inverselaplace
2
s
2
−
s
面积 8cos(4x),8-8cos(4x),0, pi/4
area
8
cos
(
4
x
)
,
8
−
8
cos
(
4
x
)
,
0
,
π
4
derivative of (2x/(2+sqrt(x)))
d
dx
(
2
x
2
+
√
x
)
derivative of cos((1-e^{4x}/(1+e^{4x)}))
d
dx
(
cos
(
1
−
e
4
x
1
+
e
4
x
)
)
integral of xcos(3pix^2)
∫
x
cos
(
3
π
x
2
)
dx
ln(x)y^'= y/x
ln
(
x
)
y
′
=
y
x
tangent f(x)=sqrt(-x),\at x=-4
tangent
f
(
x
)
=
√
−
x
,
at
x
=
−
4
y^{''}-8y^'=4t
y
′
′
−
8
y
′
=
4
t
integral of (2x)/(x^2-16)
∫
2
x
x
2
−
1
6
dx
implicit (dy)/(dx),x^2+y^2=0
implicit
dy
dx
,
x
2
+
y
2
=
0
derivative R(t)=(t+e^t)(3-sqrt(t))
derivative
R
(
t
)
=
(
t
+
e
t
)
(
3
−
√
t
)
(\partial)/(\partial x)(x/(x^3-y^5))
∂
∂
x
(
x
x
3
−
y
5
)
sum from n=0 to infinity of 7/(n(n+3))
∑
n
=
0
∞
7
n
(
n
+
3
)
面积 x=-y^2+6,y= x/2-3/2
area
x
=
−
y
2
+
6
,
y
=
x
2
−
3
2
y^'+8y=x
y
′
+
8
y
=
x
d/(d{y)}(1/(sqrt({x)^2+{y)^2+{z}^2}})
d
d
y
(
1
√
x
2
+
y
2
+
z
2
)
integral of-2ln(x)
∫
−
2
ln
(
x
)
dx
d/(dm)(c^{im})
d
dm
(
c
im
)
derivative of 5x^3+2x^2+6x+10
d
dx
(
5
x
3
+
2
x
2
+
6
x
+
1
0
)
derivative g(x)= 1/(5x^2+3x)
derivative
g
(
x
)
=
1
5
x
2
+
3
x
limit as x approaches infinity of x^{-7}
lim
x
→
∞
(
x
−
7
)
derivative of sin(cos(x^2+3x))
d
dx
(
sin
(
cos
(
x
2
+
3
x
)
)
)
derivative of-sec(x+2sec^3(x))
d
dx
(
−
sec
(
x
)
+
2
sec
3
(
x
)
)
derivative of 8x*sin(x)
d
dx
(
8
x
·
sin
(
x
)
)
integral of 1/pi sin(pix)
∫
1
π
sin
(
π
x
)
dx
derivative y=\sqrt[4]{x}
derivative
y
=
4
√
x
derivative y=(sqrt(x))/(8+x)
derivative
y
=
√
x
8
+
x
derivative of cot^7(x)
d
dx
(
cot
7
(
x
)
)
2yy^'+2=y^2+2x,y(0)=4
2
yy
′
+
2
=
y
2
+
2
x
,
y
(
0
)
=
4
derivative (2x)/((x^2+1)^2)
derivative
2
x
(
x
2
+
1
)
2
derivative of x^3+2x^2-x+4
d
dx
(
x
3
+
2
x
2
−
x
+
4
)
integral of 1/(x^2-x^3)
∫
1
x
2
−
x
3
dx
(\partial)/(\partial x)(ln(2x-y))
∂
∂
x
(
ln
(
2
x
−
y
)
)
integral from 0 to 9 of sqrt(9+3x)
∫
0
9
√
9
+
3
x
dx
derivative 3t^2
derivative
3
t
2
1
..
1160
1161
1162
1163
1164
..
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