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limit as x approaches 0+of 1/(e^x-1)
lim
x
→
0
+
(
1
e
x
−
1
)
y^{''}+16y=sec^2(4x)
y
′
′
+
1
6
y
=
sec
2
(
4
x
)
derivative (x^3)/6
derivative
x
3
6
tangent 3xy-2picos(y)=20pi,(6,pi)
tangent
3
xy
−
2
π
cos
(
y
)
=
2
0
π
,
(
6
,
π
)
integral of x^2sin(3x+2)
∫
x
2
sin
(
3
x
+
2
)
dx
integral of x(x+5)^7
∫
x
(
x
+
5
)
7
dx
sum from n=1 to infinity of (n+1)/(n!)
∑
n
=
1
∞
n
+
1
n
!
integral of 1/(4x)-10
∫
1
4
x
−
1
0
dx
derivative of 2/3 (x-1^{3/2})
d
dx
(
2
3
(
x
−
1
)
3
2
)
integral of ((ln(x))^2)/(x^3)
∫
(
ln
(
x
)
)
2
x
3
dx
y^'=-2xe^{2x},y(0)=1
y
′
=
−
2
xe
2
x
,
y
(
0
)
=
1
inverse라플라스 1/(s^1(s+1)^3)
inverselaplace
1
s
1
(
s
+
1
)
3
지역 f(x)=x^2-4,-3,1
area
f
(
x
)
=
x
2
−
4
,
−
3
,
1
integral of sqrt(x\sqrt{x)}
∫
√
x
√
x
dx
d/(dt)(acos(2t)+bsin(2t))
d
dt
(
a
cos
(
2
t
)
+
b
sin
(
2
t
)
)
tangent f(x)=(25-0.075x)x,\at x=100
tangent
f
(
x
)
=
(
2
5
−
0
.
0
7
5
x
)
x
,
at
x
=
1
0
0
integral of (4x^2-14x-6)/(x^3-2x^2-3x)
∫
4
x
2
−
1
4
x
−
6
x
3
−
2
x
2
−
3
x
dx
sum from n=1 to infinity of 1-cos(1/n)
∑
n
=
1
∞
1
−
cos
(
1
n
)
limit as x approaches+1+of (x-1)/(x-1)
lim
x
→
+
1
+
(
x
−
1
x
−
1
)
((y^'-e^{-t}+6))/y =-6
(
y
′
−
e
−
t
+
6
)
y
=
−
6
derivative-0.1x^3+600x-20
derivative
−
0
.
1
x
3
+
6
0
0
x
−
2
0
limit as x approaches 0 of cos(x+sin(x))
lim
x
→
0
(
cos
(
x
+
sin
(
x
)
)
)
limit as x approaches 1 of (x^{1/3}-1)/(x^2+2x-3)
lim
x
→
1
(
x
1
3
−
1
x
2
+
2
x
−
3
)
integral of |2x-6|
∫
|
2
x
−
6
|
dx
derivative f(x)=-5/(x^5)
derivative
f
(
x
)
=
−
5
x
5
(dx)/(dy)=xy^2
dx
dy
=
xy
2
integral of (sin(2x))/(25+cos^2(x))
∫
sin
(
2
x
)
2
5
+
cos
2
(
x
)
dx
f(u)=e^u
f
(
u
)
=
e
u
integral from 1 to 4 of 1/(2x)
∫
1
4
1
2
x
dx
limit as x approaches 6 of 7x+|x-6|
lim
x
→
6
(
7
x
+
|
x
−
6
|
)
(\partial)/(\partial x)(1/(1+e^x))
∂
∂
x
(
1
1
+
e
x
)
derivative sin(cos(7x))
derivative
sin
(
cos
(
7
x
)
)
limit as x approaches 0 of (x^2-x+1)/x
lim
x
→
0
(
x
2
−
x
+
1
x
)
y^'+6y=2t+3
y
′
+
6
y
=
2
t
+
3
inverse라플라스 (s+4)/((s+2)^2)
inverselaplace
s
+
4
(
s
+
2
)
2
(dy)/(dx)=-x/(ye^{x^2)}
dy
dx
=
−
x
ye
x
2
지역 y=x^2-1.52,y=-x^2+1.52
area
y
=
x
2
−
1
.
5
2
,
y
=
−
x
2
+
1
.
5
2
derivative of cos(xy^2)
d
dx
(
cos
(
xy
2
)
)
(\partial)/(\partial y)(2x^2y+2y+5)
∂
∂
y
(
2
x
2
y
+
2
y
+
5
)
limit as x approaches 0 of x+y
lim
x
→
0
(
x
+
y
)
derivative y=(3+5x-8sqrt(x))/x
derivative
y
=
3
+
5
x
−
8
√
x
x
(\partial)/(\partial y)(e^{2x}+yln(x))
∂
∂
y
(
e
2
x
+
y
ln
(
x
)
)
(\partial)/(\partial x)(xarctan(y/z))
∂
∂
x
(
x
arctan
(
y
z
)
)
derivative of (e^{3x}/(x^{15)})
d
dx
(
e
3
x
x
1
5
)
지역 y=2x+1,y=13-x^2,x=-1,x=2
area
y
=
2
x
+
1
,
y
=
1
3
−
x
2
,
x
=
−
1
,
x
=
2
integral of (ln(9x))/x
∫
ln
(
9
x
)
x
dx
integral of (1-cos^2(x))^2sin(x)
∫
(
1
−
cos
2
(
x
)
)
2
sin
(
x
)
dx
laplace변환 s^2+6
laplacetransform
s
2
+
6
tangent f(x)=8x^3-2x^2+2x,\at x=2
tangent
f
(
x
)
=
8
x
3
−
2
x
2
+
2
x
,
at
x
=
2
integral from 0 to t of sin(2s)
∫
0
t
sin
(
2
s
)
ds
integral of 2/(10+6x+x^2)
∫
2
1
0
+
6
x
+
x
2
dx
derivative 1/(\sqrt[4]{x)}
derivative
1
4
√
x
integral of (1-x)(1-2x)(1-3x)
∫
(
1
−
x
)
(
1
−
2
x
)
(
1
−
3
x
)
dx
integral of (sin^2(x)cos(2x))/2
∫
sin
2
(
x
)
cos
(
2
x
)
2
dx
integral from 1 to 2 of ((2+2x-x^2))/8
∫
1
2
(
2
+
2
x
−
x
2
)
8
dx
x^{''}-12x^'+36x=2te^{6t}
x
′
′
−
1
2
x
′
+
3
6
x
=
2
te
6
t
sum from n=1 to infinity of (5^n)/(n^4)
∑
n
=
1
∞
5
n
n
4
integral of (x^8)/(x^9-2)
∫
x
8
x
9
−
2
dx
integral of cos^3(5x)sin^4(5x)
∫
cos
3
(
5
x
)
sin
4
(
5
x
)
dx
integral from 0 to 5 of xe^{-x}
∫
0
5
xe
−
x
dx
integral from 2 to infinity of 3x^{-2}
∫
2
∞
3
x
−
2
dx
integral of (e^{-5ln(x)})/((1/(x^5))^2)
∫
e
−
5
ln
(
x
)
(
1
x
5
)
2
dx
integral of 6x^5-7x^4-6x^2
∫
6
x
5
−
7
x
4
−
6
x
2
dx
integral of cos(8)
∫
cos
(
8
)
(dy)/(dx)+((y^2))/(x^2)=0
dy
dx
+
(
y
2
)
x
2
=
0
limit as x approaches-1+of (x+1)^{0.5}+2
lim
x
→
−
1
+
(
(
x
+
1
)
0
.
5
+
2
)
derivative f(x)=(1/2)^x
derivative
f
(
x
)
=
(
1
2
)
x
integral of 3cos(x)+2/(sqrt(x))
∫
3
cos
(
x
)
+
2
√
x
dx
sum from n=4 to infinity of 1/(n-3)
∑
n
=
4
∞
1
n
−
3
derivative of 1/(1+2/x)
d
dx
(
1
1
+
2
x
)
integral of x^{-15}
∫
x
−
1
5
dx
derivative of 0.8cos(x+0.5sin(2x))
d
dx
(
0
.
8
cos
(
x
)
+
0
.
5
sin
(
2
x
)
)
derivative of (98/((7x-13)^3))
d
dx
(
9
8
(
7
x
−
1
3
)
3
)
limit as x approaches 1 of 5x-3
lim
x
→
1
(
5
x
−
3
)
derivative xsin(3x)
derivative
x
sin
(
3
x
)
integral of 1/((10x-1)^6)
∫
1
(
1
0
x
−
1
)
6
dx
(\partial)/(\partial x)(3-x^2+xy-2y^2)
∂
∂
x
(
3
−
x
2
+
xy
−
2
y
2
)
integral of \sqrt[7]{x}
∫
7
√
x
dx
derivative (7^x)/(x^3)
derivative
7
x
x
3
integral of (3/x-9e^{5x}+sqrt(x^9))
∫
(
3
x
−
9
e
5
x
+
√
x
9
)
dx
derivative y=mx+b
derivative
y
=
mx
+
b
integral from 4 to 6 of (x^2+2x-2)
∫
4
6
(
x
2
+
2
x
−
2
)
dx
derivative of (x^4/(5-x^3))
d
dx
(
x
4
5
−
x
3
)
integral of (4cos(x)+3sin(x))
∫
(
4
cos
(
x
)
+
3
sin
(
x
)
)
dx
지역 sqrt(x), 1/x ,[1,8]
area
√
x
,
1
x
,
[
1
,
8
]
derivative y= 1/(tan(e^{4x))}
derivative
y
=
1
tan
(
e
4
x
)
integral from 1 to 2 of integral from y to y^3 of 2e^{x/y}
∫
1
2
∫
y
y
3
2
e
x
y
dxdy
sum from n=1 to infinity of (ln(n))/(4n)
∑
n
=
1
∞
ln
(
n
)
4
n
laplace변환 sqrt(t/pi)
laplacetransform
√
t
π
integral of 1/(sqrt(x)(1+\sqrt{x))}
∫
1
√
x
(
1
+
√
x
)
dx
integral from 0 to pi/2 of-9cos^5(x)
∫
0
π
2
−
9
cos
5
(
x
)
dx
integral of (2x-5)/(x^2-5x-1)
∫
2
x
−
5
x
2
−
5
x
−
1
dx
(\partial)/(\partial x)(sin(xy)+xcos(y))
∂
∂
x
(
sin
(
xy
)
+
x
cos
(
y
)
)
derivative of (x-sqrt(x)/(x^{1/9)})
d
dx
(
x
−
√
x
x
1
9
)
지역 y=2x+5,y=14-x^2,(-1,2)
area
y
=
2
x
+
5
,
y
=
1
4
−
x
2
,
(
−
1
,
2
)
지역 y=x^{1/2},y=x^2
area
y
=
x
1
2
,
y
=
x
2
integral from 1 to e of (1-ln(x))/x
∫
1
e
1
−
ln
(
x
)
x
dx
(\partial)/(\partial b)(mx+b)
∂
∂
b
(
mx
+
b
)
limit as x approaches 0 of e^{4/(x^2)}
lim
x
→
0
(
e
4
x
2
)
derivative f(x)=3x^4(x-3)^2
derivative
f
(
x
)
=
3
x
4
(
x
−
3
)
2
1
..
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1385
1386
1387
1388
..
2459