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일반적인 미적분학 문제
integral of xsqrt(1+3x)
∫
x
√
1
+
3
x
dx
(\partial)/(\partial x)(x-2y^2-2z^2)
∂
∂
x
(
x
−
2
y
2
−
2
z
2
)
integral from 1 to 9 of (x-1)/(sqrt(x))
∫
1
9
x
−
1
√
x
dx
limit as x approaches 2 of 3x^2-4x+2
lim
x
→
2
(
3
x
2
−
4
x
+
2
)
derivative x^3(x-3)^2
derivative
x
3
(
x
−
3
)
2
derivative of x/(x^3-1)
d
dx
(
x
x
3
−
1
)
integral of (u+4)(2u+1)
∫
(
u
+
4
)
(
2
u
+
1
)
du
y^{''}-2y^'+2y=cos(t),y(0)=1,y^'(0)=0
y
′
′
−
2
y
′
+
2
y
=
cos
(
t
)
,
y
(
0
)
=
1
,
y
′
(
0
)
=
0
integral of 1/(sqrt(2+x^2))
∫
1
√
2
+
x
2
dx
integral of 1/(x^2)e^{ln(x)}
∫
1
x
2
e
ln
(
x
)
dx
derivative of (2x^3/3-8x-5)
d
dx
(
2
x
3
3
−
8
x
−
5
)
지역 y=tan(7x),y=2sin(7x)
area
y
=
tan
(
7
x
)
,
y
=
2
sin
(
7
x
)
x(dy)/(dx)+y=y^2
x
dy
dx
+
y
=
y
2
derivative x^2+x
derivative
x
2
+
x
integral from-2 to 2 of (x^3)
∫
−
2
2
(
x
3
)
dx
derivative of (54/x)
d
dx
(
5
4
x
)
integral of (2x-5)/(x^3+4x^2+4x)
∫
2
x
−
5
x
3
+
4
x
2
+
4
x
dx
integral of 1/(1/x+2)
∫
1
1
x
+
2
dx
limit as x approaches 0 of 5x-6
lim
x
→
0
(
5
x
−
6
)
지역 2y=4sqrt(x),y=4,2y+4x=8
area
2
y
=
4
√
x
,
y
=
4
,
2
y
+
4
x
=
8
integral of 1 x^2
∫
d
1
x
2
dx
tangent sin(3x)+cos(8x)
tangent
sin
(
3
x
)
+
cos
(
8
x
)
단순화 1/3 x^6(x^2-3)
simplify
1
3
x
6
(
x
2
−
3
)
derivative of (5-2x^{-2})
d
dx
(
(
5
−
2
x
)
−
2
)
derivative 1+12sqrt(t)
derivative
1
+
1
2
√
t
y^{''}+9y=sin(3t)
y
′
′
+
9
y
=
sin
(
3
t
)
derivative of \sqrt[8]{8x^7-10}
d
dx
(
8
√
8
x
7
−
1
0
)
(dy)/(dx)=arctan(-6x)
dy
dx
=
arctan
(
−
6
x
)
y=((2x+1)/(3x-1))^4
y
=
(
2
x
+
1
3
x
−
1
)
4
integral of e^{-6x}
∫
e
−
6
x
dx
sum from n=1 to infinity of (x-3)^n
∑
n
=
1
∞
(
x
−
3
)
n
limit as x approaches 1 of 4/(x-1)
lim
x
→
1
(
4
x
−
1
)
(d^2)/(dx^2)(2x^3)
d
2
dx
2
(
2
x
3
)
(dy)/(dx)-2y=1-2x
dy
dx
−
2
y
=
1
−
2
x
limit as a approaches-2 of a^2+3m-1
lim
a
→
−
2
(
a
2
+
3
m
−
1
)
y^{''}+y^'+y=5cos(4x)
y
′
′
+
y
′
+
y
=
5
cos
(
4
x
)
tangent f(x)=x^2+3x+4pi
tangent
f
(
x
)
=
x
2
+
3
x
+
4
π
limit as t approaches 0 of 2e^{-t}
lim
t
→
0
(
2
e
−
t
)
limit as x approaches 0 of (8x^2-2x)/(2x)
lim
x
→
0
(
8
x
2
−
2
x
2
x
)
integral of (2x-sqrt(x))^2
∫
(
2
x
−
√
x
)
2
dx
(\partial)/(\partial x)(4sin(x)cos(y))
∂
∂
x
(
4
sin
(
x
)
cos
(
y
)
)
(\partial}{\partial {K}}(L^{1/2)/K ^{1/2})
∂
∂
K
(
L
1
2
K
1
2
)
limit as x approaches 4 of x+4
lim
x
→
4
(
x
+
4
)
derivative f(x)=4x-7
derivative
f
(
x
)
=
4
x
−
7
integral from 0 to 4 of sqrt(y)
∫
0
4
√
y
dy
derivative of (2x+5^4)
d
dx
(
(
2
x
+
5
)
4
)
inverse라플라스 5/(s^2+2s+5)
inverselaplace
5
s
2
+
2
s
+
5
derivative of ln(1+4x^2)
d
dx
(
ln
(
1
+
4
x
2
)
)
integral from-1 to 3 of-x^2
∫
−
1
3
−
x
2
dx
derivative of 6/(5x^3)
d
dx
(
6
5
x
3
)
integral of sin^2(x/2)cos(x/2)
∫
sin
2
(
x
2
)
cos
(
x
2
)
dx
derivative f(x)=(6x+5)(x^3-2)
derivative
f
(
x
)
=
(
6
x
+
5
)
(
x
3
−
2
)
limit as x approaches+3 of 0
lim
x
→
+
3
(
0
)
derivative-y/(x+5e)
derivative
−
y
x
+
5
e
integral of cos^4(x)sin^3(x)
∫
cos
4
(
x
)
sin
3
(
x
)
dx
derivative sin(6x)
derivative
sin
(
6
x
)
limit as x approaches 0 of x^3sin(x)
lim
x
→
0
(
x
3
sin
(
x
)
)
limit as x approaches-infinity of 1-e^{-x}-xe^{-x}
lim
x
→
−
∞
(
1
−
e
−
x
−
xe
−
x
)
derivative f(x)=x^4-12x^3+3
derivative
f
(
x
)
=
x
4
−
1
2
x
3
+
3
integral of 8sin^3(x)cos(x)
∫
8
sin
3
(
x
)
cos
(
x
)
dx
(\partial)/(\partial x)(xyln(xy))
∂
∂
x
(
xy
ln
(
xy
)
)
tangent f(x)=\sqrt[3]{x},\at x=64
tangent
f
(
x
)
=
3
√
x
,
at
x
=
6
4
integral of 2x^2+5
∫
2
x
2
+
5
dx
(xdy)/(dx)=-y+2x^2y,y(1)=1
xdy
dx
=
−
y
+
2
x
2
y
,
y
(
1
)
=
1
derivative of 9x-8sqrt(x)
d
dx
(
9
x
−
8
√
x
)
limit as y approaches 2 of sqrt(4y^2-2y)
lim
y
→
2
(
√
4
y
2
−
2
y
)
integral from 0 to-0.3 of 300x
∫
0
−
0
.
3
3
0
0
xdx
integral of 3t^{-4}
∫
3
t
−
4
dt
integral of 1/((x+2)^2(x-5))
∫
1
(
x
+
2
)
2
(
x
−
5
)
dx
integral of sin(3θ)
∫
sin
(
3
θ
)
d
θ
tangent f(x)=e^{2x},\at x= 1/2 ln(3)
tangent
f
(
x
)
=
e
2
x
,
at
x
=
1
2
ln
(
3
)
derivative ((t^3)/(t^6+7))^2
derivative
(
t
3
t
6
+
7
)
2
integral of x/(sqrt(16+x^2))
∫
x
√
1
6
+
x
2
dx
limit as x approaches 3 of 2x+|x-3|
lim
x
→
3
(
2
x
+
|
x
−
3
|
)
limit as x approaches 7 of (x+5)/(x+9)
lim
x
→
7
(
x
+
5
x
+
9
)
x^2y^{''}+xy^'+9y=10x
x
2
y
′
′
+
xy
′
+
9
y
=
1
0
x
경사지 y=x^3+2
slope
y
=
x
3
+
2
integral of tan^3(6x)
∫
tan
3
(
6
x
)
dx
integral of x/(sqrt(x^2-6x+5))
∫
x
√
x
2
−
6
x
+
5
dx
integral of (7+x-3x^2)e^{-x}
∫
(
7
+
x
−
3
x
2
)
e
−
x
dx
derivative sqrt(sin(x))
derivative
√
sin
(
x
)
tangent 2x^3+3x^2-12x+8
tangent
2
x
3
+
3
x
2
−
1
2
x
+
8
limit as x approaches infinity of e^{nx}
lim
x
→
∞
(
e
nx
)
derivative of (2x/(\sqrt[3]{x-2)})
d
dx
(
2
x
3
√
x
−
2
)
integral of x(x+1)
∫
x
(
x
+
1
)
dx
implicit (dy)/(dx),e^{x/y}=x-y
implicit
dy
dx
,
e
x
y
=
x
−
y
y^{''}+16.67y^'+10000y=0
y
′
′
+
1
6
.
6
7
y
′
+
1
0
0
0
0
y
=
0
tangent y=6x^2-6x+3,(1,3)
tangent
y
=
6
x
2
−
6
x
+
3
,
(
1
,
3
)
integral of 9y
∫
9
ydy
integral of 2/3 x^{-1/3}
∫
2
3
x
−
1
3
dx
limit as n approaches 0 of (1+n)^{1/n}
lim
n
→
0
(
(
1
+
n
)
1
n
)
derivative f(x)= 7/(x^3)
derivative
f
(
x
)
=
7
x
3
용량about y=0,y=ln(x),y=0,[1,2]
volumeabout
y
=
0
,
y
=
ln
(
x
)
,
y
=
0
,
[
1
,
2
]
(dy)/(dx)=-9.81+0.00375y^2
dy
dx
=
−
9
.
8
1
+
0
.
0
0
3
7
5
y
2
laplace변환 e^{-3t}cos(-t)
laplacetransform
e
−
3
t
cos
(
−
t
)
integral of 5u^{3/2}
∫
5
u
3
2
du
derivative of (2x-6/(4-x))
d
dx
(
2
x
−
6
4
−
x
)
integral of (x^2)/((x^3+1)^2)
∫
x
2
(
x
3
+
1
)
2
dx
derivative of 9/(sqrt(x+4))
d
dx
(
9
√
x
+
4
)
derivative of (2x+5/(7x^2))
d
dx
(
2
x
+
5
7
x
2
)
1
..
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1490
..
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