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일반적인 미적분학 문제
integral from-3 to 3 of (9-x^2)^2
∫
−
3
3
(
9
−
x
2
)
2
dx
integral of (1-x^2)/(x(x^2+1))
∫
1
−
x
2
x
(
x
2
+
1
)
dx
integral of e^x+x^2
∫
e
x
+
x
2
dx
limit as x approaches 0 of 0
lim
x
→
0
(
0
)
derivative of 3x^7
d
dx
(
3
x
7
)
integral from 4 to infinity of xe^{-x}
∫
4
∞
xe
−
x
dx
derivative f(r)=sqrt(r)+\sqrt[7]{r}
derivative
f
(
r
)
=
√
r
+
7
√
r
integral of (2xe^{-3x})
∫
(
2
xe
−
3
x
)
dx
limit as x approaches 0 of (3tan(x))/x
lim
x
→
0
(
3
tan
(
x
)
x
)
y^'+2sin(2x)y=2sin(2x),y(pi/2)=3
y
′
+
2
sin
(
2
x
)
y
=
2
sin
(
2
x
)
,
y
(
π
2
)
=
3
(dx)/(dy)=xy
dx
dy
=
xy
derivative of-csc(x-sin(x))
d
dx
(
−
csc
(
x
)
−
sin
(
x
)
)
integral of 5sin^3(9x)
∫
5
sin
3
(
9
x
)
dx
(\partial)/(\partial y)(4xy-2e^{2x+y})
∂
∂
y
(
4
xy
−
2
e
2
x
+
y
)
limit as h approaches 0 of (-4)^2+2(-4)
lim
h
→
0
(
(
−
4
)
2
+
2
(
−
4
)
)
integral of (x^2)/(sqrt(21+4x-x^2))
∫
x
2
√
2
1
+
4
x
−
x
2
dx
inverse라플라스 ((s+9))/((s^2+6s+34))
inverselaplace
(
s
+
9
)
(
s
2
+
6
s
+
3
4
)
integral of x^2sqrt(x^3+19)
∫
x
2
√
x
3
+
1
9
dx
(dy)/(dx)-2/x y= 3/(x^2)y^4
dy
dx
−
2
x
y
=
3
x
2
y
4
integral from 1 to 2 of 13sqrt(4x^2-3)
∫
1
2
1
3
√
4
x
2
−
3
dx
derivative of-5x+2
d
dx
(
−
5
x
+
2
)
(\partial)/(\partial y)(2x-y^2)
∂
∂
y
(
2
x
−
y
2
)
derivative-5/(4y^3)
derivative
−
5
4
y
3
derivative of cos(x^{-5})
d
dx
(
cos
(
x
−
5
)
)
integral of (2sin(θ)-csc(θ))^2
∫
(
2
sin
(
θ
)
−
csc
(
θ
)
)
2
d
θ
derivative y=(4x-5)2
derivative
y
=
(
4
x
−
5
)
2
(x+9/x)^'
(
x
+
9
x
)
′
integral of 7cot^4(5t)
∫
7
cot
4
(
5
t
)
dt
integral from-1 to 1 of 1-x^4
∫
−
1
1
1
−
x
4
dx
(\partial)/(\partial y)(y(-2x-y+1))
∂
∂
y
(
y
(
−
2
x
−
y
+
1
)
)
integral from pi/2 to pi of-cos(x)
∫
π
2
π
−
cos
(
x
)
dx
integral of x^2e^{-x}
∫
x
2
e
−
x
dx
derivative h(t)=3ln(t^6)
derivative
h
(
t
)
=
3
ln
(
t
6
)
integral of 24+cos(x)
∫
2
4
+
cos
(
x
)
dx
tangent (-4x)/(x^2+1)(-1.2)
tangent
−
4
x
x
2
+
1
(
−
1
.
2
)
d/(d{x)}({x}^2+{x}{z}-{y}+{y}^2+{y}{z}+3{z}^2)
d
d
x
(
x
2
+
x
z
−
y
+
y
2
+
y
z
+
3
z
2
)
integral of x*e^{x/4}
∫
x
·
e
x
4
dx
(\partial)/(\partial x)(4sqrt(y/x))
∂
∂
x
(
4
√
y
x
)
d/(dy)(xy)
d
dy
(
xy
)
derivative y=(x)
derivative
y
=
(
x
)
지역 y=4x-16,y^2=4x+4
area
y
=
4
x
−
1
6
,
y
2
=
4
x
+
4
derivative y=arctan(sqrt(7x^2-1))
derivative
y
=
arctan
(
√
7
x
2
−
1
)
integral of x(cos^2(x))
∫
x
(
cos
2
(
x
)
)
dx
derivative y=x^2-2x-8
derivative
y
=
x
2
−
2
x
−
8
integral of (x^2+y)
∫
(
x
2
+
y
)
dx
d/(dy)(1/(sqrt(y^2+1)))
d
dy
(
1
√
y
2
+
1
)
y^'+2xy=2x^3
y
′
+
2
xy
=
2
x
3
derivative of (x^2-3/(x+2))
d
dx
(
x
2
−
3
x
+
2
)
integral from 0 to 4 of 4x
∫
0
4
4
xdx
integral of (sin(x))/((1+cos(x))^3)
∫
sin
(
x
)
(
1
+
cos
(
x
)
)
3
dx
x^{''}=0
x
′
′
=
0
integral of cos^5(x)sqrt(sin(x))
∫
cos
5
(
x
)
√
sin
(
x
)
dx
derivative of xln(x+2)
d
dx
(
x
ln
(
x
+
2
)
)
y^{''}+16y=1+2sin(4x)
y
′
′
+
1
6
y
=
1
+
2
sin
(
4
x
)
tangent (3x)/(4-x^2),\at x=1
tangent
3
x
4
−
x
2
,
at
x
=
1
integral from b to 1 of 2ln(x)
∫
b
1
2
ln
(
x
)
dx
integral of (x^2+2)^{3/2}
∫
(
x
2
+
2
)
3
2
dx
derivative of (x-sqrt(x)/(x^{1/5)})
d
dx
(
x
−
√
x
x
1
5
)
integral of (x^3)/(sqrt((4-x^2)^3))
∫
x
3
√
(
4
−
x
2
)
3
dx
y^'=(x+y-1)^2-1
y
′
=
(
x
+
y
−
1
)
2
−
1
(\partial)/(\partial x)(t/(x-1))
∂
∂
x
(
t
x
−
1
)
integral of 2x-2y
∫
2
x
−
2
ydx
테일러 1/(1-z^2),0
taylor
1
1
−
z
2
,
0
(\partial)/(\partial x)(1/2 ln(x))
∂
∂
x
(
1
2
ln
(
x
)
)
(x^2+1)y^'+8x(y-1)=0,y(0)=3
(
x
2
+
1
)
y
′
+
8
x
(
y
−
1
)
=
0
,
y
(
0
)
=
3
(\partial)/(\partial x)(4x^2-4xy+xyz)
∂
∂
x
(
4
x
2
−
4
xy
+
xyz
)
integral of (tan(x))/(1+cos(x))
∫
tan
(
x
)
1
+
cos
(
x
)
dx
지역 6-x^2,x^2-2,[0,3]
area
6
−
x
2
,
x
2
−
2
,
[
0
,
3
]
integral of (ln(y))/(ln(y))
∫
ln
(
y
)
ln
(
y
)
dy
e^{t^2}y^'+(t+ty^2)=0,y(0)=1
e
t
2
y
′
+
(
t
+
ty
2
)
=
0
,
y
(
0
)
=
1
tangent (64x)/(x^2+64)
tangent
6
4
x
x
2
+
6
4
(\partial)/(\partial y)(2x^3-x^2y)
∂
∂
y
(
2
x
3
−
x
2
y
)
integral of (t^2-1)(4+3t)
∫
(
t
2
−
1
)
(
4
+
3
t
)
dt
tangent f(x)=x^4,\at x=1
tangent
f
(
x
)
=
x
4
,
at
x
=
1
tangent y= 6/(sqrt(x)),(25, 6/5)
tangent
y
=
6
√
x
,
(
2
5
,
6
5
)
derivative (x^2)/(7+sqrt(x))
derivative
x
2
7
+
√
x
limit as x approaches infinity of ((sqrt(2x^2+1)))/(3x-5)
lim
x
→
∞
(
(
√
2
x
2
+
1
)
3
x
−
5
)
y^{''}-2y^'=2t
y
′
′
−
2
y
′
=
2
t
limit as x approaches 3+of (x^2+x)/(x-3)
lim
x
→
3
+
(
x
2
+
x
x
−
3
)
laplace변환 cos(t+pi/4)
laplacetransform
cos
(
t
+
π
4
)
integral of (3y+7)
∫
(
3
y
+
7
)
dy
inverse라플라스 5/(s+2)
inverselaplace
5
s
+
2
derivative x^{2x}
derivative
x
2
x
x^2(dy)/(dx)-2xy=4y^4,y(1)= 1/3
x
2
dy
dx
−
2
xy
=
4
y
4
,
y
(
1
)
=
1
3
xy^'+y^2+y=0
xy
′
+
y
2
+
y
=
0
derivative f(x)=3x^2+2x
derivative
f
(
x
)
=
3
x
2
+
2
x
derivative f(x)=sin^2(x)+cos^2(x)
derivative
f
(
x
)
=
sin
2
(
x
)
+
cos
2
(
x
)
integral from 1 to 2 of 2x
∫
1
2
2
xdx
d/(dt)(st^2)
d
dt
(
st
2
)
tangent-4x^2-3x+2,\at x=-1
tangent
−
4
x
2
−
3
x
+
2
,
at
x
=
−
1
integral of 1/(5x^4)
∫
1
5
x
4
dx
derivative of (sin(x)/(sqrt(1+cos(x))))
d
dx
(
sin
(
x
)
√
1
+
cos
(
x
)
)
integral of 22x
∫
2
2
xdx
(dx)/(dt)=(e^t-e^{-t})/(3+x)
dx
dt
=
e
t
−
e
−
t
3
+
x
derivative y= 1/2 e^{2x}
derivative
y
=
1
2
e
2
x
(\partial)/(\partial x)(2xyz+3/4 xy+z)
∂
∂
x
(
2
xyz
+
3
4
xy
+
z
)
(dy)/(dt)+0.4ty=5t,y(0)=6
dy
dt
+
0
.
4
ty
=
5
t
,
y
(
0
)
=
6
tangent y=x^3-11x,(2,-14)
tangent
y
=
x
3
−
1
1
x
,
(
2
,
−
1
4
)
(\partial)/(\partial x)(arctan(a)x^3)
∂
∂
x
(
arctan
(
a
)
x
3
)
integral of (-t)/((t+1)-sqrt(t+1))
∫
−
t
(
t
+
1
)
−
√
t
+
1
dt
1
..
1496
1497
1498
1499
1500
..
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