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일반적인 미적분학 문제
d/(da)(tan(a)+cot(a))
d
da
(
tan
(
a
)
+
cot
(
a
)
)
8y^{''}+31y=0
8
y
′
′
+
3
1
y
=
0
(dy)/(dx)=((2x+xy^2))/(4y+yx^2)
dy
dx
=
(
2
x
+
xy
2
)
4
y
+
yx
2
(dy}{dx}=\frac{6+3y)/x
dy
dx
=
6
+
3
y
x
derivative 2x^4arctan(5x^3)
derivative
2
x
4
arctan
(
5
x
3
)
integral of ln^2(2x)
∫
ln
2
(
2
x
)
dx
d/(du)(uv)
d
du
(
uv
)
limit as x approaches 0 of-(sin(x))/(3x)
lim
x
→
0
(
−
sin
(
x
)
3
x
)
integral of xsqrt(x+9)
∫
x
√
x
+
9
dx
limit as x approaches-1 of x^2-5x+6
lim
x
→
−
1
(
x
2
−
5
x
+
6
)
(\partial)/(\partial y)(3x^2-3y)
∂
∂
y
(
3
x
2
−
3
y
)
integral of ((sqrt(x^2-9)))/(x^3)
∫
(
√
x
2
−
9
)
x
3
dx
derivative of (6x+5(x^3-2))
d
dx
(
(
6
x
+
5
)
(
x
3
−
2
)
)
integral of (tan(x)+1)/(tan(x)-1)
∫
tan
(
x
)
+
1
tan
(
x
)
−
1
dx
(dy)/(dx)y=(9x-6)/(54x^2)
dy
dx
y
=
9
x
−
6
5
4
x
2
integral of-(e^{2t})/2
∫
−
e
2
t
2
dt
integral from-1 to 2 of (2x^2-4x+5)
∫
−
1
2
(
2
x
2
−
4
x
+
5
)
dx
(\partial)/(\partial x)(2x^4y-2)
∂
∂
x
(
2
x
4
y
−
2
)
integral of 1/(1+e^{6x)}
∫
1
1
+
e
6
x
dx
sum from n=1 to infinity of 5/(n+2)
∑
n
=
1
∞
5
n
+
2
integral of (x^3+3)
∫
(
x
3
+
3
)
dx
e^x(dy)/(dx)=e^{-y}+e^{2x-y}
e
x
dy
dx
=
e
−
y
+
e
2
x
−
y
지역 cos(x),sin(x)
area
cos
(
x
)
,
sin
(
x
)
2x^2y^{''}+3xy^'=y
2
x
2
y
′
′
+
3
xy
′
=
y
지역 2cos(7x),2-2cos(7x),0<= x<= pi/7
area
2
cos
(
7
x
)
,
2
−
2
cos
(
7
x
)
,
0
≤
x
≤
π
7
integral from 0 to 1 of e^{-st}*t
∫
0
1
e
−
st
·
tdt
integral of e^{-4t}
∫
e
−
4
t
dt
(dy)/(dt)=6y+cos(3t)
dy
dt
=
6
y
+
cos
(
3
t
)
integral of ((t^2+t+1)/((t+3)^3))
∫
(
t
2
+
t
+
1
(
t
+
3
)
3
)
dt
-y+10e^{-t}=y^'
−
y
+
1
0
e
−
t
=
y
′
integral of ln(6x)
∫
ln
(
6
x
)
dx
laplace변환 sin(2t)+cos(2t)
laplacetransform
sin
(
2
t
)
+
cos
(
2
t
)
integral of sin^3(3θ)sqrt(cos(3θ))
∫
sin
3
(
3
θ
)
√
cos
(
3
θ
)
d
θ
xy^'+y=-2xy^2,y(1)=-3
xy
′
+
y
=
−
2
xy
2
,
y
(
1
)
=
−
3
derivative of 4/(11-x)
d
dx
(
4
1
1
−
x
)
derivative y=xsqrt(2x+3)
derivative
y
=
x
√
2
x
+
3
integral of 7^xtan(7^x)
∫
7
x
tan
(
7
x
)
dx
limit as x approaches pi/2 of e^{sin(x)}
lim
x
→
π
2
(
e
sin
(
x
)
)
limit as x approaches 0 of (xcos(x))/x
lim
x
→
0
(
x
cos
(
x
)
x
)
derivative of 3/(x^2+9)
d
dx
(
3
x
2
+
9
)
(\partial)/(\partial y)(ye^{-x^2+y})
∂
∂
y
(
ye
−
x
2
+
y
)
integral of (x^2+3)/(xsqrt(x^2-9))
∫
x
2
+
3
x
√
x
2
−
9
dx
(\partial)/(\partial x)(cos^6(x^8y^6))
∂
∂
x
(
cos
6
(
x
8
y
6
)
)
지역 y=2x-x^2,y=2x-4
area
y
=
2
x
−
x
2
,
y
=
2
x
−
4
limit as x approaches 9 of ((x^{1/2}-3)(x+1))/(x^2-8x-9)
lim
x
→
9
(
(
x
1
2
−
3
)
(
x
+
1
)
x
2
−
8
x
−
9
)
derivative y=(3x^2-2x-4)5^x
derivative
y
=
(
3
x
2
−
2
x
−
4
)
5
x
integral of (5000ln(x+20))/((x+20)^2)
∫
5
0
0
0
ln
(
x
+
2
0
)
(
x
+
2
0
)
2
dx
derivative of-5e^{3x}
d
dx
(
−
5
e
3
x
)
integral of 4\sqrt[6]{x}
∫
4
6
√
x
dx
integral of (1+x)/(-4x-2x^2)
∫
1
+
x
−
4
x
−
2
x
2
dx
derivative of (e^{5x}/(x^{15)})
d
dx
(
e
5
x
x
1
5
)
derivative of b(x+a^3+c)
d
dx
(
b
(
x
+
a
)
3
+
c
)
(\partial)/(\partial x)(xye^{x/y})
∂
∂
x
(
xye
x
y
)
limit as x approaches infinity of x*2
lim
x
→
∞
(
x
·
2
)
integral of (x^3)/(\sqrt[3]{x^2+5)}
∫
x
3
3
√
x
2
+
5
dx
(\partial)/(\partial x)(x^4+y^4+z^4-4xyz)
∂
∂
x
(
x
4
+
y
4
+
z
4
−
4
xyz
)
integral from 0 to pi/4 of cos^7(x)
∫
0
π
4
cos
7
(
x
)
dx
(\partial)/(\partial x)(y^2-4y+xy)
∂
∂
x
(
y
2
−
4
y
+
xy
)
derivative (x^3)/8
derivative
x
3
8
integral of cos^4(6x)
∫
cos
4
(
6
x
)
dx
derivative of 1/e e^x
d
dx
(
1
e
e
x
)
derivative 1/x+1/(x-1)+1/(x-2)
derivative
1
x
+
1
x
−
1
+
1
x
−
2
integral of x^2*sin(x^3)
∫
x
2
·
sin
(
x
3
)
dx
sum from n=1 to infinity of 15(1/100)^n
∑
n
=
1
∞
1
5
(
1
1
0
0
)
n
derivative of (x^2/2+1/x)
d
dx
(
x
2
2
+
1
x
)
derivative sqrt(x)(x^5+2)
derivative
√
x
(
x
5
+
2
)
limit as x approaches 0 of (2x^2+x)^x
lim
x
→
0
(
(
2
x
2
+
x
)
x
)
y^{''}+y= 1/((cos(2x))^{3/2)}
y
′
′
+
y
=
1
(
cos
(
2
x
)
)
3
2
limit as x approaches 2+of (8+x)/(2-x)
lim
x
→
2
+
(
8
+
x
2
−
x
)
integral of (10x^2)/(sqrt(1+x^3))
∫
1
0
x
2
√
1
+
x
3
dx
y^'=-y(3-ty)
y
′
=
−
y
(
3
−
ty
)
tangent f(x)=sin(sin(x)),(4pi,0)
tangent
f
(
x
)
=
sin
(
sin
(
x
)
)
,
(
4
π
,
0
)
integral of 1/(sqrt(2x))
∫
1
√
2
x
dx
integral of x^2sec^2(x)
∫
x
2
sec
2
(
x
)
dx
integral of (x+7)^2
∫
(
x
+
7
)
2
dx
integral of (x^2)/(sqrt(2+x^3))
∫
x
2
√
2
+
x
3
dx
지역 x,(x^2)/4 ,0,2
area
x
,
x
2
4
,
0
,
2
2y^{'''}+3y^{''}-11y^'-6y=0
2
y
′
′
′
+
3
y
′
′
−
1
1
y
′
−
6
y
=
0
integral of (24)/((144x^2+1)^2)
∫
2
4
(
1
4
4
x
2
+
1
)
2
dx
integral from 0 to 9 of e^xsin(x)
∫
0
9
e
x
sin
(
x
)
dx
integral from 0 to x of sqrt(3t+5)
∫
0
x
√
3
t
+
5
dt
laplace변환 e^{-t}+e^t
laplacetransform
e
−
t
+
e
t
y^{''}+4y^'+5y=5x+3e^{-x}
y
′
′
+
4
y
′
+
5
y
=
5
x
+
3
e
−
x
2t(dy)/(dt)+y=t^4
2
t
dy
dt
+
y
=
t
4
limit as x approaches-2-of 4x^2-7
lim
x
→
−
2
−
(
4
x
2
−
7
)
integral of (sin(2x))/(cos^2(x))
∫
sin
(
2
x
)
cos
2
(
x
)
dx
limit as x approaches 0 of sin^2(x)
lim
x
→
0
(
sin
2
(
x
)
)
derivative e^{3tsin(2t)}
derivative
e
3
t
sin
(
2
t
)
limit as x approaches 7+of ln(x^2-49)
lim
x
→
7
+
(
ln
(
x
2
−
4
9
)
)
integral of 4x^9
∫
4
x
9
dx
지역 y=sin^2(x),y=sin^3(x),x=0,x=pi
area
y
=
sin
2
(
x
)
,
y
=
sin
3
(
x
)
,
x
=
0
,
x
=
π
integral from 0 to 1 of (2x-1)^2
∫
0
1
(
2
x
−
1
)
2
dx
y^{''}+400y=sec(20x)
y
′
′
+
4
0
0
y
=
sec
(
2
0
x
)
limit as x approaches-3+of 4x^2-7
lim
x
→
−
3
+
(
4
x
2
−
7
)
integral of e^{2x}(x^2+2x)
∫
e
2
x
(
x
2
+
2
x
)
dx
derivative (t+4)^{(2/3)}(2t^2-4)^3
derivative
(
t
+
4
)
(
2
3
)
(
2
t
2
−
4
)
3
limit as x approaches 2 of sqrt(x^2+12)
lim
x
→
2
(
√
x
2
+
1
2
)
(d^2)/(dx^2)(7/(8x^6))
d
2
dx
2
(
7
8
x
6
)
tangent f(x)=6x-32sqrt(x),\at x=4
tangent
f
(
x
)
=
6
x
−
3
2
√
x
,
at
x
=
4
derivative f(x)=(x^2+sec(x))/(x-2e^x)
derivative
f
(
x
)
=
x
2
+
sec
(
x
)
x
−
2
e
x
1
..
1196
1197
1198
1199
1200
..
2459