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일반적인 미적분학 문제
integral from 0 to 1 of x/(e^{6x)}
∫
0
1
x
e
6
x
dx
limit as x approaches 2+of (x^3-x)/(2-x)
lim
x
→
2
+
(
x
3
−
x
2
−
x
)
y^2dx-3xdy=0
y
2
dx
−
3
xdy
=
0
(\partial)/(\partial x)(2ze^{xy^2+z^2})
∂
∂
x
(
2
ze
xy
2
+
z
2
)
inverse라플라스 3/((s+2)^4)
inverselaplace
3
(
s
+
2
)
4
derivative of cos(tan(6x))
d
dx
(
cos
(
tan
(
6
x
)
)
)
limit as x approaches infinity of csc(1/x)-cot(1/x)
lim
x
→
∞
(
csc
(
1
x
)
−
cot
(
1
x
)
)
y^{''}-14y^'+74y=0
y
′
′
−
1
4
y
′
+
7
4
y
=
0
integral from 0 to pi/2 of sin^2(3x)
∫
0
π
2
sin
2
(
3
x
)
dx
integral of 5xln(2x)
∫
5
x
ln
(
2
x
)
dx
integral of (ln(x^{15}))/x
∫
ln
(
x
1
5
)
x
dx
integral of (x+9)/(x^2-6x+9)
∫
x
+
9
x
2
−
6
x
+
9
dx
derivative y(pi/(21))=2tan^2(7x)
derivative
y
(
π
2
1
)
=
2
tan
2
(
7
x
)
derivative of 2^{x/2}
d
dx
(
2
x
2
)
derivative of e^{(-x/2})
d
dx
(
e
−
x
2
)
integral of 15e^x
∫
1
5
e
x
dx
(\partial)/(\partial u(v))(e^{2u(v)v})
∂
∂
u
(
v
)
(
e
2
u
(
v
)
v
)
tangent-1/x ,\at x=3
tangent
−
1
x
,
at
x
=
3
derivative y=x^{3x}
derivative
y
=
x
3
x
y^'+2/x y=0
y
′
+
2
x
y
=
0
limit as x approaches infinity of 3x!
lim
x
→
∞
(
3
x
!
)
derivative of 1/(2sqrt(x+4))
d
dx
(
1
2
√
x
+
4
)
derivative (x^5-6xsqrt(x))/x
derivative
x
5
−
6
x
√
x
x
derivative ln(sqrt((4x+1)/(x^2-1)))
derivative
ln
(
√
4
x
+
1
x
2
−
1
)
derivative of sqrt(x)-sqrt(y)
d
dx
(
√
x
−
√
y
)
integral of sec(x)tan(x)-3e^x
∫
sec
(
x
)
tan
(
x
)
−
3
e
x
dx
integral from 0 to 5 of w/(w-2)
∫
0
5
w
w
−
2
dw
limit as x approaches 0 of 3xcos(x)
lim
x
→
0
(
3
x
cos
(
x
)
)
integral from 5 to 7 of 1/(x^2-1)
∫
5
7
1
x
2
−
1
dx
derivative of (1+e^x/(1-e^x))
d
dx
(
1
+
e
x
1
−
e
x
)
integral of cos^2((3pix)/l)
∫
cos
2
(
3
π
x
l
)
dx
integral of e^{4sin(x)}cos(x)
∫
e
4
sin
(
x
)
cos
(
x
)
dx
integral of (x+3)^{-1/2}
∫
(
x
+
3
)
−
1
2
dx
derivative ze^z
derivative
ze
z
(\partial)/(\partial x)((x^2-1)*(y+2))
∂
∂
x
(
(
x
2
−
1
)
·
(
y
+
2
)
)
limit as x approaches-8-of sqrt(x^2-64)
lim
x
→
−
8
−
(
√
x
2
−
6
4
)
sum from n=1 to infinity}4^{n+1 of 5^{-n}
∑
n
=
1
∞
4
n
+
1
5
−
n
implicit (dy)/(dx),y=8x
implicit
dy
dx
,
y
=
8
x
derivative of-2e^{3x}
d
dx
(
−
2
e
3
x
)
integral from 1 to 9 of 5/(3sqrt(x))
∫
1
9
5
3
√
x
dx
y^'=(e^{x-y})/(1+e^x)
y
′
=
e
x
−
y
1
+
e
x
(\partial)/(\partial x)(3x^2y+4xz^3)
∂
∂
x
(
3
x
2
y
+
4
xz
3
)
tangent y=x^4-4x^3+2
tangent
y
=
x
4
−
4
x
3
+
2
limit as x approaches-4 of (-1)/(x^2-16)
lim
x
→
−
4
(
−
1
x
2
−
1
6
)
integral of (-e^{-st})/s
∫
−
e
−
st
s
dt
derivative of-10sin(10x-cos(10x))
d
dx
(
−
1
0
sin
(
1
0
x
)
−
cos
(
1
0
x
)
)
integral of ln(9x)
∫
ln
(
9
x
)
dx
inverse라플라스 ((s+2)^3)/(s^4)
inverselaplace
(
s
+
2
)
3
s
4
integral of x^3(1-x^2)^{1/2}
∫
x
3
(
1
−
x
2
)
1
2
dx
integral of (sqrt(x^5))
∫
(
√
x
5
)
dx
integral of (2x-1)e^{2x}
∫
(
2
x
−
1
)
e
2
x
dx
(\partial)/(\partial x)(x*e^{x^3y})
∂
∂
x
(
x
·
e
x
3
y
)
integral of (1/x-6e^x)
∫
(
1
x
−
6
e
x
)
dx
integral of 3/(4+x^2)
∫
3
4
+
x
2
dx
ydy+(1+y^2)sin(t)dt=0
ydy
+
(
1
+
y
2
)
sin
(
t
)
dt
=
0
derivative of esqrt(x)
d
dx
(
e
√
x
)
derivative of (\sqrt[3]{x}-2^2)
d
dx
(
(
3
√
x
−
2
)
2
)
tangent y=1+sqrt(x)
tangent
y
=
1
+
√
x
지역 y=x,y=2x,x=1
area
y
=
x
,
y
=
2
x
,
x
=
1
integral of 14tan^3(x)sec(x)
∫
1
4
tan
3
(
x
)
sec
(
x
)
dx
derivative f(t)=(6t)/(6+sqrt(t))
derivative
f
(
t
)
=
6
t
6
+
√
t
limit as x approaches 0+of x^{x^{1/2}}
lim
x
→
0
+
(
x
x
1
2
)
d/(d{y)}(({x})/(({x)^2+{y}^2+{z}^2)^{3/2}})
d
d
y
(
x
(
x
2
+
y
2
+
z
2
)
3
2
)
integral of 1/(xsqrt(x^2-pi))
∫
1
x
√
x
2
−
π
dx
integral from 0 to 1 of e^x-x
∫
0
1
e
x
−
xdx
integral of xsin(3x)
∫
x
sin
(
3
x
)
dx
지역 y=2cos(x),y=6-4cos(x),0<= x<= 2pi
area
y
=
2
cos
(
x
)
,
y
=
6
−
4
cos
(
x
)
,
0
≤
x
≤
2
π
f(x)=18x^2-14x+9
f
(
x
)
=
1
8
x
2
−
1
4
x
+
9
derivative of ln(x^2+2x+1)
d
dx
(
ln
(
x
2
+
2
x
+
1
)
)
derivative-2xcos(x^2)-e^{-x-2}
derivative
−
2
x
cos
(
x
2
)
−
e
−
x
−
2
derivative y=(4x^4+5)/(x^2)
derivative
y
=
4
x
4
+
5
x
2
(\partial)/(\partial x)(4-2x^2-y^2)
∂
∂
x
(
4
−
2
x
2
−
y
2
)
derivative of e^{-bx^2}
d
dx
(
e
−
bx
2
)
tangent y=x^2-3x+3(0.3)
tangent
y
=
x
2
−
3
x
+
3
(
0
.
3
)
inverse라플라스 1/(s(s^2+49))
inverselaplace
1
s
(
s
2
+
4
9
)
derivative of x^{(3/2})
d
dx
(
x
(
3
2
)
)
tangent 6cos(x),\at x= pi/3
tangent
6
cos
(
x
)
,
at
x
=
π
3
derivative of cot(4x^2)
d
dx
(
cot
(
4
x
2
)
)
integral from 5 to infinity of (ln(x))/x
∫
5
∞
ln
(
x
)
x
dx
integral of 1/(5x+3)
∫
1
5
x
+
3
dx
integral of 1/(100-y)
∫
1
1
0
0
−
y
dy
(\partial)/(\partial x)(e^{x-2}-y/2)
∂
∂
x
(
e
x
−
2
−
y
2
)
derivative of (sin(x)/(3x))
d
dx
(
sin
(
x
)
3
x
)
integral of 1.5x^2
∫
1
.
5
x
2
dx
(dy)/(dx)+y^5x+8y=0
dy
dx
+
y
5
x
+
8
y
=
0
derivative (pix)/(16)
derivative
π
x
1
6
integral of (-x^2)
∫
(
−
x
2
)
dx
(dy}{dx}=\frac{7e^x)/y
dy
dx
=
7
e
x
y
sum from n=1 to infinity of ne^{8n}
∑
n
=
1
∞
ne
8
n
integral of t^{-1/2}
∫
t
−
1
2
dt
tangent-2x^2+3
tangent
−
2
x
2
+
3
derivative x/(10)-(10)/x
derivative
x
1
0
−
1
0
x
(dv}{dt}+\frac{3v)/2 =9.8
dv
dt
+
3
v
2
=
9
.
8
integral of \sqrt[3]{x}(x+x^2)'
∫
3
√
x
(
x
+
x
2
)
′
dx
(dy)/(dx)= y/x+5x+1
dy
dx
=
y
x
+
5
x
+
1
(\partial)/(\partial x)(4ysqrt(x))
∂
∂
x
(
4
y
√
x
)
y^'=5xe^y,y(0)=0
y
′
=
5
xe
y
,
y
(
0
)
=
0
integral from 0 to infinity of xe^{-4x}
∫
0
∞
xe
−
4
x
dx
integral of 1/(sqrt(x^2-256))
∫
1
√
x
2
−
2
5
6
dx
limit as x approaches-7 of |x+7|
lim
x
→
−
7
(
|
x
+
7
|
)
1
..
1488
1489
1490
1491
1492
..
2459