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일반적인 미적분학 문제
(dy)/(dx)=e^{y/x}+y/x
dy
dx
=
e
y
x
+
y
x
integral of x^3(9+x^4)^6
∫
x
3
(
9
+
x
4
)
6
dx
integral of 45sec^4(x)
∫
4
5
sec
4
(
x
)
dx
sum from n=1 to infinity of ((n+2))/(2^n)
∑
n
=
1
∞
(
n
+
2
)
2
n
(\partial)/(\partial x)(4(y/x)^{1/2})
∂
∂
x
(
4
(
y
x
)
1
2
)
지역 f(x)=2x^2+2,[-2,3]
area
f
(
x
)
=
2
x
2
+
2
,
[
−
2
,
3
]
integral of 1/(x^2sqrt(4+x^2))
∫
1
x
2
√
4
+
x
2
dx
integral of (e^x)/(e^{2x)-3e^x+2}
∫
e
x
e
2
x
−
3
e
x
+
2
dx
derivative of sqrt(tan^2(3x+1))
d
dx
(
√
tan
2
(
3
x
)
+
1
)
integral of t^2e^{-t/3}
∫
t
2
e
−
t
3
dt
sum from n=7 to infinity of 1/(6n)
∑
n
=
7
∞
1
6
n
경사지 y=x^2+5x,x=8
slope
y
=
x
2
+
5
x
,
x
=
8
integral of (x^2-2x+3)
∫
(
x
2
−
2
x
+
3
)
dx
integral of (3x^3)/(x^2+1)
∫
3
x
3
x
2
+
1
dx
sum from n=0 to infinity of 1/(sqrt(n))
∑
n
=
0
∞
1
√
n
(\partial)/(\partial x)(x^{0.7}y^{0.3})
∂
∂
x
(
x
0
.
7
y
0
.
3
)
integral from 0 to 1 of 3e^{-2x}
∫
0
1
3
e
−
2
x
dx
sum from n=1 to infinity of (7*n!)/(n^n)
∑
n
=
1
∞
7
·
n
!
n
n
(\partial)/(\partial x)(-cos(4x))
∂
∂
x
(
−
cos
(
4
x
)
)
limit as t approaches 0 of (tan(6t))/(sin(2t))
lim
t
→
0
(
tan
(
6
t
)
sin
(
2
t
)
)
integral of (ax+b)/(px+q)
∫
ax
+
b
px
+
q
dx
x((dy)/(dx))-y=x
x
(
dy
dx
)
−
y
=
x
integral from 0 to L of x/(x)
∫
0
L
x
d
+
x
dx
integral of ()/(t^3sqrt(t^2-9))
∫
dt
t
3
√
t
2
−
9
dx
(\partial)/(\partial x)((2x+5y)e^y)
∂
∂
x
(
(
2
x
+
5
y
)
e
y
)
(\partial)/(\partial x)(x+y-xy)
∂
∂
x
(
x
+
y
−
xy
)
integral from 0 to 8 of (x+1)^2
∫
0
8
(
x
+
1
)
2
dx
derivative y=arcsin(1/(x^5))
derivative
y
=
arcsin
(
1
x
5
)
limit as x approaches 0 of (ln(1-6x))/x
lim
x
→
0
(
ln
(
1
−
6
x
)
x
)
limit as x approaches-8 of (|x+8|)/(x+8)
lim
x
→
−
8
(
|
x
+
8
|
x
+
8
)
derivative-(4x)/y
derivative
−
4
x
y
derivative f(x)=sqrt(x)cos(x)
derivative
f
(
x
)
=
√
x
cos
(
x
)
integral from 1 to 2 of (e^{1/(x^5)})/(x^6)
∫
1
2
e
1
x
5
x
6
dx
limit as x approaches 2-of x-a
lim
x
→
2
−
(
x
−
a
)
integral of (9-z^2)(6-2z)
∫
(
9
−
z
2
)
(
6
−
2
z
)
dz
integral of sin(2x)e^{-sx}
∫
sin
(
2
x
)
e
−
sx
dx
integral from 4 to infinity of e^{-8x}
∫
4
∞
e
−
8
x
dx
(2dy)/(dx)+10y=5
2
dy
dx
+
1
0
y
=
5
derivative (e^x+e^{-x})/4
derivative
e
x
+
e
−
x
4
y^'+2y=xy^3
y
′
+
2
y
=
xy
3
derivative f(x)=9x+2
derivative
f
(
x
)
=
9
x
+
2
limit as t approaches 2 of (t+2)^{3/2}(2t+4)^{1/3}
lim
t
→
2
(
(
t
+
2
)
3
2
(
2
t
+
4
)
1
3
)
integral from 1/7 to 3 of 16xln(7x)
∫
1
7
3
1
6
x
ln
(
7
x
)
dx
integral from 0 to 4 of sqrt(17)
∫
0
4
√
1
7
dx
integral from 1 to t of (37)/(x^3)
∫
1
t
3
7
x
3
dx
y^'=-x^2-1/x*y
y
′
=
−
x
2
−
1
x
·
y
integral of 1/(sqrt(1-64x^2))
∫
1
√
1
−
6
4
x
2
dx
integral of (2x+3)/(x^3+x^2-2x)
∫
2
x
+
3
x
3
+
x
2
−
2
x
dx
sum from n=2 to infinity of 1/n (-1)^n
∑
n
=
2
∞
1
n
(
−
1
)
n
지역 y^2=16-x,(y+2)^2=x+4
area
y
2
=
1
6
−
x
,
(
y
+
2
)
2
=
x
+
4
derivative (e^s)/(7s+1)
derivative
e
s
7
s
+
1
derivative f(x)=(xe^{2x-4}),x=2
derivative
f
(
x
)
=
(
xe
2
x
−
4
)
,
x
=
2
sum from n=1 to infinity of (n-7)/(n+7)
∑
n
=
1
∞
n
−
7
n
+
7
derivative f(x)=sec^5(x)
derivative
f
(
x
)
=
sec
5
(
x
)
derivative of (128000/x+x^2)
d
dx
(
1
2
8
0
0
0
x
+
x
2
)
(\partial)/(\partial x)(3x^2+4xy+2y^2)
∂
∂
x
(
3
x
2
+
4
xy
+
2
y
2
)
(\partial)/(\partial x)((9xy)/(x-y))
∂
∂
x
(
9
xy
x
−
y
)
tangent 4cos(x),\at x=-pi/3
tangent
4
cos
(
x
)
,
at
x
=
−
π
3
integral of y/(2+y^2)
∫
y
2
+
y
2
dy
지역 (x^2-12),(x-6)
area
(
x
2
−
1
2
)
,
(
x
−
6
)
derivative of x^3-x-1
d
dx
(
x
3
−
x
−
1
)
derivative (x-2)^2-sin(3x)
derivative
(
x
−
2
)
2
−
sin
(
3
x
)
integral of (3-2x)/(5x+7)
∫
3
−
2
x
5
x
+
7
dx
integral from 1 to 2 of 9r^4ln(r)
∫
1
2
9
r
4
ln
(
r
)
dr
y^'+2ty=t
y
′
+
2
ty
=
t
(dy)/(dx)=(2x)/(3y)
dy
dx
=
2
x
3
y
derivative (cos(x))/(x^8)
derivative
cos
(
x
)
x
8
tangent y=8xsin(x)
tangent
y
=
8
x
sin
(
x
)
integral from 0 to 0.5 of 2x
∫
0
0
.
5
2
xdx
tangent-0.04x^2-0.8x+70
tangent
−
0
.
0
4
x
2
−
0
.
8
x
+
7
0
integral of sqrt(1+4t^2)
∫
√
1
+
4
t
2
dt
limit as x approaches 2+of (-5)/(x-2)
lim
x
→
2
+
(
−
5
x
−
2
)
limit as x approaches-4+of 3/(x^2-16)
lim
x
→
−
4
+
(
3
x
2
−
1
6
)
derivative f(x)=x^3-6x+9
derivative
f
(
x
)
=
x
3
−
6
x
+
9
integral of (1/(2x))
∫
(
1
2
x
)
dx
derivative of (2x-3/(2x+5))
d
dx
(
2
x
−
3
2
x
+
5
)
integral of (x-3)*cos(x)
∫
(
x
−
3
)
·
cos
(
x
)
dx
integral of (5r^2)/(r+3)
∫
5
r
2
r
+
3
dr
derivative of x^2ln(5x)
d
dx
(
x
2
ln
(
5
x
)
)
derivative (x-2)^2
derivative
(
x
−
2
)
2
요인 7p^3+4p
factor
7
p
3
+
4
p
derivative 2e^{3x}
derivative
2
e
3
x
(\partial)/(\partial x)(20xy)
∂
∂
x
(
2
0
xy
)
integral of ((sqrt(x)-2)^2)/x
∫
(
√
x
−
2
)
2
x
dx
(\partial)/(\partial x)(5^{2x})
∂
∂
x
(
5
2
x
)
integral from 0 to 2 of sqrt(1+x^2)
∫
0
2
√
1
+
x
2
dx
integral of 1/(xsqrt(1-(ln(x))^2))
∫
1
x
√
1
−
(
ln
(
x
)
)
2
dx
integral of ((x+2)^2)/(\sqrt[3]{3-x)}
∫
(
x
+
2
)
2
3
√
3
−
x
dx
inverse라플라스 s/((s+4)^2)
inverselaplace
s
(
s
+
4
)
2
sum from n=1 to infinity of (9n)/(7n+1)
∑
n
=
1
∞
9
n
7
n
+
1
지역 y=sqrt(x),y=0,y=x-2
area
y
=
√
x
,
y
=
0
,
y
=
x
−
2
limit as x approaches 3+of 2/(x-3)
lim
x
→
3
+
(
2
x
−
3
)
y^'=y-4y^2
y
′
=
y
−
4
y
2
y^'=(x^2)/(y(1+x^3))
y
′
=
x
2
y
(
1
+
x
3
)
derivative of 2^{cot(5x})
d
dx
(
2
cot
(
5
x
)
)
derivative of 1/(x(ln(x)^2))
d
dx
(
1
x
(
ln
(
x
)
)
2
)
integral of ((x-2)sqrt(1-x^2)+x)/(1-x^2)
∫
(
x
−
2
)
√
1
−
x
2
+
x
1
−
x
2
dx
integral of xsec^2(5x)
∫
x
sec
2
(
5
x
)
dx
y^{''}+4y=-2
y
′
′
+
4
y
=
−
2
integral of cos(φ)
∫
cos
(
φ
)
d
φ
1
..
1172
1173
1174
1175
1176
..
2459