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일반적인 미적분학 문제
integral of 1/(7x+2)
∫
1
7
x
+
2
dx
derivative of-y^2x
d
dx
(
−
y
2
x
)
integral of cos(2θ)
∫
cos
(
2
θ
)
d
θ
derivative f(x)=3x^2+2ax+b
derivative
f
(
x
)
=
3
x
2
+
2
ax
+
b
y^{''}-2y^'+5y=5x+3
y
′
′
−
2
y
′
+
5
y
=
5
x
+
3
limit as x approaches 3 of (3-x)/(|x-3|)
lim
x
→
3
(
3
−
x
|
x
−
3
|
)
integral of (8x+1-9e^x)
∫
(
8
x
+
1
−
9
e
x
)
dx
inverselaplace (e^{-s})/(s^2+3s+2)
inverselaplace
e
−
s
s
2
+
3
s
+
2
integral of (e^{-x})/((9e^{-2x)+1)^{3/2}}
∫
e
−
x
(
9
e
−
2
x
+
1
)
3
2
dx
derivative sqrt(1-x^2)
derivative
√
1
−
x
2
(\partial)/(\partial x)(x/(x^2+y^2)-y^2)
∂
∂
x
(
x
x
2
+
y
2
−
y
2
)
integral of sin(13x)
∫
sin
(
1
3
x
)
dx
integral from 0 to 1 of ln(4x)
∫
0
1
ln
(
4
x
)
dx
integral of-4/x
∫
−
4
x
dx
tangent (x-2)(x^2+4)
tangent
(
x
−
2
)
(
x
2
+
4
)
derivative 6cos(x)
derivative
6
cos
(
x
)
derivative-2/(9(1+x)^{5/3)}
derivative
−
2
9
(
1
+
x
)
5
3
derivative of tan((pix/2))
d
dx
(
tan
(
π
x
2
)
)
derivative y=3+(12)/(2-x)
derivative
y
=
3
+
1
2
2
−
x
derivative 10x(x^2+7)^4
derivative
1
0
x
(
x
2
+
7
)
4
derivative ((x+4)/(x-4))^5
derivative
(
x
+
4
x
−
4
)
5
integral of 1/(2-x^2)
∫
1
2
−
x
2
dx
sum from n=4 to infinity of 8/(n^2-1)
∑
n
=
4
∞
8
n
2
−
1
지역 2x^2,2x+6,-1,0
area
2
x
2
,
2
x
+
6
,
−
1
,
0
implicit xy+4y=10
implicit
xy
+
4
y
=
1
0
limit as x approaches 2 of (5x^3)/(x+3)
lim
x
→
2
(
5
x
3
x
+
3
)
integral of (1/((x+1)^2))
∫
(
1
(
x
+
1
)
2
)
dx
(\partial)/(\partial y)(xe^{yz})
∂
∂
y
(
xe
yz
)
integral of 1/(4sec(y))
∫
1
4
sec
(
y
)
dy
(dy}{dx}=\frac{xsqrt(x^2-1))/y
dy
dx
=
x
√
x
2
−
1
y
integral of (3p^2-2)^2e^{-4p}
∫
(
3
p
2
−
2
)
2
e
−
4
p
dp
derivative 2x^2+2x+3
derivative
2
x
2
+
2
x
+
3
derivative of (1+xe^x)
d
dx
(
(
1
+
x
)
e
x
)
(\partial}{\partial z}(ln(\frac{xy)/z))
∂
∂
z
(
ln
(
xy
z
)
)
지역 y=x^2,x= y/2
area
y
=
x
2
,
x
=
y
2
derivative f(x)=-5/(\sqrt[3]{x)}
derivative
f
(
x
)
=
−
5
3
√
x
limit as t approaches 0 of 3e^{2t}
lim
t
→
0
(
3
e
2
t
)
integral of-2sin^2(x)
∫
−
2
sin
2
(
x
)
dx
(dy)/(dx)+2xy=4x
dy
dx
+
2
xy
=
4
x
integral of (10)/((25x^2+1)^2)
∫
1
0
(
2
5
x
2
+
1
)
2
dx
integral from 1 to 5 of 7r^2ln(r)
∫
1
5
7
r
2
ln
(
r
)
dr
limit as x approaches-2 of 3/(x^2-4)
lim
x
→
−
2
(
3
x
2
−
4
)
integral of (x-2)/(x^3)
∫
x
−
2
x
3
dx
derivative of ((-2x-1/(-4x+2))^5)
d
dx
(
(
−
2
x
−
1
−
4
x
+
2
)
5
)
integral from 2 to 4 of 2x^2-3x+1
∫
2
4
2
x
2
−
3
x
+
1
dx
(\partial)/(\partial x)(cos(xln(y)))
∂
∂
x
(
cos
(
x
ln
(
y
)
)
)
limit as x approaches+0+of (36-4x^2)/x
lim
x
→
+
0
+
(
3
6
−
4
x
2
x
)
integral of 2xsqrt(2x-1)
∫
2
x
√
2
x
−
1
dx
derivative of 1/(6x^{5/6})
d
dx
(
1
6
x
5
6
)
경사지 (1,1),(4,-1/2)
slope
(
1
,
1
)
,
(
4
,
−
1
2
)
(\partial)/(\partial x)(r)
∂
∂
x
(
r
)
tangent y=(-8x)/(x^2+1),(-1,4)
tangent
y
=
−
8
x
x
2
+
1
,
(
−
1
,
4
)
derivative x^2(240-x/3)
derivative
x
2
(
2
4
0
−
x
3
)
tangent 1/2 x^4-8
tangent
1
2
x
4
−
8
xy(dy)/(dx)+4x^2+y^2=0
xy
dy
dx
+
4
x
2
+
y
2
=
0
derivative of 5/(2x^2)
d
dx
(
5
2
x
2
)
지역 x=y^2-4y,x=2y-y^2
area
x
=
y
2
−
4
y
,
x
=
2
y
−
y
2
integral of 1/(t^2sqrt(400-t^2))
∫
1
t
2
√
4
0
0
−
t
2
dt
derivative of cos(arctan(3x))
d
dx
(
cos
(
arctan
(
3
x
)
)
)
integral from 0 to 1/10 of xln(10x)
∫
0
1
1
0
x
ln
(
1
0
x
)
dx
limit as x approaches 0 of sqrt(2)
lim
x
→
0
(
√
2
)
tangent f(x)=3tan(x),\at x= pi/3
tangent
f
(
x
)
=
3
tan
(
x
)
,
at
x
=
π
3
integral from-infinity to 0 of x
∫
−
∞
0
xdx
1/2*(dy)/(dx)=(2x)/(3y)
1
2
·
dy
dx
=
2
x
3
y
(d^2)/(dx^2)(3e^{x^2})
d
2
dx
2
(
3
e
x
2
)
integral of (x-1)e^{x^2-2x}
∫
(
x
−
1
)
e
x
2
−
2
x
dx
laplacetransform 1/2 t
laplacetransform
1
2
t
integral of (3-2x)^3
∫
(
3
−
2
x
)
3
dx
(\partial)/(\partial x)(2x^2y+sin(x^3))
∂
∂
x
(
2
x
2
y
+
sin
(
x
3
)
)
tangent y=4e^x+x,(0,4)
tangent
y
=
4
e
x
+
x
,
(
0
,
4
)
integral from-pi to pi of x*sin(n*x)
∫
−
π
π
x
·
sin
(
n
·
x
)
dx
integral of-sin(x)sec(x)tan(x)
∫
−
sin
(
x
)
sec
(
x
)
tan
(
x
)
dx
integral of 4x^3-3/(x^4)
∫
4
x
3
−
3
x
4
dx
derivative sqrt(3-9x)
derivative
√
3
−
9
x
derivative of 4x-3/x+1/(x^2)
d
dx
(
4
x
−
3
x
+
1
x
2
)
integral of ln(x)(sqrt(1-(ln(x))^2))/x
∫
ln
(
x
)
√
1
−
(
ln
(
x
)
)
2
x
dx
integral of 1/(sqrt(2x))cos(sqrt(2x))
∫
1
√
2
x
cos
(
√
2
x
)
dx
limit as x approaches 8-of (x-9)/(x-8)
lim
x
→
8
−
(
x
−
9
x
−
8
)
지역 3x,7x^2
area
3
x
,
7
x
2
derivative of 3^{x^4-2x^2}
d
dx
(
3
x
4
−
2
x
2
)
limit as x approaches 0 of (5x-3)^2
lim
x
→
0
(
(
5
x
−
3
)
2
)
inverselaplace ((2s+1))/((s+1)^2)
inverselaplace
(
2
s
+
1
)
(
s
+
1
)
2
xyy^'=y^2+xsqrt(4x^2+y^2)
xyy
′
=
y
2
+
x
√
4
x
2
+
y
2
derivative e^w
derivative
e
w
tangent x^3-2x^2-5x+6,\at x=2
tangent
x
3
−
2
x
2
−
5
x
+
6
,
at
x
=
2
derivative of \sqrt[5]{3x}
d
dx
(
5
√
3
x
)
integral of 8x^{-9}
∫
8
x
−
9
dx
integral of sin(2θ)
∫
sin
(
2
θ
)
d
θ
inverselaplace f(s)= 1/(s(s-3))
inverselaplace
f
(
s
)
=
1
s
(
s
−
3
)
derivative of arccot(sqrt(2x))
d
dx
(
arccot
(
√
2
x
)
)
limit as x approaches 1+of (x+10)/(x+3)
lim
x
→
1
+
(
x
+
1
0
x
+
3
)
derivative (x^8-2x^4-10x)/(x^4)
derivative
x
8
−
2
x
4
−
1
0
x
x
4
지역 6ln(x),xln(x)
area
6
ln
(
x
)
,
x
ln
(
x
)
d/(dt)(-8sin(t))
d
dt
(
−
8
sin
(
t
)
)
derivative-5/(x^4)
derivative
−
5
x
4
limit as x approaches-1 of x^2-3x
lim
x
→
−
1
(
x
2
−
3
x
)
integral of (4x)/1
∫
4
x
1
dx
(\partial)/(\partial z)(y+z)
∂
∂
z
(
y
+
z
)
derivative f(x)=2x+sqrt(x)
derivative
f
(
x
)
=
2
x
+
√
x
derivative of sin(x^2+3x+1)
d
dx
(
sin
(
x
2
+
3
x
+
1
)
)
1
2
3
4
5
6
7
..
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