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일반적인 미적분학 문제
y^'=x^2sec(y)
y
′
=
x
2
sec
(
y
)
integral from 0 to 1 of xe^{-3x^2}
∫
0
1
xe
−
3
x
2
dx
sum from n=0 to infinity of arctan(2n)
∑
n
=
0
∞
arctan
(
2
n
)
경사지 (2,2),(0,-1)
slope
(
2
,
2
)
,
(
0
,
−
1
)
limit as x approaches 0-of 5/(sin(x))
lim
x
→
0
−
(
5
sin
(
x
)
)
laplace변환 acos(2pi+θ)
laplacetransform
a
cos
(
2
π
+
θ
)
(dy)/(dt)=-4y+3e^{-t}
dy
dt
=
−
4
y
+
3
e
−
t
integral of \sqrt[3]{x^2}+xsqrt(x)
∫
3
√
x
2
+
x
√
x
dx
limit as x approaches 0 of (x^2-9x)/x
lim
x
→
0
(
x
2
−
9
x
x
)
경사지 (3,3),(2,-2)
slope
(
3
,
3
)
,
(
2
,
−
2
)
integral of xcos(n)x
∫
x
cos
(
n
)
xdx
derivative of (x+3ln(x^2))
d
dx
(
(
x
+
3
)
ln
(
x
2
)
)
y+2y^7=(y^3+6x)y^'
y
+
2
y
7
=
(
y
3
+
6
x
)
y
′
derivative x^2-x
derivative
x
2
−
x
limit as x approaches 0+of x/(x+1)
lim
x
→
0
+
(
x
x
+
1
)
(\partial)/(\partial x)((x+2y+3z)^{3/2})
∂
∂
x
(
(
x
+
2
y
+
3
z
)
3
2
)
derivative y=6e^{3x}
derivative
y
=
6
e
3
x
derivative of 6x^2+5
d
dx
(
6
x
2
+
5
)
integral of 1/(x^2*sqrt(x^2+1))
∫
1
x
2
·
√
x
2
+
1
dx
integral of 8/(9+r^2)
∫
8
9
+
r
2
dr
derivative f(x)=((4x)^3)/((3-5x)^5)
derivative
f
(
x
)
=
(
4
x
)
3
(
3
−
5
x
)
5
integral of 4xln(4x)
∫
4
x
ln
(
4
x
)
dx
derivative ln(e^xsqrt(x))
derivative
ln
(
e
x
√
x
)
테일러 1/(1-x),(pi/4)
taylor
1
1
−
x
,
(
π
4
)
integral of ((2x+1))/((x+2)^4(x-1)^4)
∫
(
2
x
+
1
)
(
x
+
2
)
4
(
x
−
1
)
4
dx
(dy)/(dx)=3x^2e^{-y}
dy
dx
=
3
x
2
e
−
y
inverse라플라스 1/(2s+2)
inverselaplace
1
2
s
+
2
integral of (x^4)/(1+x^{10)}
∫
x
4
1
+
x
1
0
dx
integral of 3e^{2x+e^{2x}}
∫
3
e
2
x
+
e
2
x
dx
tangent 6/x
tangent
6
x
integral of (2x^4-1)(5x^3+6x)
∫
(
2
x
4
−
1
)
(
5
x
3
+
6
x
)
dx
경사지 f(-3)=-2x^2+4x-7/(x^2)
slope
f
(
−
3
)
=
−
2
x
2
+
4
x
−
7
x
2
(dy)/(dx)=y(xy^4-1)
dy
dx
=
y
(
xy
4
−
1
)
f(x)=-4/x
f
(
x
)
=
−
4
x
sum from n=0 to infinity of 5(3/4)^n
∑
n
=
0
∞
5
(
3
4
)
n
integral of sech^4(x)tanh(x)
∫
sech
4
(
x
)
tanh
(
x
)
dx
4xy^'+4y=3
4
xy
′
+
4
y
=
3
지역 x^5+1,x+1,-1,0
area
x
5
+
1
,
x
+
1
,
−
1
,
0
5x-6ysqrt(x^2+1)(dy)/(dx)=0
5
x
−
6
y
√
x
2
+
1
dy
dx
=
0
limit as x approaches 2 of x^2-3x+8
lim
x
→
2
(
x
2
−
3
x
+
8
)
integral of-2x^6sin(3x)
∫
−
2
x
6
sin
(
3
x
)
dx
inverse라플라스 ((s+5))/(s^2+5s+4)
inverselaplace
(
s
+
5
)
s
2
+
5
s
+
4
derivative of xsqrt(2x+5)
d
dx
(
x
√
2
x
+
5
)
integral of (x^2+x^{-2})/(x^3-3x^{-1)}
∫
x
2
+
x
−
2
x
3
−
3
x
−
1
dx
y^'+7(tan(7x))y=5cos(7x)
y
′
+
7
(
tan
(
7
x
)
)
y
=
5
cos
(
7
x
)
derivative (x^5)/(x^3)
derivative
x
5
x
3
integral of 5/(x^2sqrt(x^2-9))
∫
5
x
2
√
x
2
−
9
dx
derivative of xe^{-x^2y}
d
dx
(
xe
−
x
2
y
)
(d^2)/(dx^2)(3xsin(x^2))
d
2
dx
2
(
3
x
sin
(
x
2
)
)
integral of x/(x-9)
∫
x
x
−
9
dx
integral of 1/(xsqrt(x^3-1))
∫
1
x
√
x
3
−
1
dx
integral of (-3)/(x^2)+11-4^x
∫
−
3
x
2
+
1
1
−
4
x
dx
derivative sin^5(x^3)
derivative
sin
5
(
x
3
)
limit as x approaches 5 of |x-5|
lim
x
→
5
(
|
x
−
5
|
)
y^'-y/2 =e^{-t}
y
′
−
y
2
=
e
−
t
(e^x-y)dx+(e^y-x)dy=0
(
e
x
−
y
)
dx
+
(
e
y
−
x
)
dy
=
0
(x+1)(dy)/(dx)=x+6
(
x
+
1
)
dy
dx
=
x
+
6
integral of-2/(sqrt(100-9t^2))
∫
−
2
√
1
0
0
−
9
t
2
dt
limit as x approaches-1 of sin((pix)/6)
lim
x
→
−
1
(
sin
(
π
x
6
)
)
integral of 4x^{3/2}
∫
4
x
3
2
dx
(\partial)/(\partial x)(sqrt(x^2+y^2-5))
∂
∂
x
(
√
x
2
+
y
2
−
5
)
integral from 0 to pi/2 of cos((2x)/3)
∫
0
π
2
cos
(
2
x
3
)
dx
tangent f(x)=x^3-x,\at x=1
tangent
f
(
x
)
=
x
3
−
x
,
at
x
=
1
derivative xsqrt(3x-4)
derivative
x
√
3
x
−
4
sum from n=1 to infinity of 2(-e)^{-n}
∑
n
=
1
∞
2
(
−
e
)
−
n
integral of (x^5)/(sqrt(x^2+7))
∫
x
5
√
x
2
+
7
dx
integral of 1/(sqrt(5+4x-x^2))
∫
1
√
5
+
4
x
−
x
2
dx
limit as x approaches-infinity of ((sqrt(4x^2+1)))/((2-7x))
lim
x
→
−
∞
(
(
√
4
x
2
+
1
)
(
2
−
7
x
)
)
xy^'+4y=-25xsin(x^5)
xy
′
+
4
y
=
−
2
5
x
sin
(
x
5
)
derivative of 3/(sqrt(7x^4-5x^2+1))
d
dx
(
3
√
7
x
4
−
5
x
2
+
1
)
(dy)/(dx)=tan(4x)
dy
dx
=
tan
(
4
x
)
integral of sqrt(16-t^2)
∫
√
1
6
−
t
2
dt
(\partial)/(\partial y)(1-x-y)
∂
∂
y
(
1
−
x
−
y
)
limit as x approaches 0.1 of (e^x-1)/x
lim
x
→
0
.
1
(
e
x
−
1
x
)
integral from 2 to 3 of (29)/(sqrt(3-x))
∫
2
3
2
9
√
3
−
x
dx
derivative f(x)=(6x-x^2)^{10}
derivative
f
(
x
)
=
(
6
x
−
x
2
)
1
0
derivative of sin^5(3x)
d
dx
(
sin
5
(
3
x
)
)
derivative 5ln(x)+cos(x)
derivative
5
ln
(
x
)
+
cos
(
x
)
y^'=(y+8)/(x+6)
y
′
=
y
+
8
x
+
6
integral of e^x+y
∫
e
x
+
ydx
integral of cos(r^2)r
∫
cos
(
r
2
)
rdr
limit as x approaches 3 of (x-3)/(x+6)
lim
x
→
3
(
x
−
3
x
+
6
)
derivative y=10^{3x}
derivative
y
=
1
0
3
x
y^'=4-9x^2-6x^5
y
′
=
4
−
9
x
2
−
6
x
5
integral from 0 to 2 of 8x-4x^2
∫
0
2
8
x
−
4
x
2
dx
derivative of cos(x+sin(x)+1/2 x^2+1/x)
d
dx
(
cos
(
x
)
+
sin
(
x
)
+
1
2
x
2
+
1
x
)
integral of sin(20x)cos(15x)
∫
sin
(
2
0
x
)
cos
(
1
5
x
)
dx
integral of (3^x+2/x)
∫
(
3
x
+
2
x
)
dx
integral from 2 to 5 of 1/(sqrt(x-1))
∫
2
5
1
√
x
−
1
dx
integral of x^2(2x^3+4)^5
∫
x
2
(
2
x
3
+
4
)
5
dx
integral of x/k
∫
x
k
dx
테일러 x^2+x^31
taylor
x
2
+
x
3
1
derivative (4t^2-t)(t^3-8t^2+12)
derivative
(
4
t
2
−
t
)
(
t
3
−
8
t
2
+
1
2
)
지역 y=sin(x),y=2sin^2(x),x=0,x= pi/2
area
y
=
sin
(
x
)
,
y
=
2
sin
2
(
x
)
,
x
=
0
,
x
=
π
2
limit as x approaches pi-of x/(cos(x)+1)
lim
x
→
π
−
(
x
cos
(
x
)
+
1
)
y^{''}+4y^'+3y=0
y
′
′
+
4
y
′
+
3
y
=
0
limit as x approaches 0-of 4+6/(x^2)
lim
x
→
0
−
(
4
+
6
x
2
)
tangent f(x)=x^2,\at x=-1
tangent
f
(
x
)
=
x
2
,
at
x
=
−
1
integral of 1/(sqrt(z))
∫
1
√
z
dz
(dx)/(dt)+5tx^3+x/t =0
dx
dt
+
5
tx
3
+
x
t
=
0
1
..
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