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일반적인 미적분학 문제
sum from n=10000 to infinity of 1/n
∑
n
=
1
0
0
0
0
∞
1
n
integral of (x-arctan(2x))/(1+4x^2)
∫
x
−
arctan
(
2
x
)
1
+
4
x
2
dx
integral of log_{3}(\sqrt[5]{2x})
∫
log
3
(
5
√
2
x
)
dx
derivative of cos(x+cos(y))
d
dx
(
cos
(
x
)
+
cos
(
y
)
)
derivative of (sqrt(x)/(3+x))
d
dx
(
√
x
3
+
x
)
integral of (x^2)/((1+x^2))
∫
x
2
(
1
+
x
2
)
dx
(dy)/(dt)+y=2
dy
dt
+
y
=
2
integral of (6x+6)/(5x^2+26x+5)
∫
6
x
+
6
5
x
2
+
2
6
x
+
5
dx
derivative of 3x^2+2x
d
dx
(
3
x
2
+
2
x
)
(\partial)/(\partial x)(sin(x^3+y^2))
∂
∂
x
(
sin
(
x
3
+
y
2
)
)
y^'+5y=1
y
′
+
5
y
=
1
경사지 (-3,2),(5,-4)
slope
(
−
3
,
2
)
,
(
5
,
−
4
)
limit as x approaches-1 of x^2+x+1
lim
x
→
−
1
(
x
2
+
x
+
1
)
derivative of (x^2/((1+x)))
d
dx
(
x
2
(
1
+
x
)
)
d/(dt)(e^{3t})
d
dt
(
e
3
t
)
limit as x approaches-4 of-7
lim
x
→
−
4
(
−
7
)
laplace변환 6e^{-2t}
laplacetransform
6
e
−
2
t
d/(dy)(ln(cos(x/(y^2))))
d
dy
(
ln
(
cos
(
x
y
2
)
)
)
integral of ln(x^n)
∫
ln
(
x
n
)
dx
integral of (sec^4(x))/(tan^5(x))
∫
sec
4
(
x
)
tan
5
(
x
)
dx
경사지 (3/10 ,-1/2),(1/5 , 1/5)
slope
(
3
1
0
,
−
1
2
)
,
(
1
5
,
1
5
)
(\partial)/(\partial x)(y^3sin(5x))
∂
∂
x
(
y
3
sin
(
5
x
)
)
derivative \sqrt[3]{1+8x}
derivative
3
√
1
+
8
x
derivative z/(z+d/z)
derivative
z
z
+
d
z
derivative sqrt(ln(4x))
derivative
√
ln
(
4
x
)
(\partial)/(\partial y)(2x-2xy)
∂
∂
y
(
2
x
−
2
xy
)
f^'(x)=x^{1/3}(2x-1)(x+1)
f
′
(
x
)
=
x
1
3
(
2
x
−
1
)
(
x
+
1
)
tangent f(x)=2sqrt(x)+1,\at x= 1/4
tangent
f
(
x
)
=
2
√
x
+
1
,
at
x
=
1
4
integral of 4e^{x/2}
∫
4
e
x
2
dx
derivative of (2^{2/3}-x^{2/3}^{3/2})
d
dx
(
(
2
2
3
−
x
2
3
)
3
2
)
derivative of (x^{e^x}/(1+x^2))
d
dx
(
x
e
x
1
+
x
2
)
derivative of sin(e^{sqrt(x)})
d
dx
(
sin
(
e
√
x
)
)
d/(dθ)(e^{2θ})
d
d
θ
(
e
2
θ
)
integral of 1/(x(ln(x^2)))
∫
1
x
(
ln
(
x
2
)
)
dx
integral of ln(e^{xy}cos(x))
∫
ln
(
e
xy
cos
(
x
)
)
dy
integral of x^4sqrt(ax^5-b)
∫
x
4
√
ax
5
−
b
dx
(\partial)/(\partial x)(ln(x+6y+9z))
∂
∂
x
(
ln
(
x
+
6
y
+
9
z
)
)
integral from 0 to pi/2 of tan(x/2)
∫
0
π
2
tan
(
x
2
)
dx
25y^{''}-40y^'+16y=0,y(0)=4,y^'(0)=-5
2
5
y
′
′
−
4
0
y
′
+
1
6
y
=
0
,
y
(
0
)
=
4
,
y
′
(
0
)
=
−
5
integral of ln(x^{1/2})
∫
ln
(
x
1
2
)
dx
inverse라플라스 s/((s-1)^2)
inverselaplace
s
(
s
−
1
)
2
(\partial)/(\partial x)(e^{e^x})
∂
∂
x
(
e
e
x
)
d/(dθ)(sin(θ)+cos(θ))
d
d
θ
(
sin
(
θ
)
+
cos
(
θ
)
)
integral of 8x-9
∫
8
x
−
9
dx
integral of (x+4)cos(npix)
∫
(
x
+
4
)
cos
(
n
π
x
)
dx
integral from 1 to 4 of 1/(w^2)
∫
1
4
1
w
2
dw
integral of (x+2)^2(1-x)^6
∫
(
x
+
2
)
2
(
1
−
x
)
6
dx
지역 5-x^2,sin(x),0,2
area
5
−
x
2
,
sin
(
x
)
,
0
,
2
(d^4)/(dx^4)(8e^{-2x})
d
4
dx
4
(
8
e
−
2
x
)
(dy)/(dx)=(x-2)e^{2y}
dy
dx
=
(
x
−
2
)
e
2
y
tangent y=(6x^2-6x+2)(1+2x),\at x=1
tangent
y
=
(
6
x
2
−
6
x
+
2
)
(
1
+
2
x
)
,
at
x
=
1
(\partial)/(\partial y)(cos(x^2+y^3))
∂
∂
y
(
cos
(
x
2
+
y
3
)
)
laplace변환 sin^2(7t)
laplacetransform
sin
2
(
7
t
)
derivative of-1/3
d
dx
(
−
1
3
)
integral of cos^{16}(x)sin(x)
∫
cos
1
6
(
x
)
sin
(
x
)
dx
derivative of (x^2-1^4(2-3x))
d
dx
(
(
x
2
−
1
)
4
(
2
−
3
x
)
)
derivative of (x+1^{2/3})
d
dx
(
(
x
+
1
)
2
3
)
(\partial)/(\partial x)(x^2-x-12y+1)
∂
∂
x
(
x
2
−
x
−
1
2
y
+
1
)
derivative of 524.8*x^{0.75}
d
dx
(
5
2
4
.
8
·
x
0
.
7
5
)
derivative of 5ln(2x)
d
dx
(
5
ln
(
2
x
)
)
integral from 0 to 3pi of 7x^2sin(1/6 x)
∫
0
3
π
7
x
2
sin
(
1
6
x
)
dx
derivative y= x/9-9/x
derivative
y
=
x
9
−
9
x
derivative of 3+3cos(x)
d
dx
(
3
+
3
cos
(
x
)
)
integral of 15xsqrt(1-x)
∫
1
5
x
√
1
−
x
dx
integral of 1/((x^2+6x+13))
∫
1
(
x
2
+
6
x
+
1
3
)
dx
derivative of 2^{sqrt(x^2+3x+4)}
d
dx
(
2
√
x
2
+
3
x
+
4
)
derivative x^3-3x
derivative
x
3
−
3
x
derivative of x9^x
d
dx
(
x
9
x
)
derivative of ax^{a-1}ln(x+x^{a-1})
d
dx
(
ax
a
−
1
ln
(
x
)
+
x
a
−
1
)
derivative-(6e^{6/x})/(x^2)
derivative
−
6
e
6
x
x
2
derivative of (5x^2/(2sqrt(b^2+x^2)))
d
dx
(
5
x
2
2
√
b
2
+
x
2
)
(y^2+xy)dx+x^2dy=0
(
y
2
+
xy
)
dx
+
x
2
dy
=
0
20y^{''}+11y^'-3y=0
2
0
y
′
′
+
1
1
y
′
−
3
y
=
0
d/(d{y)}(({z})/(({x)^2+{y}^2+{z}^2)^{3/2}})
d
d
y
(
z
(
x
2
+
y
2
+
z
2
)
3
2
)
limit as x approaches 1 of (x^2-3x+2)/(x^3-1)
lim
x
→
1
(
x
2
−
3
x
+
2
x
3
−
1
)
integral of 3/(x^2sqrt(25-x^2))
∫
3
x
2
√
2
5
−
x
2
dx
f(x)= 2/(x+2)
f
(
x
)
=
2
x
+
2
(\partial)/(\partial y)((x^2+y)e^{y/2})
∂
∂
y
(
(
x
2
+
y
)
e
y
2
)
integral of e^{-2x}sin(2x)
∫
e
−
2
x
sin
(
2
x
)
dx
integral of (x^4)/(x^2+1)
∫
x
4
x
2
+
1
dx
integral from 1 to 3 of (x-1)ln(x)
∫
1
3
(
x
−
1
)
ln
(
x
)
dx
derivative of 4/3 {p}(xi{r}(x)(x)^3)
d
dx
(
4
3
p
(
x
)
i
r
(
x
)
(
x
)
3
)
(\partial)/(\partial x)(yln(x^4+y^3+2)-7)
∂
∂
x
(
y
ln
(
x
4
+
y
3
+
2
)
−
7
)
derivative (4/3)pix^3
derivative
(
4
3
)
pix
3
derivative of (x^3+2x^4)
d
dx
(
(
x
3
+
2
x
)
4
)
f(x)=((x-1)^2)/((x+2))
f
(
x
)
=
(
x
−
1
)
2
(
x
+
2
)
implicit xsin(y)+ysin(x)=6
implicit
x
sin
(
y
)
+
y
sin
(
x
)
=
6
y^'+5xe^y=0
y
′
+
5
xe
y
=
0
(\partial)/(\partial x)(2ycos(9y^2x))
∂
∂
x
(
2
y
cos
(
9
y
2
x
)
)
limit as x approaches 0 of x^{1/2}
lim
x
→
0
(
x
1
2
)
integral of 2xtan(x)
∫
2
x
tan
(
x
)
dx
limit as x approaches 2-of sqrt(4-x^2)
lim
x
→
2
−
(
√
4
−
x
2
)
sum from n=0 to infinity of 6/(n^2-1)
∑
n
=
0
∞
6
n
2
−
1
laplace변환-5t^3
laplacetransform
−
5
t
3
(y^')/(1+y^2)+t/(e^{t^2)}=0,y(0)=1
y
′
1
+
y
2
+
t
e
t
2
=
0
,
y
(
0
)
=
1
derivative of (11/x)
d
dx
(
1
1
x
)
integral of 2x(x^2-7)^6
∫
2
x
(
x
2
−
7
)
6
dx
derivative \sqrt[7]{x^2}+2sqrt(x^7)
derivative
7
√
x
2
+
2
√
x
7
integral from 1/7 to 3 of 12xln(7x)
∫
1
7
3
1
2
x
ln
(
7
x
)
dx
derivative of (sin(x)/(x^3))
d
dx
(
sin
(
x
)
x
3
)
1
..
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1096
1097
1098
1099
..
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