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일반적인 미적분학 문제
limit as x approaches-3 of sqrt(x^2-8)
lim
x
→
−
3
(
√
x
2
−
8
)
integral of sec(2x)tan(2x)
∫
sec
(
2
x
)
tan
(
2
x
)
dx
integral of x*e^{2x}
∫
x
·
e
2
x
dx
integral of sqrt(2)sin(x)
∫
√
2
sin
(
x
)
dx
integral of cos^3(x)cos(3x)
∫
cos
3
(
x
)
cos
(
3
x
)
dx
limit as n approaches infinity of 1/(sqrt(n^2+2n)-n)
lim
n
→
∞
(
1
√
n
2
+
2
n
−
n
)
derivative (sec(x))/(7+sec(x))
derivative
sec
(
x
)
7
+
sec
(
x
)
y^{''}-36y^'=0
y
′
′
−
3
6
y
′
=
0
integral of-2e^{-x}x
∫
−
2
e
−
x
xdx
integral of 1/(sqrt(x^2+1))
∫
1
√
x
2
+
1
dx
integral of ((x-2)sqrt(x+4))
∫
(
(
x
−
2
)
√
x
+
4
)
dx
limit as x approaches 0 of x*(e^{1/x}-1)
lim
x
→
0
(
x
·
(
e
1
x
−
1
)
)
derivative y=arctan(sqrt(2t))
derivative
y
=
arctan
(
√
2
t
)
(\partial)/(\partial x)(2x^2y^4)
∂
∂
x
(
2
x
2
y
4
)
integral of cos^4(2x)
∫
cos
4
(
2
x
)
dx
derivative 7arctan(x+sqrt(1+x^2))
derivative
7
arctan
(
x
+
√
1
+
x
2
)
(\partial)/(\partial x)(xy(18-x-y))
∂
∂
x
(
xy
(
1
8
−
x
−
y
)
)
integral of e^{cos(x)}(-sin(x))
∫
e
cos
(
x
)
(
−
sin
(
x
)
)
dx
integral of (x^2-3)^5x
∫
(
x
2
−
3
)
5
xdx
integral of-sqrt(4-x^2)
∫
−
√
4
−
x
2
dx
(x^2+2y^2)=xyy^'
(
x
2
+
2
y
2
)
=
xyy
′
y^'=(y^3-3)/((3xy^2))
y
′
=
y
3
−
3
(
3
xy
2
)
derivative f(x)=(5x)/(e^x)
derivative
f
(
x
)
=
5
x
e
x
derivative 1/(3x^2+2x)
derivative
1
3
x
2
+
2
x
derivative of 3(x^2+y^2^2)
d
dx
(
3
(
x
2
+
y
2
)
2
)
integral from 0 to 1 of x^{-1}
∫
0
1
x
−
1
dx
derivative y=4cot(3-2x)
derivative
y
=
4
cot
(
3
−
2
x
)
integral from 0 to 2 of (4x-2x^2)
∫
0
2
(
4
x
−
2
x
2
)
dx
limit as x approaches 2 of x/((x-2))
lim
x
→
2
(
x
(
x
−
2
)
)
integral of (20)/(xsqrt(1+2x))
∫
2
0
x
√
1
+
2
x
dx
integral of x/(x^2+2x+5)
∫
x
x
2
+
2
x
+
5
dx
limit as x approaches 0 of (e^{3x-1})/x
lim
x
→
0
(
e
3
x
−
1
x
)
(dy)/(dx)y=(x^2+3x)^2
dy
dx
y
=
(
x
2
+
3
x
)
2
integral from 0 to 2 of xsqrt(x^2+1)
∫
0
2
x
√
x
2
+
1
dx
inverse라플라스 (3s)/((s+3)^2(s+6))
inverselaplace
3
s
(
s
+
3
)
2
(
s
+
6
)
integral from 0 to ln(5) of 4(5-xe^x)
∫
0
ln
(
5
)
4
(
5
−
xe
x
)
dx
limit as x approaches-infinity of 4/x
lim
x
→
−
∞
(
4
x
)
integral of ((sin(sqrt(x)))/(sqrt(x)))
∫
(
sin
(
√
x
)
√
x
)
dx
derivative f(x)=x^7+x^5+x^3+x+1
derivative
f
(
x
)
=
x
7
+
x
5
+
x
3
+
x
+
1
경사지 (3.3)(4.5)
slope
(
3
.
3
)
(
4
.
5
)
integral from 0 to pi/3 of cos^3(3x)
∫
0
π
3
cos
3
(
3
x
)
dx
integral of (cos(x))/(sin^2(x)-4)
∫
cos
(
x
)
sin
2
(
x
)
−
4
dx
(\partial)/(\partial x)((e^{-x/2})(2xy))
∂
∂
x
(
(
e
−
x
2
)
(
2
xy
)
)
integral from 0 to 1 of (sqrt(1-x^2))
∫
0
1
(
√
1
−
x
2
)
dx
integral from-2 to 0 of (8x^2+8x)
∫
−
2
0
(
8
x
2
+
8
x
)
dx
t^2y^'+ty=1
t
2
y
′
+
ty
=
1
integral of 4sec^4(x)
∫
4
sec
4
(
x
)
dx
integral of-x+1
∫
−
x
+
1
dx
y^{''}+49y=cos(8t)
y
′
′
+
4
9
y
=
cos
(
8
t
)
xy^'+y=14sqrt(x)
xy
′
+
y
=
1
4
√
x
integral of e^{3x+9}-3x^2
∫
e
3
x
+
9
−
3
x
2
dx
y^{''}+4y=8
y
′
′
+
4
y
=
8
integral of 2+cos(x)
∫
2
+
cos
(
x
)
dx
limit as x approaches 2 of 3x^2-7x+5
lim
x
→
2
(
3
x
2
−
7
x
+
5
)
integral of sec^4(3x)
∫
sec
4
(
3
x
)
dx
integral from-3 to 3 of 1/(sqrt(9-x^2))
∫
−
3
3
1
√
9
−
x
2
dx
integral from 0 to 5 of (6t)/((t-6)^2)
∫
0
5
6
t
(
t
−
6
)
2
dt
integral of ((1+sqrt(x))^4)/(sqrt(x))
∫
(
1
+
√
x
)
4
√
x
dx
derivative of 2/(1+e^x)
d
dx
(
2
1
+
e
x
)
sum from n=0 to infinity of (n+1)/n
∑
n
=
0
∞
n
+
1
n
integral of sec^4(t/2)
∫
sec
4
(
t
2
)
dt
integral of x^2(x-1)^2
∫
x
2
(
x
−
1
)
2
dx
테일러 2/((3x+1)),x=2
taylor
2
(
3
x
+
1
)
,
x
=
2
integral of 1/(sqrt(-x^2+8x-15))
∫
1
√
−
x
2
+
8
x
−
1
5
dx
integral of (e^{3x}+3e^x+2)/(e^x)
∫
e
3
x
+
3
e
x
+
2
e
x
dx
f(t)=-1/(t^2)
f
(
t
)
=
−
1
t
2
integral of 2arctan(3x)
∫
2
arctan
(
3
x
)
dx
integral of-xe^{-ln(x)}
∫
−
xe
−
ln
(
x
)
dx
tangent f(x)=2x^3+3x^2,\at x=1
tangent
f
(
x
)
=
2
x
3
+
3
x
2
,
at
x
=
1
integral of x^2f(x)
∫
x
2
f
(
x
)
dx
integral of 4e^t
∫
4
e
t
dt
(dy)/(dx)=10+5sin(x/4)-y/(100)
dy
dx
=
1
0
+
5
sin
(
x
4
)
−
y
1
0
0
derivative of 25(x^2-y^2)
d
dx
(
2
5
(
x
2
−
y
2
)
)
derivative of (10^x/(10^x+4))
d
dx
(
1
0
x
1
0
x
+
4
)
integral from 0 to 2pi of xsin(x)cos(x)
∫
0
2
π
x
sin
(
x
)
cos
(
x
)
dx
inverse라플라스 1/(s^2+6s+7)
inverselaplace
1
s
2
+
6
s
+
7
(dy)/(dx)= x/(x^2-7x+12),y(5)=0
dy
dx
=
x
x
2
−
7
x
+
1
2
,
y
(
5
)
=
0
derivative of e^{-6x^2}
d
dx
(
e
−
6
x
2
)
limit as x approaches infinity of 6+1/x
lim
x
→
∞
(
6
+
1
x
)
d/(d{z)}({x}{y}^2-{x}{y}^2{z}^3+2{x}^2{y}{z}^2)
d
d
z
(
x
y
2
−
x
y
2
z
3
+
2
x
2
y
z
2
)
derivative of 2x^3-x^2+3x
d
dx
(
2
x
3
−
x
2
+
3
x
)
derivative y=sqrt(x^2+5)
derivative
y
=
√
x
2
+
5
integral of e^{-x}(1-x)
∫
e
−
x
(
1
−
x
)
dx
(\partial)/(\partial x)(x/(x^7-y^6))
∂
∂
x
(
x
x
7
−
y
6
)
integral of (x^2-5)^5(2x)
∫
(
x
2
−
5
)
5
(
2
x
)
dx
derivative of 5/((4x^{-2)})
d
dx
(
5
(
4
x
)
−
2
)
partialfraction (x^2)/(1+x)
partialfraction
x
2
1
+
x
integral of e^{(-t^2)/2}
∫
e
−
t
2
2
dt
limit as x approaches+(-2)-of 1/(x^2-4)
lim
x
→
+
(
−
2
)
−
(
1
x
2
−
4
)
derivative of cos(wt)
d
dx
(
cos
(
wt
)
)
integral of (ln^2(x))/x
∫
ln
2
(
x
)
x
dx
derivative x5^{6x+1}
derivative
x
5
6
x
+
1
derivative f(x)=(x^2-1)/(x+3)
derivative
f
(
x
)
=
x
2
−
1
x
+
3
(\partial)/(\partial x)(6xy+e^xln(y)-5)
∂
∂
x
(
6
xy
+
e
x
ln
(
y
)
−
5
)
integral from 0 to 1 of ln(1-x)
∫
0
1
ln
(
1
−
x
)
dx
integral from 0 to pi/(20) of tan(10x)
∫
0
π
2
0
tan
(
1
0
x
)
dx
derivative of (x+4/(cos(x)))
d
dx
(
x
+
4
cos
(
x
)
)
(\partial)/(\partial x)(xe^{y^2}+yln(x))
∂
∂
x
(
xe
y
2
+
y
ln
(
x
)
)
derivative f(x)=(2x-3)*sqrt(x)
derivative
f
(
x
)
=
(
2
x
−
3
)
·
√
x
integral of 1-2/(x^2)
∫
1
−
2
x
2
dx
1
..
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1482
1483
1484
1485
..
2459