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일반적인 미적분학 문제
테일러 ln(-3x)+2
taylor
ln
(
−
3
x
)
+
2
(\partial)/(\partial x)(e^0)
∂
∂
x
(
e
0
)
integral of (7x)/(e^x)
∫
7
x
e
x
dx
경사지 y=sin(xy)+pi,(1,pi)
slope
y
=
sin
(
xy
)
+
π
,
(
1
,
π
)
tangent f(x)=x^4+3e^x,\at x=0
tangent
f
(
x
)
=
x
4
+
3
e
x
,
at
x
=
0
integral of 42x(x+7)^5
∫
4
2
x
(
x
+
7
)
5
dx
derivative of 26(2e^{x^2}x^2+e^{x^2})
d
dx
(
2
6
(
2
e
x
2
x
2
+
e
x
2
)
)
y^'=3y^2+xy^2,y(0)=1
y
′
=
3
y
2
+
xy
2
,
y
(
0
)
=
1
integral of e^t(sin(t)+cos(t))
∫
e
t
(
sin
(
t
)
+
cos
(
t
)
)
dt
integral from-3 to 2 of x^2
∫
−
3
2
x
2
dx
integral of 1/(4sin(x)-3cos(x))
∫
1
4
sin
(
x
)
−
3
cos
(
x
)
dx
integral from 1 to infinity of 1/(x^0)
∫
1
∞
1
x
0
dx
(1-2/y+x)(dy)/(dx)+y=2x-1
(
1
−
2
y
+
x
)
dy
dx
+
y
=
2
x
−
1
integral from-1 to 1 of (e^x)^2
∫
−
1
1
(
e
x
)
2
dx
integral of (5/(t^2)+4t^2)
∫
(
5
t
2
+
4
t
2
)
dt
integral of 1/(5-x^2)
∫
1
5
−
x
2
dx
derivative of 20x^3-6x^2+x
d
dx
(
2
0
x
3
−
6
x
2
+
x
)
inverse라플라스 1/(s^2-4s+4)
inverselaplace
1
s
2
−
4
s
+
4
derivative of 2/(xy)
d
dx
(
2
xy
)
integral from 0 to pi/4 of 2sec(x)
∫
0
π
4
2
sec
(
x
)
dx
f^'(x)=x^2e^{x^2}
f
′
(
x
)
=
x
2
e
x
2
tangent (3x)/(x+1)
tangent
3
x
x
+
1
derivative 2x^2-1/16 ln(x)
derivative
2
x
2
−
1
1
6
ln
(
x
)
integral of cos^3(x)sin^6(x)
∫
cos
3
(
x
)
sin
6
(
x
)
dx
y=8in^x+c
y
=
8
in
x
+
c
limit as t approaches 0+of arctan(1/t)
lim
t
→
0
+
(
arctan
(
1
t
)
)
integral of (4cos(θ))^2
∫
(
4
cos
(
θ
)
)
2
d
θ
(\partial)/(\partial t)(e^{sin(x+ct)})
∂
∂
t
(
e
sin
(
x
+
ct
)
)
y^{''}+4y^'+4y=x^{-1/2}
y
′
′
+
4
y
′
+
4
y
=
x
−
1
2
integral of 2cos(x)sin(x)
∫
2
cos
(
x
)
sin
(
x
)
dx
derivative of 14.8sin(pi/6*x-pi/2+10)
d
dx
(
1
4
.
8
sin
(
π
6
·
x
−
π
2
)
+
1
0
)
integral of (2x^3+2x-3)
∫
(
2
x
3
+
2
x
−
3
)
dx
(\partial)/(\partial x)(9xcos(x)cos(y))
∂
∂
x
(
9
x
cos
(
x
)
cos
(
y
)
)
integral of log_{e}(2x)
∫
log
e
(
2
x
)
dx
derivative (x-1)^{2/3}
derivative
(
x
−
1
)
2
3
(\partial)/(\partial x)(x/y-y/z)
∂
∂
x
(
x
y
−
y
z
)
derivative of 81sin(3x)
d
dx
(
8
1
sin
(
3
x
)
)
integral of 2x^2-3x+5
∫
2
x
2
−
3
x
+
5
dx
(dy}{dt}+\frac{23y)/t = 1/t
dy
dt
+
2
3
y
t
=
1
t
지역 1390-34x,88x,[11.3934400000000…,12.3934400000000…]
area
1
3
9
0
−
3
4
x
,
8
8
x
,
[
1
1
.
3
9
3
4
4
0
0
0
0
0
0
0
0
…
,
1
2
.
3
9
3
4
4
0
0
0
0
0
0
0
0
…
]
derivative f(x)=n!(3-x)^{-1}
derivative
f
(
x
)
=
n
!
(
3
−
x
)
−
1
(\partial)/(\partial x)(xy^2e^y)
∂
∂
x
(
xy
2
e
y
)
y^{''}-4y^'+8=0
y
′
′
−
4
y
′
+
8
=
0
integral of (x^2+4)^{-2}
∫
(
x
2
+
4
)
−
2
dx
integral of 1/(1+z^2)
∫
1
1
+
z
2
dz
t^2y^{''}+13ty^'+36y=0
t
2
y
′
′
+
1
3
ty
′
+
3
6
y
=
0
9y^{''}-60y^'+51y=0,y(0)=1,y^'(0)=0
9
y
′
′
−
6
0
y
′
+
5
1
y
=
0
,
y
(
0
)
=
1
,
y
′
(
0
)
=
0
derivative of (sin(2x+1)^2)
d
dx
(
(
sin
(
2
x
)
+
1
)
2
)
tangent y=x^2-1,(-2,3)
tangent
y
=
x
2
−
1
,
(
−
2
,
3
)
tangent f(x)=4x^2-4x+1,\at x=4
tangent
f
(
x
)
=
4
x
2
−
4
x
+
1
,
at
x
=
4
(\partial)/(\partial x)(y*e^x)
∂
∂
x
(
y
·
e
x
)
derivative f(x)=sqrt(x/(x+3))
derivative
f
(
x
)
=
√
x
x
+
3
sum from n=1 to infinity}((-1)^{n+1 of 2n)/(n+1)
∑
n
=
1
∞
(
−
1
)
n
+
1
2
n
n
+
1
integral from-pi/4 to 0 of 6sec^3(x)
∫
−
π
4
0
6
sec
3
(
x
)
dx
limit as x approaches 2-of (|x-2|)/(x-2)
lim
x
→
2
−
(
|
x
−
2
|
x
−
2
)
(\partial)/(\partial x)((18xy)/(x+y))
∂
∂
x
(
1
8
xy
x
+
y
)
limit as x approaches 8 of 15
lim
x
→
8
(
1
5
)
integral of sin(x)ln(sin(x))
∫
sin
(
x
)
ln
(
sin
(
x
)
)
dx
tangent x^6,\at x=3
tangent
x
6
,
at
x
=
3
limit as x approaches 0 of x/(sqrt(x)-1)
lim
x
→
0
(
x
√
x
−
1
)
(dy)/(dx)+y=e^{3x}
dy
dx
+
y
=
e
3
x
(dy)/(dx)-y=3e^{8x}
dy
dx
−
y
=
3
e
8
x
derivative (cos(x))/(x^4)
derivative
cos
(
x
)
x
4
derivative of sqrt(5x+7)
d
dx
(
√
5
x
+
7
)
derivative (ln(x))/(sqrt(x))
derivative
ln
(
x
)
√
x
integral from 0 to 1 of x\sqrt[3]{1-x}
∫
0
1
x
3
√
1
−
x
dx
integral of 1/((1+e^{-x))}
∫
1
(
1
+
e
−
x
)
dx
(\partial)/(\partial x)(sin(x/2))
∂
∂
x
(
sin
(
x
2
)
)
integral from 1 to 4 of x^2-2x+3
∫
1
4
x
2
−
2
x
+
3
dx
(dy)/(dx)=((y^2+3xy+x^2))/(x^2)
dy
dx
=
(
y
2
+
3
xy
+
x
2
)
x
2
derivative of sqrt((2-x^3))
d
dx
(
√
(
2
−
x
)
3
)
integral of-1/(2x)
∫
−
1
2
x
dx
limit as x approaches pi/3-of cot(3x)
lim
x
→
π
3
−
(
cot
(
3
x
)
)
tangent f(x)=x^2-4,(3,5)
tangent
f
(
x
)
=
x
2
−
4
,
(
3
,
5
)
derivative of 2x^6-5x^{-1/2}
d
dx
(
2
x
6
−
5
x
−
1
2
)
derivative sin^2(pit)
derivative
sin
2
(
π
t
)
sum from n=1 to infinity of n
∑
n
=
1
∞
n
integral from-infinity to 0 of 1/(4-7x)
∫
−
∞
0
1
4
−
7
x
dx
limit as t approaches-2 of (t+2)/(t^3+8)
lim
t
→
−
2
(
t
+
2
t
3
+
8
)
derivative e^{x-2}-(sqrt(x))/2
derivative
e
x
−
2
−
√
x
2
limit as x approaches-2-of 1/(x^2-4)
lim
x
→
−
2
−
(
1
x
2
−
4
)
d/(dt)(arctan(y/x))
d
dt
(
arctan
(
y
x
)
)
integral of 1/(e^xcos^2(e^{-x))}
∫
1
e
x
cos
2
(
e
−
x
)
dx
integral of sqrt(y)cos(y)
∫
√
y
cos
(
y
)
dy
integral from 0 to infinity of e^{-0.5x}
∫
0
∞
e
−
0
.
5
x
dx
integral of (cos(sqrt(x)))/(2sqrt(x))
∫
cos
(
√
x
)
2
√
x
dx
integral of e^x-x
∫
e
x
−
xdx
2xydy+(x^2-y^2)dx=0
2
xydy
+
(
x
2
−
y
2
)
dx
=
0
integral of (5+x^7)^87x^6
∫
(
5
+
x
7
)
8
7
x
6
dx
integral of 1/(x^2sqrt(x^2+1))
∫
1
x
2
√
x
2
+
1
dx
integral of xcos(ax^2)
∫
x
cos
(
ax
2
)
dx
integral from 0 to infinity of 14e^{-7x}
∫
0
∞
1
4
e
−
7
x
dx
derivative 8x-3
derivative
8
x
−
3
limit as x approaches 0 of xcot(5x)
lim
x
→
0
(
x
cot
(
5
x
)
)
integral of (2x-5)(x-3)^9
∫
(
2
x
−
5
)
(
x
−
3
)
9
dx
(y^2+16)dx-(1/((3x+5)^2))dy=0
(
y
2
+
1
6
)
dx
−
(
1
(
3
x
+
5
)
2
)
dy
=
0
integral of (12)/(12+e^x)
∫
1
2
1
2
+
e
x
dx
derivative t/(t+1)
derivative
t
t
+
1
integral of cot^3(11x)
∫
cot
3
(
1
1
x
)
dx
tangent y=x^3-3x+2(2.4)
tangent
y
=
x
3
−
3
x
+
2
(
2
.
4
)
1
..
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1410
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1412
1413
..
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