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일반적인 미적분학 문제
integral of 8/(x-1)
∫
8
x
−
1
dx
integral of (10)/(x+1)
∫
1
0
x
+
1
dx
(\partial)/(\partial x)((5x-y)/(y^2+3x^2))
∂
∂
x
(
5
x
−
y
y
2
+
3
x
2
)
지역 y=(x^3+1)^{-1},x=0,x=1
area
y
=
(
x
3
+
1
)
−
1
,
x
=
0
,
x
=
1
integral of x^2+4x+4
∫
x
2
+
4
x
+
4
dx
integral from 0 to 4 of-x+1
∫
0
4
−
x
+
1
dx
limit as x approaches infinity of (sqrt(x))/(6+e^x)
lim
x
→
∞
(
√
x
6
+
e
x
)
integral of ((4-t+t^2)/(t^2))
∫
(
4
−
t
+
t
2
t
2
)
dt
derivative of ln(sqrt(x^2+20))
d
dx
(
ln
(
√
x
2
+
2
0
)
)
(\partial)/(\partial x)((2y)/(x^2+1))
∂
∂
x
(
2
y
x
2
+
1
)
limit as x approaches 3 of (x-2)/(x+2)
lim
x
→
3
(
x
−
2
x
+
2
)
limit as x approaches 1800 of 28pi^2
lim
x
→
1
8
0
0
(
2
8
π
2
)
derivative (x^2-8x+5)/(x^2+8)
derivative
x
2
−
8
x
+
5
x
2
+
8
integral of 1/(4xsqrt(x^2-16))
∫
1
4
x
√
x
2
−
1
6
dx
derivative of 1-cos(5x)
d
dx
(
1
−
cos
(
5
x
)
)
limit as x approaches 1 of (x+3)/(x+1)
lim
x
→
1
(
x
+
3
x
+
1
)
laplacetransform-6t^2\delta(t-5)
laplacetransform
−
6
t
2
δ
(
t
−
5
)
derivative 5-5x^3
derivative
5
−
5
x
3
derivative of (2x/(7-cot(x)))
d
dx
(
2
x
7
−
cot
(
x
)
)
laplacetransform 1(t)
laplacetransform
1
(
t
)
integral of 26arctan(sqrt(x))
∫
2
6
arctan
(
√
x
)
dx
integral of e^{x^2-4}+5x+6
∫
e
x
2
−
4
+
5
x
+
6
dx
derivative y=(sqrt(x))/(2+x)
derivative
y
=
√
x
2
+
x
limit as x approaches-2-of sqrt(-x-2)+4
lim
x
→
−
2
−
(
√
−
x
−
2
+
4
)
limit as t approaches 2 of [e^{-3t}i]
lim
t
→
2
(
[
e
−
3
t
i
]
)
integral from-5 to-7 of (-5)^{-3}
∫
−
5
−
7
(
−
5
)
−
3
dx
derivative of 2/5 x^5-3x^2+8x-5
d
dx
(
2
5
x
5
−
3
x
2
+
8
x
−
5
)
derivative y=csc^2(x)-2
derivative
y
=
csc
2
(
x
)
−
2
5y^{''}+y^'=0
5
y
′
′
+
y
′
=
0
y^'=sin(3x)
y
′
=
sin
(
3
x
)
derivative of ln(cos(0))
d
dx
(
ln
(
cos
(
0
)
)
)
integral of (4x+6)/(x^2+4)
∫
4
x
+
6
x
2
+
4
dx
integral of 2/(3y-4)
∫
2
3
y
−
4
dy
integral from-2 to 3 of \sqrt[3]{x}
∫
−
2
3
3
√
x
dx
integral of x^3sqrt(x^2-2)
∫
x
3
√
x
2
−
2
dx
y^'+1/2 y=x
y
′
+
1
2
y
=
x
integral from 0 to 1 of sqrt(4x^2+1)
∫
0
1
√
4
x
2
+
1
dx
integral of 6/(3sin(x)-4cos(x))
∫
6
3
sin
(
x
)
−
4
cos
(
x
)
dx
integral of 2/(x^2)-(x^2)/2
∫
2
x
2
−
x
2
2
dx
sum from n=1 to infinity of ne^{-7n}
∑
n
=
1
∞
ne
−
7
n
derivative of arctan^{tan(x}(x))
d
dx
(
arctan
tan
(
x
)
(
x
)
)
integral of (sqrt(x))/(sqrt(1+x^3))
∫
√
x
√
1
+
x
3
dx
derivative of-8x-cos(x)
d
dx
(
−
8
x
−
cos
(
x
)
)
sum from n=7 to infinity of e^5-2n
∑
n
=
7
∞
e
5
−
2
n
derivative of x^3sqrt(x-4)
d
dx
(
x
3
√
x
−
4
)
integral of cot(z)
∫
cot
(
z
)
dz
derivative pi/4 e^{4x+15}
derivative
π
4
e
4
x
+
1
5
limit as x approaches 0 of 4/((5+x)^2-2)
lim
x
→
0
(
4
(
5
+
x
)
2
−
2
)
derivative y=ln(x^{14})
derivative
y
=
ln
(
x
1
4
)
derivative of tan^2(x+1)
d
dx
(
tan
2
(
x
)
+
1
)
integral of ((8+3x-x^2))/((2x+3)(x+2)^2)
∫
(
8
+
3
x
−
x
2
)
(
2
x
+
3
)
(
x
+
2
)
2
dx
(\partial)/(\partial x)(3e^{xy})
∂
∂
x
(
3
e
xy
)
테일러-ln(1-x)
taylor
−
ln
(
1
−
x
)
derivative of ln(x^2+5x)
d
dx
(
ln
(
x
2
+
5
x
)
)
integral from 0 to 1 of 1/(sqrt(3-2x))
∫
0
1
1
√
3
−
2
x
dx
tangent f(x)=x^2,\at x=4
tangent
f
(
x
)
=
x
2
,
at
x
=
4
derivative of 2+3e^{-3/x}
d
dx
(
2
+
3
e
−
3
x
)
derivative of (x^4+3x^2-5^4)
d
dx
(
(
x
4
+
3
x
2
−
5
)
4
)
derivative of 3xe^{5x}
d
dx
(
3
xe
5
x
)
derivative of 5^{-1/x}
d
dx
(
5
−
1
x
)
derivative sqrt(3x+1)
derivative
√
3
x
+
1
derivative of 6x^2+5x^3y^4-10y^5
d
dx
(
6
x
2
+
5
x
3
y
4
−
1
0
y
5
)
integral of tan(3x)sin(3x)
∫
tan
(
3
x
)
sin
(
3
x
)
dx
integral of (5x+4)^6
∫
(
5
x
+
4
)
6
dx
f(x)=(2x+1)^6
f
(
x
)
=
(
2
x
+
1
)
6
t((dy)/(dt))=t^3+13t^3y
t
(
dy
dt
)
=
t
3
+
1
3
t
3
y
derivative of 9xe^{-x}
d
dx
(
9
xe
−
x
)
derivative (14)/((s+7)^2)
derivative
1
4
(
s
+
7
)
2
integral of cos(z)
∫
cos
(
z
)
(1+x^2)y^{''}-2xy^'+2y=0
(
1
+
x
2
)
y
′
′
−
2
xy
′
+
2
y
=
0
(d^3)/(dx^3)(ln(x+2))
d
3
dx
3
(
ln
(
x
+
2
)
)
derivative f(t)=sqrt(9t^2-t)
derivative
f
(
t
)
=
√
9
t
2
−
t
integral of (8x^2)/(sqrt(9-x^2))
∫
8
x
2
√
9
−
x
2
dx
지역-2x^2+3,0x
area
−
2
x
2
+
3
,
0
x
derivative (t^2)/(t-11)
derivative
t
2
t
−
1
1
limit as x approaches-4 of x^2+2/(x+4)
lim
x
→
−
4
(
x
2
+
2
x
+
4
)
integral of xsqrt(7-x)
∫
x
√
7
−
x
dx
integral from 2 to 3 of (13)/(sqrt(3-x))
∫
2
3
1
3
√
3
−
x
dx
integral of (12-12x)/(1-sqrt(x))
∫
1
2
−
1
2
x
1
−
√
x
dx
(\partial)/(\partial y)(cos(y/x))
∂
∂
y
(
cos
(
y
x
)
)
경사지 X^2-2X-15
slope
X
2
−
2
X
−
1
5
integral of 7x^4
∫
7
x
4
dx
tangent f(x)=7x^2+5x-8
tangent
f
(
x
)
=
7
x
2
+
5
x
−
8
limit as x approaches 0 of 3/(sin(3x))
lim
x
→
0
(
3
sin
(
3
x
)
)
tangent e^{-x}
tangent
e
−
x
y^'=2x+4y
y
′
=
2
x
+
4
y
integral of x/(sqrt(2+3x))
∫
x
√
2
+
3
x
dx
integral of (sqrt(x))/(1-x)
∫
√
x
1
−
x
dx
integral from-1 to 0 of 2x-e^x
∫
−
1
0
2
x
−
e
x
dx
derivative t/4
derivative
t
4
derivative of 5(x^2+7^4(2x))
d
dx
(
5
(
x
2
+
7
)
4
(
2
x
)
)
limit as h approaches 0 of ((1+h)^3-1)/h
lim
h
→
0
(
(
1
+
h
)
3
−
1
h
)
integral of 1/(1+cos(x))
∫
1
1
+
cos
(
x
)
dx
derivative of 5xsqrt(64-x^2)
d
dx
(
5
x
√
6
4
−
x
2
)
partialfraction x/(1-x^2)
partialfraction
x
1
−
x
2
f(x)=8sqrt(x)
f
(
x
)
=
8
√
x
derivative of log_{3}(xe^x)
d
dx
(
log
3
(
xe
x
)
)
tangent y=(x^3-4x)^8,(2,0)
tangent
y
=
(
x
3
−
4
x
)
8
,
(
2
,
0
)
d/(dt)((e^{tb}-e^{ta})/(t(b-a)))
d
dt
(
e
tb
−
e
ta
t
(
b
−
a
)
)
y^{''}+9y=12sin(3t)
y
′
′
+
9
y
=
1
2
sin
(
3
t
)
1
..
9
10
11
12
13
..
1823