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일반적인 미적분학 문제
y^'=x-y+1
y
′
=
x
−
y
+
1
derivative f(x)=(1300+8x-0.0004x^2)/x
derivative
f
(
x
)
=
1
3
0
0
+
8
x
−
0
.
0
0
0
4
x
2
x
inverse라플라스 (s+1)/(s^2+1)
inverselaplace
s
+
1
s
2
+
1
integral of ((1+sin(x))/(cos^2(x)))
∫
(
1
+
sin
(
x
)
cos
2
(
x
)
)
dx
f^{''}(x)=2x
f
′
′
(
x
)
=
2
x
integral from 0 to ln(2) of 4/(e^x+3)
∫
0
ln
(
2
)
4
e
x
+
3
dx
(dy)/(dx)x^2+yx=1,y(6)=9
dy
dx
x
2
+
yx
=
1
,
y
(
6
)
=
9
integral of e^e
∫
e
e
de
x((dy)/(dx))=sqrt(1-y^2)
x
(
dy
dx
)
=
√
1
−
y
2
limit as x approaches infinity of ((x+1)/(x+3))^{x/5}
lim
x
→
∞
(
(
x
+
1
x
+
3
)
x
5
)
(dy)/(dx)+9y=e^xy^{-4}
dy
dx
+
9
y
=
e
x
y
−
4
y^{''}+81y=sin(9t)
y
′
′
+
8
1
y
=
sin
(
9
t
)
integral of (2x+4)cos(x^2+4x-6)
∫
(
2
x
+
4
)
cos
(
x
2
+
4
x
−
6
)
dx
integral of xsin(npix)
∫
x
sin
(
n
π
x
)
dx
derivative of 3sin(1/6 x)
d
dx
(
3
sin
(
1
6
)
x
)
integral from 0 to x of t(e^{t^3}-1)
∫
0
x
t
(
e
t
3
−
1
)
dt
integral from 1 to 3 of 2x-3
∫
1
3
2
x
−
3
dx
x(8-y)=(dy)/(dx)
x
(
8
−
y
)
=
dy
dx
integral of cos^3(3θ)sin^{-2}(3θ)
∫
cos
3
(
3
θ
)
sin
−
2
(
3
θ
)
d
θ
derivative of 6x^{-3}
d
dx
(
6
x
−
3
)
limit as x approaches infinity of y^x
lim
x
→
∞
(
y
x
)
derivative (2t+1)/(t+3)
derivative
2
t
+
1
t
+
3
(\partial)/(\partial x)(e^{x^2-y})
∂
∂
x
(
e
x
2
−
y
)
derivative 8x+9xe^x
derivative
8
x
+
9
xe
x
integral of 2ln(t)
∫
2
ln
(
t
)
dt
y^'=1-7x^2
y
′
=
1
−
7
x
2
integral of (x-2)/(x+3)
∫
x
−
2
x
+
3
dx
integral of cos((npix)/L)
∫
cos
(
n
π
x
L
)
dx
derivative of 2(x^4)
d
dx
(
2
(
x
)
4
)
derivative of (6x^2+4/(3y^2-4))
d
dx
(
6
x
2
+
4
3
y
2
−
4
)
derivative of (4x^2+4(2x^2+2x))
d
dx
(
(
4
x
2
+
4
)
(
2
x
2
+
2
x
)
)
derivative of 3^{2x^2}*sqrt(x)
d
dx
(
3
2
x
2
·
√
x
)
derivative of (10/(x^2+1))
d
dx
(
1
0
x
2
+
1
)
limit as x approaches-4 of 1/2 x-1
lim
x
→
−
4
(
1
2
x
−
1
)
derivative (7e^xx^{5/2})/2+e^xx^{7/2}
derivative
7
e
x
x
5
2
2
+
e
x
x
7
2
integral of 0.4*e^{-2000x}
∫
0
.
4
·
e
−
2
0
0
0
x
dx
(\partial)/(\partial x)((x^2+2)/(x^2-2))
∂
∂
x
(
x
2
+
2
x
2
−
2
)
limit as x approaches-3 of (5-x)^{4/3}
lim
x
→
−
3
(
(
5
−
x
)
4
3
)
integral of 1/(xsqrt((x^2+1)))
∫
1
x
√
(
x
2
+
1
)
dx
derivative y=5cos^2(pix)
derivative
y
=
5
cos
2
(
π
x
)
derivative of ln(2x+3y)
d
dx
(
ln
(
2
x
+
3
y
)
)
(2x^2y+2y+5)dx+(2x^3+2x)dy=0
(
2
x
2
y
+
2
y
+
5
)
dx
+
(
2
x
3
+
2
x
)
dy
=
0
integral of e^{-ax}x
∫
e
−
ax
xdx
integral from 0 to 1 of (-5x)/(e^{2x)}
∫
0
1
−
5
x
e
2
x
dx
derivative of 16(x+2^3)
d
dx
(
1
6
(
x
+
2
)
3
)
laplace변환 2/5
laplacetransform
2
5
derivative f(x)=(3x)/(7x^2+1)
derivative
f
(
x
)
=
3
x
7
x
2
+
1
(\partial)/(\partial x)(3y-x/(y^2))
∂
∂
x
(
3
y
−
x
y
2
)
laplace변환 2-0.5e^{-10t}
laplacetransform
2
−
0
.
5
e
−
1
0
t
derivative f(x)=(x^2-1)/(x-1)
derivative
f
(
x
)
=
x
2
−
1
x
−
1
limit as x approaches-5 of (4(2x+3)^2-196)/(x+5)
lim
x
→
−
5
(
4
(
2
x
+
3
)
2
−
1
9
6
x
+
5
)
integral of (x+7)\sqrt[3]{3-2x}
∫
(
x
+
7
)
3
√
3
−
2
x
dx
derivative of ln(((2x+1^2)/((x-1))))
d
dx
(
ln
(
(
2
x
+
1
)
2
(
x
−
1
)
)
)
inverse라플라스 ((2s+1))/(s^2+10+25)
inverselaplace
(
2
s
+
1
)
s
2
+
1
0
+
2
5
지역 tan(3x),2sin(3x),-pi/9 , pi/9
area
tan
(
3
x
)
,
2
sin
(
3
x
)
,
−
π
9
,
π
9
integral of x^2sqrt(7+x)
∫
x
2
√
7
+
x
dx
integral of t^2sqrt(7t-5)
∫
t
2
√
7
t
−
5
dt
limit as x approaches 0+of ln|x|
lim
x
→
0
+
(
ln
|
x
|
)
derivative 4sec^2(x)
derivative
4
sec
2
(
x
)
derivative (x^2)/(7+4x)
derivative
x
2
7
+
4
x
limit as x approaches infinity of 1/2
lim
x
→
∞
(
1
2
)
integral of sec^2(θ)-1
∫
sec
2
(
θ
)
−
1
d
θ
integral of b/a
∫
b
a
dx
derivative of x^2(x-3^2)
d
dx
(
x
2
(
x
−
3
)
2
)
tangent f(x)=8sqrt(x),(16,32)
tangent
f
(
x
)
=
8
√
x
,
(
1
6
,
3
2
)
derivative y=ln(3x^2cot(sec^2(4x)))
derivative
y
=
ln
(
3
x
2
cot
(
sec
2
(
4
x
)
)
)
tangent-8x^2-2x
tangent
−
8
x
2
−
2
x
limit as t approaches 1 of (e^t-e)/(t-1)
lim
t
→
1
(
e
t
−
e
t
−
1
)
derivative of x^2-16In(x^2)
d
dx
(
x
2
−
1
6
In
(
x
2
)
)
sum from n=2 to infinity of 5/(6^n)
∑
n
=
2
∞
5
6
n
integral of e^x-2/(sqrt(x))
∫
e
x
−
2
√
x
dx
(x+y)y^'=1
(
x
+
y
)
y
′
=
1
limit as x approaches 3 of+(x-3)
lim
x
→
3
(
+
(
x
−
3
)
)
derivative e*3^x
derivative
e
·
3
x
integral from 1 to 3 of (x^3-3x^2+x+3)
∫
1
3
(
x
3
−
3
x
2
+
x
+
3
)
dx
integral from 1 to 7 of pi(sqrt(x-1))^2
∫
1
7
π
(
√
x
−
1
)
2
dx
derivative y=3x^{2/3}-2x
derivative
y
=
3
x
2
3
−
2
x
integral from-3 to 0 of (x^2-4x+7)
∫
−
3
0
(
x
2
−
4
x
+
7
)
dx
integral of (x+3)sqrt(2-x)
∫
(
x
+
3
)
√
2
−
x
dx
limit as x approaches 4-of 5(x)-7
lim
x
→
4
−
(
5
(
x
)
−
7
)
derivative arccos(sqrt(1-x^2))
derivative
arccos
(
√
1
−
x
2
)
tangent y=2x^2+5x
tangent
y
=
2
x
2
+
5
x
integral of (sqrt(x)+1/(9sqrt(x)))
∫
(
√
x
+
1
9
√
x
)
dx
integral of ln(1+x^3)
∫
ln
(
1
+
x
3
)
dx
y^{''}-3y^'+2y=0,y(0)=4,y^'(0)=7
y
′
′
−
3
y
′
+
2
y
=
0
,
y
(
0
)
=
4
,
y
′
(
0
)
=
7
(\partial)/(\partial z)(sqrt(x^2+y^2+z^2))
∂
∂
z
(
√
x
2
+
y
2
+
z
2
)
y^'+9xe^y=0
y
′
+
9
xe
y
=
0
integral of (x-1)^2(e^{x+1}-1)
∫
(
x
−
1
)
2
(
e
x
+
1
−
1
)
dx
tangent x^2-7x+7
tangent
x
2
−
7
x
+
7
(\partial}{\partial y}(\frac{3x)/y)
∂
∂
y
(
3
x
y
)
derivative of 2-cos(x)
d
dx
(
2
−
cos
(
x
)
)
(\partial)/(\partial x)(xy+6x)
∂
∂
x
(
xy
+
6
x
)
integral of (cos^5(x))/(sqrt(sin(x)))
∫
cos
5
(
x
)
√
sin
(
x
)
dx
sum from n=1 to infinity of 1/(nsqrt(n))
∑
n
=
1
∞
1
n
√
n
integral from 3/2 to 5/2 of e^{-st}
∫
3
2
5
2
e
−
st
dt
y^'=4-y
y
′
=
4
−
y
integral of (2/(x^3)+3/(x^2)+5)
∫
(
2
x
3
+
3
x
2
+
5
)
dx
inverse라플라스 (e^{-s})/(s(s+2))
inverselaplace
e
−
s
s
(
s
+
2
)
derivative of (5x^2-7xe^x)
d
dx
(
(
5
x
2
−
7
x
)
e
x
)
limit as x approaches 0 of x^2cos(9/x)
lim
x
→
0
(
x
2
cos
(
9
x
)
)
1
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