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일반적인 미적분학 문제
laplace변환 e^{-x}
laplacetransform
e
−
x
integral of-6xln^2(x)
∫
−
6
x
ln
2
(
x
)
dx
integral of sin^3(t)
∫
sin
3
(
t
)
dt
11(t+1)(dy)/(dt)-9y=18t
1
1
(
t
+
1
)
dy
dt
−
9
y
=
1
8
t
integral from 1 to e^2 of x^4ln(x)
∫
1
e
2
x
4
ln
(
x
)
dx
integral of 5xe^{-3x}
∫
5
xe
−
3
x
dx
(dy)/(dx)=x+9
dy
dx
=
x
+
9
limit as x approaches 2-of x/(x^2-4)
lim
x
→
2
−
(
x
x
2
−
4
)
f(x)= 1/(x^2-9)
f
(
x
)
=
1
x
2
−
9
derivative y=(tan(-1(9x)))2
derivative
y
=
(
tan
(
−
1
(
9
x
)
)
)
2
derivative f(x)=(3t-1)(2t-2)^{-1}
derivative
f
(
x
)
=
(
3
t
−
1
)
(
2
t
−
2
)
−
1
integral of (ar)/(sqrt(a^2-r^2))
∫
ar
√
a
2
−
r
2
dr
derivative of (sqrt(2)/2)
d
dx
(
√
2
2
)
integral of (e^x)/(e^{2x)+3e^x+2}
∫
e
x
e
2
x
+
3
e
x
+
2
dx
integral of 5e^{5x}
∫
5
e
5
x
dx
tangent f(x)=-6x^2-9,\at x=0
tangent
f
(
x
)
=
−
6
x
2
−
9
,
at
x
=
0
limit as x approaches-4-of f(x)
lim
x
→
−
4
−
(
f
(
x
)
)
derivative of e^x*2^x
d
dx
(
e
x
·
2
x
)
limit as x approaches 0 of (e^x-1)/(sin(4x))
lim
x
→
0
(
e
x
−
1
sin
(
4
x
)
)
laplace변환 e^{-t}sin(t)
laplacetransform
e
−
t
sin
(
t
)
(\partial)/(\partial x)(6y-2x)
∂
∂
x
(
6
y
−
2
x
)
derivative-3/(x^4)
derivative
−
3
x
4
tangent y=sqrt(25-x^2),(3,4)
tangent
y
=
√
2
5
−
x
2
,
(
3
,
4
)
integral of (e^{-2x})/(e^{-2x)+1}
∫
e
−
2
x
e
−
2
x
+
1
dx
limit as x approaches-2 of-x^2+2x-6
lim
x
→
−
2
(
−
x
2
+
2
x
−
6
)
integral of 1/(x^3)sin(1/(x^2))
∫
1
x
3
sin
(
1
x
2
)
dx
sum from n=1 to infinity of 1/(3n+2)
∑
n
=
1
∞
1
3
n
+
2
(dy)/(dx)x^2y=y-7
dy
dx
x
2
y
=
y
−
7
integral from-1 to 3 of x^2-2x-3
∫
−
1
3
x
2
−
2
x
−
3
dx
integral of 6/(xln(3x))
∫
6
x
ln
(
3
x
)
dx
sum from n=1 to infinity of 5/(nsqrt(n))
∑
n
=
1
∞
5
n
√
n
integral of (2t^2+sec^2(t))
∫
(
2
t
2
+
sec
2
(
t
)
)
dt
integral of x^2(20x^7-7x^4+6)
∫
x
2
(
2
0
x
7
−
7
x
4
+
6
)
dx
derivative sin(x^5)
derivative
sin
(
x
5
)
지역 x=7y^2,x=4+3y^2
area
x
=
7
y
2
,
x
=
4
+
3
y
2
integral of xln(x)-x
∫
x
ln
(
x
)
−
xdx
integral of 1/(2x^2-5x+3)
∫
1
2
x
2
−
5
x
+
3
dx
integral from 0 to 1 of x^{1/3}-x^3
∫
0
1
x
1
3
−
x
3
dx
integral of x\sqrt[9]{36+x^2}
∫
x
9
√
3
6
+
x
2
dx
integral of cos(3x)cos(2x)cos(x)
∫
cos
(
3
x
)
cos
(
2
x
)
cos
(
x
)
dx
y^'=((6x^4e^{y/x}+x^2y^2))/(x^3y)
y
′
=
(
6
x
4
e
y
x
+
x
2
y
2
)
x
3
y
sum from n=0 to infinity of 1/((n^2-1))
∑
n
=
0
∞
1
(
n
2
−
1
)
derivative of ln(3x^2+1)
d
dx
(
ln
(
3
x
2
+
1
)
)
limit as x approaches 1-of-2/(sqrt(1-x))
lim
x
→
1
−
(
−
2
√
1
−
x
)
limit as x approaches 0 of ln(sin(x))
lim
x
→
0
(
ln
(
sin
(
x
)
)
)
solvefor x,y=sin(xy)
solvefor
x
,
y
=
sin
(
xy
)
derivative (ln(2x))^2
derivative
(
ln
(
2
x
)
)
2
integral of-e^{-3x}(x-3)(x-6)
∫
−
e
−
3
x
(
x
−
3
)
(
x
−
6
)
dx
(x+1)(dy)/(dx)-x+4y=0
(
x
+
1
)
dy
dx
−
x
+
4
y
=
0
y^'-y=8te^{2t},y(0)=1
y
′
−
y
=
8
te
2
t
,
y
(
0
)
=
1
integral from 0 to 0.5 of 8000x
∫
0
0
.
5
8
0
0
0
xdx
limit as n approaches infinity of n/(2n)
lim
n
→
∞
(
n
2
n
)
y^'-xy=x
y
′
−
xy
=
x
integral of (3x+8)/(x(x-2)^2)
∫
3
x
+
8
x
(
x
−
2
)
2
dx
derivative of (2x^2-1/(3x+5))
d
dx
(
2
x
2
−
1
3
x
+
5
)
derivative of 2sqrt(x)+2/(sqrt(x))
d
dx
(
2
√
x
+
2
√
x
)
(\partial)/(\partial x)(x^3*y^5+2x^4*y)
∂
∂
x
(
x
3
·
y
5
+
2
x
4
·
y
)
integral of (2x+3)/(9x^2-12x+8)
∫
2
x
+
3
9
x
2
−
1
2
x
+
8
dx
limit as x approaches infinity of (1-5e^{2x})/(3e^x+4e^{2x)}
lim
x
→
∞
(
1
−
5
e
2
x
3
e
x
+
4
e
2
x
)
derivative of 6tan(x)
d
dx
(
6
tan
(
x
)
)
derivative of ln(csc(x+cot(x)))
d
dx
(
ln
(
csc
(
x
)
+
cot
(
x
)
)
)
limit as x approaches infinity of-2x+8
lim
x
→
∞
(
−
2
x
+
8
)
(\partial)/(\partial x)(x/(x^5-y^4))
∂
∂
x
(
x
x
5
−
y
4
)
integral from-R to R of sqrt(R^2-x^2)
∫
−
R
R
√
R
2
−
x
2
dx
(\partial)/(\partial y)(xe^{-y/x})
∂
∂
y
(
xe
−
y
x
)
integral from 1 to infinity of 5/(x^3)
∫
1
∞
5
x
3
dx
integral of (sec(x)tan(x))/(1+sec(x))
∫
sec
(
x
)
tan
(
x
)
1
+
sec
(
x
)
dx
derivative of 1/(2^x)
d
dx
(
1
2
x
)
integral from 0 to pi/(27) of xtan^2(9x)
∫
0
π
2
7
x
tan
2
(
9
x
)
dx
limit as x approaches 0 of (tan(10x))/x
lim
x
→
0
(
tan
(
1
0
x
)
x
)
derivative of sin(1/(x-1))
d
dx
(
sin
(
1
x
−
1
)
)
y^{''}+4y=3sin(2t)
y
′
′
+
4
y
=
3
sin
(
2
t
)
derivative 5^{x^5}
derivative
5
x
5
integral of 1/(ln(2x))
∫
1
ln
(
2
x
)
dx
지역 2y=5sqrt(x),y=3,2y+2x=7
area
2
y
=
5
√
x
,
y
=
3
,
2
y
+
2
x
=
7
integral of x(3^x)
∫
x
(
3
x
)
dx
integral of (1/(-0.4t^3))
∫
(
1
−
0
.
4
t
3
)
dt
limit as x approaches 2 of 3(2x+5)
lim
x
→
2
(
3
(
2
x
+
5
)
)
integral of (x^2+7x+3)^4(2x+7)
∫
(
x
2
+
7
x
+
3
)
4
(
2
x
+
7
)
dx
limit as h approaches 0 of (sin(h))/(6h)
lim
h
→
0
(
sin
(
h
)
6
h
)
derivative of sqrt(7+x)
d
dx
(
√
7
+
x
)
limit as x approaches infinity of 0/(+x)
lim
x
→
∞
(
0
+
x
)
y^{''}+2y^'-3y=e^{-x},y(0)=0
y
′
′
+
2
y
′
−
3
y
=
e
−
x
,
y
(
0
)
=
0
derivative f(x)= 4/(1-6x)
derivative
f
(
x
)
=
4
1
−
6
x
sum from n=1 to infinity of 4/(3^{n-1)}
∑
n
=
1
∞
4
3
n
−
1
limit as x approaches 2 of log_{10x}(x)
lim
x
→
2
(
log
1
0
x
(
x
)
)
(\partial)/(\partial x)(3xy^2-ln(x))
∂
∂
x
(
3
xy
2
−
ln
(
x
)
)
inverse라플라스 (2s)/((s+1)^2)
inverselaplace
2
s
(
s
+
1
)
2
(xdy)/(dx)-y=x^2sin(x)
xdy
dx
−
y
=
x
2
sin
(
x
)
derivative of arccsc(7x^3+9)
d
dx
(
arccsc
(
7
x
3
+
9
)
)
integral of 6x-1
∫
6
x
−
1
dx
integral of (ln(7x))/(x^9)
∫
ln
(
7
x
)
x
9
dx
derivative ln(xsqrt(x^2-1))
derivative
ln
(
x
√
x
2
−
1
)
경사지 (-3,-2),(1,-5)
slope
(
−
3
,
−
2
)
,
(
1
,
−
5
)
integral of cos(x)(1+7sin^2(x))
∫
cos
(
x
)
(
1
+
7
sin
2
(
x
)
)
dx
derivative ln(2x)
derivative
ln
(
2
x
)
sum from n=0 to infinity of 1/(n^4+6)
∑
n
=
0
∞
1
n
4
+
6
tangent f(x)=sqrt(x),\at x=5
tangent
f
(
x
)
=
√
x
,
at
x
=
5
f^{''}(t)-f(t)=-8t,f(3)=-8
f
′
′
(
t
)
−
f
(
t
)
=
−
8
t
,
f
(
3
)
=
−
8
derivative f(x)=(2x-1)/(4x+8)
derivative
f
(
x
)
=
2
x
−
1
4
x
+
8
1
..
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1397
1398
1399
1400
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