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일반적인 미적분학 문제
integral from 0 to pi/4 of sin^4(2x)
∫
0
π
4
sin
4
(
2
x
)
dx
derivative 5/(x^4)
derivative
5
x
4
derivative (2x)/(5-cot(x))
derivative
2
x
5
−
cot
(
x
)
derivative of ln^2(5x)
d
dx
(
ln
2
(
5
x
)
)
limit as (x,y) approaches (2,3) of x+y^2
lim
(
x
,
y
)
→
(
2
,
3
)
(
x
+
y
2
)
tangent f(x)=2x^3+42x^2+270x+4
tangent
f
(
x
)
=
2
x
3
+
4
2
x
2
+
2
7
0
x
+
4
integral of sin(x)sec^8(x)
∫
sin
(
x
)
sec
8
(
x
)
dx
integral of ((2x)/(x^2+5))
∫
(
2
x
x
2
+
5
)
dx
derivative of 9tan(xsec(x))
d
dx
(
9
tan
(
x
)
sec
(
x
)
)
integral of 1/(1+\sqrt[3]{x)}
∫
1
1
+
3
√
x
dx
tangent 5/(4+x^2),\at x=2
tangent
5
4
+
x
2
,
at
x
=
2
integral of 3csc^2(x)
∫
3
csc
2
(
x
)
dx
y^'+cot(x)y-xe^x=0
y
′
+
cot
(
x
)
y
−
xe
x
=
0
integral of (2x+1)e^{x(x+1)}
∫
(
2
x
+
1
)
e
x
(
x
+
1
)
dx
limit as x approaches 3 of 2x^2-5x+3
lim
x
→
3
(
2
x
2
−
5
x
+
3
)
derivative (10x^2-20x+20)e^x
derivative
(
1
0
x
2
−
2
0
x
+
2
0
)
e
x
derivative y=4e^{2x}
derivative
y
=
4
e
2
x
integral from 0 to 4 of 0.125x
∫
0
4
0
.
1
2
5
xdx
sum from n=1 to infinity of 6e^{-2n}
∑
n
=
1
∞
6
e
−
2
n
integral of 5e^{2-x}
∫
5
e
2
−
x
dx
f(θ)=2θ
f
(
θ
)
=
2
θ
integral of 5/(x-3)
∫
5
x
−
3
dx
integral of 8^{sin(x)}cos(x)
∫
8
sin
(
x
)
cos
(
x
)
dx
derivative of 4x^3-26x^2+40x
d
dx
(
4
x
3
−
2
6
x
2
+
4
0
x
)
y^{''}+5y^'+4y=-19te^{5t}
y
′
′
+
5
y
′
+
4
y
=
−
1
9
te
5
t
derivative of x^3-3x^2+1
d
dx
(
x
3
−
3
x
2
+
1
)
derivative of ln(sqrt(1+x^2))
d
dx
(
ln
(
√
1
+
x
2
)
)
integral of 1/(10x^6)
∫
1
1
0
x
6
dx
f(x)=xsqrt(x+1)
f
(
x
)
=
x
√
x
+
1
(y-sin^2(x))dx+sin(x)dy=0
(
y
−
sin
2
(
x
)
)
dx
+
sin
(
x
)
dy
=
0
y^'e^{-12x}+12e^{-12x}y=-6e^{-8x}
y
′
e
−
1
2
x
+
1
2
e
−
1
2
x
y
=
−
6
e
−
8
x
laplace변환 e^{-2t}sin(2)(t)
laplacetransform
e
−
2
t
sin
(
2
)
(
t
)
(\partial}{\partial x}(\frac{3xy^2)/2)
∂
∂
x
(
3
xy
2
2
)
derivative of x^2-2x-8
d
dx
(
x
2
−
2
x
−
8
)
xy^'+y=9xy^2,y(1)=2
xy
′
+
y
=
9
xy
2
,
y
(
1
)
=
2
지역 x^3-6x,-2x
area
x
3
−
6
x
,
−
2
x
지역 x^2-6x,-x^2+6
area
x
2
−
6
x
,
−
x
2
+
6
derivative f(x)=2x^2-4x+3
derivative
f
(
x
)
=
2
x
2
−
4
x
+
3
y^{''}+y^'+y=1+t+t^2
y
′
′
+
y
′
+
y
=
1
+
t
+
t
2
x(dy)/(dx)=(2y)
x
dy
dx
=
(
2
y
)
integral from 0 to 3 of 1/(4x^2+9)
∫
0
3
1
4
x
2
+
9
dx
derivative of log_{e}(ax)
d
dx
(
log
e
(
ax
)
)
integral of sec^3(3x)
∫
sec
3
(
3
x
)
dx
derivative of 10^{3x}
d
dx
(
1
0
3
x
)
(\partial}{\partial x}(\frac{x^2)/y)
∂
∂
x
(
x
2
y
)
limit as x approaches 2 of x^2-3
lim
x
→
2
(
x
2
−
3
)
6x^2y^'=y^'+2xe^{-y}
6
x
2
y
′
=
y
′
+
2
xe
−
y
(\partial)/(\partial x)(x^3cos(y))
∂
∂
x
(
x
3
cos
(
y
)
)
integral of sqrt(1-t^2)
∫
√
1
−
t
2
dt
(\partial)/(\partial y)(4xy-x^4-y^4)
∂
∂
y
(
4
xy
−
x
4
−
y
4
)
(\partial)/(\partial x)((U(x,y))/((1+x/y)^2))
∂
∂
x
(
U
(
x
,
y
)
(
1
+
x
y
)
2
)
(\partial)/(\partial x)((9y)/(x^4))
∂
∂
x
(
9
y
x
4
)
limit as x approaches 2 of-3
lim
x
→
2
(
−
3
)
integral of sec^2(x)(1-cot^2(x))
∫
sec
2
(
x
)
(
1
−
cot
2
(
x
)
)
dx
limit as x approaches 0 of (1+5x)^{1/x}
lim
x
→
0
(
(
1
+
5
x
)
1
x
)
derivative f(x)= 1/(1-x)
derivative
f
(
x
)
=
1
1
−
x
derivative of 300x-1/2 x^2
d
dx
(
3
0
0
x
−
1
2
x
2
)
derivative of 2x^{-6}+x^{-1}
d
dx
(
2
x
−
6
+
x
−
1
)
integral of 8e^{3x}
∫
8
e
3
x
dx
sum from n=1 to infinity of (n-1)/(6n-1)
∑
n
=
1
∞
n
−
1
6
n
−
1
integral of cos(7x+4)
∫
cos
(
7
x
+
4
)
dx
inverse라플라스 8/(s^2+9)*e^{-5s}
inverselaplace
8
s
2
+
9
·
e
−
5
s
derivative (sec(x))^2
derivative
(
sec
(
x
)
)
2
integral of 3sin(x/2)-2cos((2x)/5)
∫
3
sin
(
x
2
)
−
2
cos
(
2
x
5
)
dx
derivative of 2xy^2+4
d
dx
(
2
xy
2
+
4
)
derivative of (1+3x^5)
d
dx
(
(
1
+
3
x
)
5
)
integral of 1/(X^2)
∫
1
X
2
dX
integral of (5x^2-12)/((x^2-6x+13)^2)
∫
5
x
2
−
1
2
(
x
2
−
6
x
+
1
3
)
2
dx
integral of (4x)/(x^3-x^2-x+1)
∫
4
x
x
3
−
x
2
−
x
+
1
dx
implicit yx=c
implicit
yx
=
c
derivative of 4/(2x+5)
d
dx
(
4
2
x
+
5
)
derivative ln(sqrt((x-5)/(x-4)))
derivative
ln
(
√
x
−
5
x
−
4
)
derivative of-xe^{-(x^2/2})
d
dx
(
−
xe
−
x
2
2
)
f^'(x)=2sec(x)+3tan(x)-tan(pi/3)
f
′
(
x
)
=
2
sec
(
x
)
+
3
tan
(
x
)
−
tan
(
π
3
)
y^{''}+(1/x)y^'=0
y
′
′
+
(
1
x
)
y
′
=
0
integral of 4e^2
∫
4
e
2
dx
y^'=(-(xy+1))/(xy+1)
y
′
=
−
(
xy
+
1
)
xy
+
1
y^'=(x-3)(y+1)^{2/3}
y
′
=
(
x
−
3
)
(
y
+
1
)
2
3
integral from 0 to pi/2 of-8sin^2(3x)
∫
0
π
2
−
8
sin
2
(
3
x
)
dx
(dy)/(dx)=cos(x)
dy
dx
=
cos
(
x
)
derivative of 4/x+2sec(x)
d
dx
(
4
x
+
2
sec
(
x
)
)
(2y+2t-7)dt+(4y+2t-1)dy=0,y(-1)=2
(
2
y
+
2
t
−
7
)
dt
+
(
4
y
+
2
t
−
1
)
dy
=
0
,
y
(
−
1
)
=
2
(\partial)/(\partial y)(x^{6y})
∂
∂
y
(
x
6
y
)
derivative f(x)=sqrt(2x-3)
derivative
f
(
x
)
=
√
2
x
−
3
derivative f(x)=(1+3x^4)^2+3x^3
derivative
f
(
x
)
=
(
1
+
3
x
4
)
2
+
3
x
3
y^{''}+y^'+2y=0,y(0)=2,y^'(0)=0
y
′
′
+
y
′
+
2
y
=
0
,
y
(
0
)
=
2
,
y
′
(
0
)
=
0
inverse라플라스 8/(s^2+1)
inverselaplace
8
s
2
+
1
1/y dy=(x+1)/(1-x^2)dx
1
y
dy
=
x
+
1
1
−
x
2
dx
y=4x^4+1/3 x^3+x+1
y
=
4
x
4
+
1
3
x
3
+
x
+
1
integral of 1/(x^2-3x+2)
∫
1
x
2
−
3
x
+
2
dx
integral of (4x+4)/(2x+1)
∫
4
x
+
4
2
x
+
1
dx
(dy)/(dt)+2t(y-5)=0
dy
dt
+
2
t
(
y
−
5
)
=
0
derivative of 2(ln(x)^3)
d
dx
(
2
(
ln
(
x
)
)
3
)
integral of arctan(x/2)
∫
arctan
(
x
2
)
dx
limit as x approaches 3 of e(x+1)
lim
x
→
3
(
e
(
x
+
1
)
)
limit as x approaches 3 of (3x+2)/(x-3)
lim
x
→
3
(
3
x
+
2
x
−
3
)
derivative of e^{ax}+72x
d
dx
(
e
ax
+
7
2
x
)
inverse라플라스 4/(s(s^2-4s+5))
inverselaplace
4
s
(
s
2
−
4
s
+
5
)
derivative (-5x-9)/(2x+8)
derivative
−
5
x
−
9
2
x
+
8
maclaurin sin(x),1.5
maclaurin
sin
(
x
)
,
1
.
5
1
..
1401
1402
1403
1404
1405
..
2459