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일반적인 미적분학 문제
derivative of 20
d
dx
(
2
0
)
integral from-2 to 2 of 1/((x+4)(x-4))
∫
−
2
2
1
(
x
+
4
)
(
x
−
4
)
dx
sum from i=0 to infinity of 2^i
∑
i
=
0
∞
2
i
y^'=(y^2)/(x^2)+y/x
y
′
=
y
2
x
2
+
y
x
derivative (sqrt(x^2+4))/3+(11-x)/4
derivative
√
x
2
+
4
3
+
1
1
−
x
4
integral from 0 to 2 of 5x^2
∫
0
2
5
x
2
dx
derivative 6sin(3x)
derivative
6
sin
(
3
x
)
integral of (x^4-3)^2
∫
(
x
4
−
3
)
2
dx
d/(dt)(-2sin(2t))
d
dt
(
−
2
sin
(
2
t
)
)
limit as x approaches 4 of 4x
lim
x
→
4
(
4
x
)
integral of (ln(x))/(xsqrt(x))
∫
ln
(
x
)
x
√
x
dx
sum from n=1 to infinity of 1/((n(n+2)))
∑
n
=
1
∞
1
(
n
(
n
+
2
)
)
integral of (1/(x^{-0.1)})
∫
(
1
x
−
0
.
1
)
dx
y^'=(x+y-1)^2
y
′
=
(
x
+
y
−
1
)
2
(\partial)/(\partial x)(2xy+5y^2)
∂
∂
x
(
2
xy
+
5
y
2
)
derivative (arctan(9x))^2
derivative
(
arctan
(
9
x
)
)
2
derivative (e^x)/(5x-2)
derivative
e
x
5
x
−
2
integral from 0 to 2pi of sin^2(9x)
∫
0
2
π
sin
2
(
9
x
)
dx
laplace변환 4t
laplacetransform
4
t
limit as x approaches 0 of ln(1+sin(x))
lim
x
→
0
(
ln
(
1
+
sin
(
x
)
)
)
(dy)/(dx)=x^7y
dy
dx
=
x
7
y
derivative of ln(sinh(x))
d
dx
(
ln
(
sinh
(
x
)
)
)
integral of cos((npix)/2)
∫
cos
(
n
π
x
2
)
dx
integral of ((sqrt(100-x^2)))/x
∫
(
√
1
0
0
−
x
2
)
x
dx
limit as x approaches infinity of 7e^x
lim
x
→
∞
(
7
e
x
)
maclaurin (1-x)^{-1/2}
maclaurin
(
1
−
x
)
−
1
2
f(x)=x^2e^{2x}
f
(
x
)
=
x
2
e
2
x
(cos(2x))^'
(
cos
(
2
x
)
)
′
derivative of 2*x
d
dx
(
2
·
x
)
derivative of sqrt(x)+2x
d
dx
(
√
x
+
2
x
)
derivative of 6e^{3x}
d
dx
(
6
e
3
x
)
integral of (a^2-x^{2/3})
∫
(
a
2
−
x
2
3
)
dx
limit as x approaches 0+of ln(1+sin(x))
lim
x
→
0
+
(
ln
(
1
+
sin
(
x
)
)
)
derivative e^{sin^2(x)}
derivative
e
sin
2
(
x
)
integral of x^3sin(2x)
∫
x
3
sin
(
2
x
)
dx
derivative of-3sin(2x-6cos(x))
d
dx
(
−
3
sin
(
2
x
)
−
6
cos
(
x
)
)
derivative of sin(25x^2+6x+4)
d
dx
(
sin
(
2
5
x
2
+
6
x
+
4
)
)
derivative of (8x/(x^2+4))
d
dx
(
8
x
x
2
+
4
)
(dy)/(dx)=(1+2y^2)/(y*sin(x))
dy
dx
=
1
+
2
y
2
y
·
sin
(
x
)
derivative of ({f}(x)/({g)(x)+1})
d
dx
(
f
(
x
)
g
(
x
)
+
1
)
tangent-2sin(x),\at x= 3/4 pi
tangent
−
2
sin
(
x
)
,
at
x
=
3
4
π
derivative of acos(3x+bsin(3x))
d
dx
(
a
cos
(
3
x
)
+
b
sin
(
3
x
)
)
integral of (3t^2-4t-4)
∫
(
3
t
2
−
4
t
−
4
)
dt
derivative sin^3(x^3-2x)
derivative
sin
3
(
x
3
−
2
x
)
integral from 0 to 3 of te^{-t}
∫
0
3
te
−
t
dt
integral of 6x^2-5x+3
∫
6
x
2
−
5
x
+
3
dx
integral of (6sin(2x)-4cos(4x))
∫
(
6
sin
(
2
x
)
−
4
cos
(
4
x
)
)
dx
지역 y^2=4x,4x-3y=4
area
y
2
=
4
x
,
4
x
−
3
y
=
4
derivative (arctan(9x))^2
derivative
(
arctan
(
9
x
)
)
2
derivative 1/(x^5)
derivative
1
x
5
derivative 9e^{-x}-3e^{-4x}
derivative
9
e
−
x
−
3
e
−
4
x
integral of sec(t)(5sec(t)+2tan(t))
∫
sec
(
t
)
(
5
sec
(
t
)
+
2
tan
(
t
)
)
dt
integral from 1 to 5 of x/(sqrt(2x-1))
∫
1
5
x
√
2
x
−
1
dx
limit as x approaches 0 of cos(x)+sin(x)
lim
x
→
0
(
cos
(
x
)
+
sin
(
x
)
)
tangent (x+2)^2+(y-3)^2=37,(4,2)
tangent
(
x
+
2
)
2
+
(
y
−
3
)
2
=
3
7
,
(
4
,
2
)
(dy)/(dx)=((y^2-1))/(x^2-1),y(7)=7
dy
dx
=
(
y
2
−
1
)
x
2
−
1
,
y
(
7
)
=
7
integral of e^{x/5}
∫
e
x
5
dx
y^'=8x^3+2 y/x
y
′
=
8
x
3
+
2
y
x
(dy)/(dt)=-2y,y(0)=2
dy
dt
=
−
2
y
,
y
(
0
)
=
2
integral of 1/((4+x^2)^3)
∫
1
(
4
+
x
2
)
3
dx
sum from n=1 to infinity of n(5/4)^n
∑
n
=
1
∞
n
(
5
4
)
n
(\partial)/(\partial x)(x^3y^5)
∂
∂
x
(
x
3
y
5
)
derivative of \sqrt[3]{x^2+3x-4}
d
dx
(
3
√
x
2
+
3
x
−
4
)
integral of (sin(x))/(1+x^2)
∫
sin
(
x
)
1
+
x
2
dx
derivative (x^{12})^5
derivative
(
x
1
2
)
5
derivative of 1/2 x-1/4
d
dx
(
1
2
x
−
1
4
)
(\partial)/(\partial x)(3xye^{-x^2y})
∂
∂
x
(
3
xye
−
x
2
y
)
sum from n=2 to infinity of 1/(n-1)-1/n
∑
n
=
2
∞
1
n
−
1
−
1
n
derivative of sqrt((x^2/4+17))
d
dx
(
√
x
2
4
+
1
7
)
limit as n approaches infinity of-1+1/n
lim
n
→
∞
(
−
1
+
1
n
)
integral of (x^2+3x-1)/(x^3+8)
∫
x
2
+
3
x
−
1
x
3
+
8
dx
integral of x\sqrt[6]{1+x^2}
∫
x
6
√
1
+
x
2
dx
integral of (cos(pi/2))/(x^2)
∫
cos
(
π
2
)
x
2
dx
derivative of x^2(1+y^3)
d
dx
(
x
2
(
1
+
y
)
3
)
derivative of cos^{ln(7x}(x))
d
dx
(
cos
ln
(
7
x
)
(
x
)
)
integral of ((2x+sqrt(x)))/(x^3)
∫
(
2
x
+
√
x
)
x
3
dx
integral of (x)^2
∫
(
x
)
2
dx
derivative y=4-e^x
derivative
y
=
4
−
e
x
integral of 1/x (x+1)^2
∫
1
x
(
x
+
1
)
2
dx
limit as x approaches 0 of xe^{-2/(x^2)}
lim
x
→
0
(
xe
−
2
x
2
)
integral of (x^4)/(x^5+1)
∫
x
4
x
5
+
1
dx
(dy)/(dx)=(cos(19x))/(e^{19y)}
dy
dx
=
cos
(
1
9
x
)
e
1
9
y
derivative of xcos(x-picos(x)+2sin(x))
d
dx
(
x
cos
(
x
)
−
π
cos
(
x
)
+
2
sin
(
x
)
)
6y^{''}+y^'-y=0
6
y
′
′
+
y
′
−
y
=
0
derivative 144-x^2
derivative
1
4
4
−
x
2
integral from 0 to pi/3 of cos^3(x)
∫
0
π
3
cos
3
(
x
)
dx
derivative of sqrt(2-e^x)
d
dx
(
√
2
−
e
x
)
integral of sin^4(4x)cos^3(4x)
∫
sin
4
(
4
x
)
cos
3
(
4
x
)
dx
integral of 7te^t
∫
7
te
t
dt
((2+x)dy)/(dx)=3y
(
2
+
x
)
dy
dx
=
3
y
limit as x approaches a of x
lim
x
→
a
(
x
)
limit as x approaches 7 of sqrt(8x-3)
lim
x
→
7
(
√
8
x
−
3
)
(\partial)/(\partial u)(tan(uv^3))
∂
∂
u
(
tan
(
uv
3
)
)
(xy^2+x^3)dx+(y^3+x^2y)dy=0
(
xy
2
+
x
3
)
dx
+
(
y
3
+
x
2
y
)
dy
=
0
derivative of tan(cos(x))
d
dx
(
tan
(
cos
(
x
)
)
)
implicit (dy)/(dx),y=x
implicit
dy
dx
,
y
=
x
integral of 1/(x^2+2x)
∫
1
x
2
+
2
x
dx
integral of (4-3sin(2x))^4cos(2x)
∫
(
4
−
3
sin
(
2
x
)
)
4
cos
(
2
x
)
dx
derivative h(a)=2x-5
derivative
h
(
a
)
=
2
x
−
5
inverse라플라스 ln((s+5)/(s^2+2s+6))
inverselaplace
ln
(
s
+
5
s
2
+
2
s
+
6
)
1
..
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