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일반적인 미적분학 문제
integral from 3 to 9 of 1/(xln(x))
∫
3
9
1
x
ln
(
x
)
dx
tangent y=sqrt(2x+1),\at x= 1/2
tangent
y
=
√
2
x
+
1
,
at
x
=
1
2
integral of (x^2+1)/(2x)
∫
x
2
+
1
2
x
dx
integral of x/(x^3+x)
∫
x
x
3
+
x
dx
sum from n=0 to infinity of 2^{-n/2}
∑
n
=
0
∞
2
−
n
2
derivative y=ln(5x^2+3y^2)
derivative
y
=
ln
(
5
x
2
+
3
y
2
)
limit as x approaches 4+of (2x)/(x-4)
lim
x
→
4
+
(
2
x
x
−
4
)
integral of (tan^3(7/z))/(z^2)
∫
tan
3
(
7
z
)
z
2
dz
(\partial)/(\partial z)(xe^{2yz})
∂
∂
z
(
xe
2
yz
)
(\partial)/(\partial x)(2/((x-3t)^2+1))
∂
∂
x
(
2
(
x
−
3
t
)
2
+
1
)
derivative (5x+4)/(5x-4)
derivative
5
x
+
4
5
x
−
4
integral of (x-4)
∫
(
x
−
4
)
dx
limit as x approaches 1-of 1/((x-1))
lim
x
→
1
−
(
1
(
x
−
1
)
)
(\partial)/(\partial y)(4x^3+4xy-1)
∂
∂
y
(
4
x
3
+
4
xy
−
1
)
tangent ((x^2-1))/((x^2+x+1))
tangent
(
x
2
−
1
)
(
x
2
+
x
+
1
)
d/(dθ)(5/(2cos(θ)+7sin(θ)))
d
d
θ
(
5
2
cos
(
θ
)
+
7
sin
(
θ
)
)
(dy}{dx}=\frac{(x+1))/y
dy
dx
=
(
x
+
1
)
y
(\partial)/(\partial y)(xye^{-5y})
∂
∂
y
(
xye
−
5
y
)
derivative of (16/(x^3))
d
dx
(
1
6
x
3
)
5y^'+y=-3
5
y
′
+
y
=
−
3
tangent f(x)=3x^4-8x^3+2
tangent
f
(
x
)
=
3
x
4
−
8
x
3
+
2
derivative of 5e^{-2x}sin(3x)
d
dx
(
5
e
−
2
x
sin
(
3
x
)
)
maclaurin (1+x)^{-5/3}
maclaurin
(
1
+
x
)
−
5
3
(\partial)/(\partial x)(ln(xy))
∂
∂
x
(
ln
(
xy
)
)
derivative of x^3e^{-x}
d
dx
(
x
3
e
−
x
)
limit as x approaches 9 of x+7
lim
x
→
9
(
x
+
7
)
d/(dt)(10^{2sqrt(t)})
d
dt
(
1
0
2
√
t
)
derivative of 3^t(5t^4+7t+{y}(t,x(t,x)^4))
d
dx
(
3
t
(
5
t
4
+
7
t
+
y
(
t
,
x
)
(
t
,
x
)
4
)
)
derivative y=x^{2/5}(x+3)
derivative
y
=
x
2
5
(
x
+
3
)
integral of (sin(7x))/(1+cos^2(7x))
∫
sin
(
7
x
)
1
+
cos
2
(
7
x
)
dx
derivative of (x^3-4/(x-1))
d
dx
(
x
3
−
4
x
−
1
)
(dy)/(dx)=(ln(x))/(xy),y(1)=2
dy
dx
=
ln
(
x
)
xy
,
y
(
1
)
=
2
derivative y=((t^3+t))/((t^4-2))
derivative
y
=
(
t
3
+
t
)
(
t
4
−
2
)
integral of 1/((y^2-1))
∫
1
(
y
2
−
1
)
dy
derivative cos^3(x)+sin^4(x)
derivative
cos
3
(
x
)
+
sin
4
(
x
)
integral of (3x-2)/(x+1)
∫
3
x
−
2
x
+
1
dx
(\partial)/(\partial x)((2x^2)/((2x+7y)^2))
∂
∂
x
(
2
x
2
(
2
x
+
7
y
)
2
)
limit as x approaches-3 of |-x-1|
lim
x
→
−
3
(
|
−
x
−
1
|
)
integral of 1/((x-3)(x-1))
∫
1
(
x
−
3
)
(
x
−
1
)
dx
derivative 6/5-6/5 e^{-20t}
derivative
6
5
−
6
5
e
−
2
0
t
f(x)=(2-xe^x)/(x+e^x)
f
(
x
)
=
2
−
xe
x
x
+
e
x
longdivision (x^2+1)/(x^2-4)
longdivision
x
2
+
1
x
2
−
4
integral of (x+6)/(x^2+9)
∫
x
+
6
x
2
+
9
dx
integral from-3 to-2 of 5(2x+4)^{1/3}
∫
−
3
−
2
5
(
2
x
+
4
)
1
3
dx
(dy)/(dx)=4-y
dy
dx
=
4
−
y
integral of (x^3)/9
∫
x
3
9
dx
derivative f(x)=(7x)/(3+x^2)
derivative
f
(
x
)
=
7
x
3
+
x
2
y^'+y/x-sqrt(y)=0,y(1)=0
y
′
+
y
x
−
√
y
=
0
,
y
(
1
)
=
0
integral of (sec^2(x)-sin(x))
∫
(
sec
2
(
x
)
−
sin
(
x
)
)
dx
테일러 sqrt(x),x=4
taylor
√
x
,
x
=
4
integral of (3x+1)/((x-2)(x+3))
∫
3
x
+
1
(
x
−
2
)
(
x
+
3
)
dx
integral of x-ln(x)
∫
x
−
ln
(
x
)
dx
integral from 0 to pi/8 of cos^2(2x)
∫
0
π
8
cos
2
(
2
x
)
dx
테일러 x^5cos(x^2)
taylor
x
5
cos
(
x
2
)
derivative of (3x^{5x})
d
dx
(
(
3
x
)
5
x
)
integral of sqrt(ax+b)
∫
√
ax
+
b
dx
derivative of in(xinx)
d
dx
(
in
(
xinx
)
)
derivative of 11-x+4ln(2x-1)
d
dx
(
1
1
−
x
+
4
ln
(
2
x
−
1
)
)
limit as x approaches 0 of (|x-4|)/(x-4)
lim
x
→
0
(
|
x
−
4
|
x
−
4
)
derivative of x+y+1
d
dx
(
x
+
y
+
1
)
derivative f(x)=2e^{2e^x+x}
derivative
f
(
x
)
=
2
e
2
e
x
+
x
derivative 3/(y^4)
derivative
3
y
4
y^{''}+2y^'+y=2^{-t}
y
′
′
+
2
y
′
+
y
=
2
−
t
derivative (cos(x))/x
derivative
cos
(
x
)
x
integral of ((e^x-1)/(e^x+1))
∫
(
e
x
−
1
e
x
+
1
)
dx
derivative of sqrt(25+(12-x^2)+x)
d
dx
(
√
2
5
+
(
1
2
−
x
)
2
+
x
)
integral of e^{iax}
∫
e
iax
dx
integral of e^{e^t}
∫
e
e
t
dt
(\partial)/(\partial y)(x^2y+3xy+y^2)
∂
∂
y
(
x
2
y
+
3
xy
+
y
2
)
(1/(1-x^2))^'
(
1
1
−
x
2
)
′
integral of x/(\sqrt[3]{x+8)}
∫
x
3
√
x
+
8
dx
laplace변환 e^{3t}cos(6t)
laplacetransform
e
3
t
cos
(
6
t
)
integral of 3a^7x^6
∫
3
a
7
x
6
dx
limit as x approaches 1 of e^{(x^2-x)}
lim
x
→
1
(
e
(
x
2
−
x
)
)
derivative of x^3-3x^2+2
d
dx
(
x
3
−
3
x
2
+
2
)
derivative 1+e^{-x}
derivative
1
+
e
−
x
integral of (x+1)e^{-x}
∫
(
x
+
1
)
e
−
x
dx
integral of xe^{0.2x}
∫
xe
0
.
2
x
dx
derivative f(x)=x^3+3x
derivative
f
(
x
)
=
x
3
+
3
x
테일러 x^{5/7}
taylor
x
5
7
derivative f(x)=(x+9)/(x-9)
derivative
f
(
x
)
=
x
+
9
x
−
9
t^2y^{''}-5ty^'+9y=0
t
2
y
′
′
−
5
ty
′
+
9
y
=
0
derivative xcos(3x)
derivative
x
cos
(
3
x
)
y^'=xe^y,y(0)=0
y
′
=
xe
y
,
y
(
0
)
=
0
derivative of arctan^2(1/x)
d
dx
(
arctan
2
(
1
x
)
)
derivative of 2sin(x-3cos(x))
d
dx
(
2
sin
(
x
)
−
3
cos
(
x
)
)
integral of 20arctan(sqrt(x))
∫
2
0
arctan
(
√
x
)
dx
derivative of 5e^{-x}-6e^x
d
dx
(
5
e
−
x
−
6
e
x
)
derivative y=sqrt(4+3x)
derivative
y
=
√
4
+
3
x
derivative of (ln(x)^{sqrt(ln(x))})
d
dx
(
(
ln
(
x
)
)
√
ln
(
x
)
)
integral from 0 to 1 of x^3e^x
∫
0
1
x
3
e
x
dx
limit as x approaches 25 of 2x+2sqrt(x)
lim
x
→
2
5
(
2
x
+
2
√
x
)
integral of-9cos(x)
∫
−
9
cos
(
x
)
dx
limit as x approaches 3 of (x-1)/(x^2-2)
lim
x
→
3
(
x
−
1
x
2
−
2
)
derivative of x^6+x
d
dx
(
x
6
+
x
)
xy^2dx=dy-xdx
xy
2
dx
=
dy
−
xdx
limit as x approaches 0 of sin((4pi)/x)
lim
x
→
0
(
sin
(
4
π
x
)
)
derivative f(x)=\sqrt[5]{x^2}
derivative
f
(
x
)
=
5
√
x
2
limit as x approaches 0 of (tan(9x))/x
lim
x
→
0
(
tan
(
9
x
)
x
)
integral of sqrt(144-4x^2)
∫
√
1
4
4
−
4
x
2
dx
1
..
1379
1380
1381
1382
1383
..
2459