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일반적인 미적분학 문제
maclaurin 1/(1+x^3)
maclaurin
1
1
+
x
3
(\partial)/(\partial y)(4y-2x)
∂
∂
y
(
4
y
−
2
x
)
integral of sqrt(4-x^2)x
∫
√
4
−
x
2
xdx
(\partial)/(\partial x)((e^y)/(x+y^7))
∂
∂
x
(
e
y
x
+
y
7
)
derivative of-4/((1+2x^2))
d
dx
(
−
4
(
1
+
2
x
)
2
)
derivative of 3/(4sqrt(x))
d
dx
(
3
4
√
x
)
integral from 0 to pi/4 of 8sec^2(x)
∫
0
π
4
8
sec
2
(
x
)
dx
derivative of (ln(x-1)/((x-1)^3))
d
dx
(
ln
(
x
−
1
)
(
x
−
1
)
3
)
derivative f(x)=cos(2)(x)
derivative
f
(
x
)
=
cos
(
2
)
(
x
)
integral of 1/(sqrt(25-9x^2))
∫
1
√
2
5
−
9
x
2
dx
derivative y=ln((5+e^x)/(5-e^x))
derivative
y
=
ln
(
5
+
e
x
5
−
e
x
)
integral of xsqrt(3x-4)
∫
x
√
3
x
−
4
dx
integral of (x^2+1)/(x^3+3x)
∫
x
2
+
1
x
3
+
3
x
dx
4x-6ysqrt(x^2+1)((dy)/(dx))=0
4
x
−
6
y
√
x
2
+
1
(
dy
dx
)
=
0
sum from n=1 to infinity of 1/(n^{0.08)}
∑
n
=
1
∞
1
n
0
.
0
8
derivative of axe^{3x}
d
dx
(
axe
3
x
)
derivative 3x^5
derivative
3
x
5
(\partial)/(\partial y)(1+y^2)
∂
∂
y
(
1
+
y
2
)
derivative of (x^2-1/(sqrt(x^3)))
d
dx
(
x
2
−
1
√
x
3
)
integral of tan^{11}(x)sec^8(x)
∫
tan
1
1
(
x
)
sec
8
(
x
)
dx
derivative (2+x)^2
derivative
(
2
+
x
)
2
integral from 0 to 1 of sec^3(x)
∫
0
1
sec
3
(
x
)
dx
y^'=(x+y+4)^2
y
′
=
(
x
+
y
+
4
)
2
sum from n=0 to infinity of e^{-(7n)/2}
∑
n
=
0
∞
e
−
7
n
2
integral of 7x^2
∫
7
x
2
dx
tangent g(x)=3x^4,(-2,48)
tangent
g
(
x
)
=
3
x
4
,
(
−
2
,
4
8
)
integral of ((x-4))/((x^2-x+2))
∫
(
x
−
4
)
(
x
2
−
x
+
2
)
dx
integral of e^{-9x}tan(e^{-9x})
∫
e
−
9
x
tan
(
e
−
9
x
)
dx
integral from 0 to pi/2 of sin^2(θ)cos^2(θ)
∫
0
π
2
sin
2
(
θ
)
cos
2
(
θ
)
d
θ
derivative of e^{x^{x^x}}
d
dx
(
e
x
x
x
)
integral of (-3+4)e^{-x}
∫
(
−
3
+
4
)
e
−
x
dx
(1+x)(dy)/(dx)=4y
(
1
+
x
)
dy
dx
=
4
y
derivative cy^{-8}
derivative
cy
−
8
derivative of 2x^{0.5}
d
dx
(
2
x
0
.
5
)
derivative y=e^{7/9 x}
derivative
y
=
e
7
9
x
integral of 2sin^3(xco)s^7x
∫
2
sin
3
(
xco
)
s
7
x
tangent f(x)= 9/x ,\at x=5
tangent
f
(
x
)
=
9
x
,
at
x
=
5
derivative of (2x-3/(x^2))
d
dx
(
2
x
−
3
x
2
)
sum from n=0 to infinity of i^n
∑
n
=
0
∞
i
n
derivative (x+1/x)^4
derivative
(
x
+
1
x
)
4
derivative of (sec(x)/(3+sec(x)))
d
dx
(
sec
(
x
)
3
+
sec
(
x
)
)
(\partial)/(\partial z)(x^2e^{yz^2})
∂
∂
z
(
x
2
e
yz
2
)
(dx)/(dy)=70-4x
dx
dy
=
7
0
−
4
x
integral from 3 to infinity of e^{-7x}
∫
3
∞
e
−
7
x
dx
limit as x approaches 7-of 4/((x-7)^2)
lim
x
→
7
−
(
4
(
x
−
7
)
2
)
derivative y=-6x+k
derivative
y
=
−
6
x
+
k
integral from 0 to 1 of 1(x^2+1)e^{-x}
∫
0
1
1
(
x
2
+
1
)
e
−
x
dx
단순화 5/(x^5)+3/(x^2)
simplify
5
x
5
+
3
x
2
tangent-3x^2-5x
tangent
−
3
x
2
−
5
x
derivative of (x^2/(x+10))
d
dx
(
x
2
x
+
1
0
)
sum from n=1 to infinity of 2/(n^2)
∑
n
=
1
∞
2
n
2
derivative y=sqrt(x)(x-1)^2
derivative
y
=
√
x
(
x
−
1
)
2
derivative of x/(a^2x^2+bx+49)
d
dx
(
x
a
2
x
2
+
bx
+
4
9
)
integral of (x^2+5x-8)/(sqrt(x))
∫
x
2
+
5
x
−
8
√
x
dx
limit as x approaches infinity of 2x+8
lim
x
→
∞
(
2
x
+
8
)
derivative sqrt(17x)
derivative
√
1
7
x
derivative of (2x/(sqrt(1+4x^2)))
d
dx
(
2
x
√
1
+
4
x
2
)
limit as x approaches 2 of a^2x+2a
lim
x
→
2
(
a
2
x
+
2
a
)
(1+y)xdx-(1+x)ydy=0
(
1
+
y
)
xdx
−
(
1
+
x
)
ydy
=
0
integral of 1/((1+4y^2))
∫
1
(
1
+
4
y
2
)
dy
derivative of e^{-1/2 x}
d
dx
(
e
−
1
2
x
)
inverse라플라스 (3e^{-7s}}{s^2}+\frac{7e^{-7s})/s+(2e^{-7s})/s
inverselaplace
3
e
−
7
s
s
2
+
7
e
−
7
s
s
+
2
e
−
7
s
s
integral of 2xe^{-2x}
∫
2
xe
−
2
x
dx
derivative of (x^3+5/(x^2+2x+3))
d
dx
(
x
3
+
5
x
2
+
2
x
+
3
)
테일러 f(x)=x^3
taylor
f
(
x
)
=
x
3
integral of log_{6}(x)
∫
log
6
(
x
)
dx
(\partial)/(\partial x)(4xye^{-x^2-y^2})
∂
∂
x
(
4
xye
−
x
2
−
y
2
)
(\partial)/(\partial x)(xy+2x-ln(x^2y))
∂
∂
x
(
xy
+
2
x
−
ln
(
x
2
y
)
)
integral of (x^2+3)
∫
(
x
2
+
3
)
dx
derivative (x^4+1)^5
derivative
(
x
4
+
1
)
5
derivative of 5/((2x^3)+2cos(x))
d
dx
(
5
(
2
x
)
3
+
2
cos
(
x
)
)
derivative y=x^2sqrt(3x+5)
derivative
y
=
x
2
√
3
x
+
5
derivative of (5/3 x^2)
d
dx
(
(
5
3
)
x
2
)
integral of (4x)^2
∫
(
4
x
)
2
dx
integral from 4 to 8 of t^2ln(3t)
∫
4
8
t
2
ln
(
3
t
)
dt
integral of 1/(6sqrt(x)(3+\sqrt{x))}
∫
1
6
√
x
(
3
+
√
x
)
dx
(x^2-xy+2y^2)dx+(x^2-2xy)dy=0
(
x
2
−
xy
+
2
y
2
)
dx
+
(
x
2
−
2
xy
)
dy
=
0
derivative log_{2}(3-2x)
derivative
log
2
(
3
−
2
x
)
(1/(1+x))^'
(
1
1
+
x
)
′
limit as x approaches 0 of 1+csc(x)
lim
x
→
0
(
1
+
csc
(
x
)
)
integral of (sec(x)+tan(x))
∫
(
sec
(
x
)
+
tan
(
x
)
)
dx
derivative 4arctan((x^2+1)^2)
derivative
4
arctan
(
(
x
2
+
1
)
2
)
integral from 7 to 8 of xsqrt(x-7)
∫
7
8
x
√
x
−
7
dx
(\partial)/(\partial x)(yx+y+z)
∂
∂
x
(
yx
+
y
+
z
)
integral of 7xcos(x)
∫
7
x
cos
(
x
)
dx
d/(dt)(t-t^2)
d
dt
(
t
−
t
2
)
inverse라플라스 4/((s-2)^2)
inverselaplace
4
(
s
−
2
)
2
derivative of (e^{2x}/(x+1))
d
dx
(
e
2
x
x
+
1
)
integral of 2(x+1)
∫
2
(
x
+
1
)
dx
y^{''}+4y^'+5y=0,y(0)=-1,y^'(0)=-3
y
′
′
+
4
y
′
+
5
y
=
0
,
y
(
0
)
=
−
1
,
y
′
(
0
)
=
−
3
integral of sin(x)cos(nx)
∫
sin
(
x
)
cos
(
nx
)
dx
(dy)/(dx)y=8x
dy
dx
y
=
8
x
limit as x approaches 0+of x/(x-3)
lim
x
→
0
+
(
x
x
−
3
)
y^{''}+2y^'+5y=t^3
y
′
′
+
2
y
′
+
5
y
=
t
3
derivative of (x^2+x-2/(x^2))
d
dx
(
x
2
+
x
−
2
x
2
)
(\partial)/(\partial y)(ln(y)ln(x^2+1))
∂
∂
y
(
ln
(
y
)
ln
(
x
2
+
1
)
)
integral of ((x^3)/3)'sin(x)
∫
(
x
3
3
)
′
sin
(
x
)
dx
derivative of 2/(2x-1)
d
dx
(
2
2
x
−
1
)
derivative sqrt(1+sec(2x))
derivative
√
1
+
sec
(
2
x
)
laplace변환 cos(θ)
laplacetransform
cos
(
θ
)
1
..
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1398
1399
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1401
..
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