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일반적인 미적분학 문제
sum from n=0 to infinity of 2/(3^n)
∑
n
=
0
∞
2
3
n
f(x)=(1+x^2)(1+sqrt(x))
f
(
x
)
=
(
1
+
x
2
)
(
1
+
√
x
)
limit as n approaches infinity of e/n
lim
n
→
∞
(
e
n
)
limit as x approaches 1 of (2x-7)^3
lim
x
→
1
(
(
2
x
−
7
)
3
)
derivative of 6x^2-6x-36
d
dx
(
6
x
2
−
6
x
−
3
6
)
integral of |x+1|
∫
|
x
+
1
|
dx
integral of 5(x+2)^2
∫
5
(
x
+
2
)
2
dx
derivative-12x^5+75x^4
derivative
−
1
2
x
5
+
7
5
x
4
inverse라플라스 1/(s(3s+1))
inverselaplace
1
s
(
3
s
+
1
)
integral of x^2sqrt(6+x)
∫
x
2
√
6
+
x
dx
integral from-3 to-2 of 1/x
∫
−
3
−
2
1
x
dx
integral of 0.5e^{-0.5x}
∫
0
.
5
e
−
0
.
5
x
dx
derivative of 4pi
d
dx
(
4
π
)
inverse라플라스 5s
inverselaplace
5
s
derivative (ce^t)/(1+ce^t)
derivative
ce
t
1
+
ce
t
(\partial)/(\partial x)((((x+4))/(y+5))^{1/2})
∂
∂
x
(
(
(
x
+
4
)
y
+
5
)
1
2
)
integral of (x^2+7x-5)cos(2x)
∫
(
x
2
+
7
x
−
5
)
cos
(
2
x
)
dx
derivative f(x)=x(2x-1)(3x+2)
derivative
f
(
x
)
=
x
(
2
x
−
1
)
(
3
x
+
2
)
integral of (x^2(3-x))/(sqrt(x^4-4x^3))
∫
x
2
(
3
−
x
)
√
x
4
−
4
x
3
dx
y^{''}-4y^'+13y=0,y(0)=-3,y^'(0)=-1
y
′
′
−
4
y
′
+
1
3
y
=
0
,
y
(
0
)
=
−
3
,
y
′
(
0
)
=
−
1
derivative of (e^{-2.8x}-e^{-4.6x}/(1.8))
d
dx
(
e
−
2
.
8
x
−
e
−
4
.
6
x
1
.
8
)
tangent arcsin(2x)
tangent
arcsin
(
2
x
)
inverse라플라스 (80)/(s^2+40s)
inverselaplace
8
0
s
2
+
4
0
s
derivative of e^x+2^{-x}+2cos(x-6)
d
dx
(
e
x
+
2
−
x
+
2
cos
(
x
)
−
6
)
(\partial}{\partial y}(\frac{x^3)/3)
∂
∂
y
(
x
3
3
)
integral of 1/(12x^2)
∫
1
1
2
x
2
dx
derivative 3+0.35sin((360t)/(4.5))
derivative
3
+
0
.
3
5
sin
(
3
6
0
t
4
.
5
)
뿌리 x-a
roots
x
−
a
integral of (3e^x)/(e^{2x)+2e^x+1}
∫
3
e
x
e
2
x
+
2
e
x
+
1
dx
(\partial)/(\partial y)(xy^2z)
∂
∂
y
(
xy
2
z
)
integral from 0 to 2pi of e^{iθ}
∫
0
2
π
e
i
θ
d
θ
integral from 0 to infinity of 4xe^{-4x}
∫
0
∞
4
xe
−
4
x
dx
xy*dx=(x^2+4)dy
xy
·
dx
=
(
x
2
+
4
)
dy
derivative cos(sin(7x))
derivative
cos
(
sin
(
7
x
)
)
limit as h approaches 0 of (|h|)/h
lim
h
→
0
(
|
h
|
h
)
tangent 4sqrt(x)
tangent
4
√
x
integral of-\sqrt[3]{x}
∫
−
3
√
x
dx
(\partial)/(\partial x)(y^{4/x})
∂
∂
x
(
y
4
x
)
limit as 0 approaches 0 of ln(0)
lim
0
→
0
(
ln
(
0
)
)
limit as x approaches-infinity of (4-7x)/(2+3x)
lim
x
→
−
∞
(
4
−
7
x
2
+
3
x
)
(\partial)/(\partial y)(xln(x)+yln(x))
∂
∂
y
(
x
ln
(
x
)
+
y
ln
(
x
)
)
integral of 1/(b-ay)
∫
1
b
−
ay
dy
integral of (x^2-4x+5)
∫
(
x
2
−
4
x
+
5
)
dx
derivative 4+3sqrt(x)
derivative
4
+
3
√
x
derivative of arcsin(x/(10))
d
dx
(
arcsin
(
x
1
0
)
)
(\partial)/(\partial x)(-4/(x^2y))
∂
∂
x
(
−
4
x
2
y
)
x^{''}-20x^'+91x=0
x
′
′
−
2
0
x
′
+
9
1
x
=
0
derivative f(t)=t^{1/2}(13t+2)
derivative
f
(
t
)
=
t
1
2
(
1
3
t
+
2
)
derivative 9/((9-x^8)^{3/2)}
derivative
9
(
9
−
x
8
)
3
2
integral from 3 to 5 of (x^2)/8
∫
3
5
x
2
8
dx
sum from n=1 to infinity of n/(1000n+1)
∑
n
=
1
∞
n
1
0
0
0
n
+
1
derivative of 3^xx^3
d
dx
(
3
x
x
3
)
derivative of 1-|x^3|
d
dx
(
1
−
|
x
3
|
)
(d^4)/(dx^4)(13e^{x^2})
d
4
dx
4
(
1
3
e
x
2
)
derivative (x^2-100)/(x-10)
derivative
x
2
−
1
0
0
x
−
1
0
derivative f(x)= 1/(sqrt(2))
derivative
f
(
x
)
=
1
√
2
derivative of (x+1^2(x+2)^3)
d
dx
(
(
x
+
1
)
2
(
x
+
2
)
3
)
integral of x^2sqrt(x^3)
∫
x
2
√
x
3
dx
(\partial)/(\partial x)(sin(7y-x))
∂
∂
x
(
sin
(
7
y
−
x
)
)
테일러 5ln(x^2),1
taylor
5
ln
(
x
2
)
,
1
derivative of 5tan(xsec(x))
d
dx
(
5
tan
(
x
)
sec
(
x
)
)
tangent f(x)=x^2-sqrt(x),(1,0)
tangent
f
(
x
)
=
x
2
−
√
x
,
(
1
,
0
)
limit as x approaches 9 of ((x^2-4x-45))/(x^2-81)
lim
x
→
9
(
(
x
2
−
4
x
−
4
5
)
x
2
−
8
1
)
integral of-2cos(t)sin^2(t)
∫
−
2
cos
(
t
)
sin
2
(
t
)
dt
derivative of 12x^2+4
d
dx
(
1
2
x
2
+
4
)
경사지intercept (-1,-2),(-2,3)
slopeintercept
(
−
1
,
−
2
)
,
(
−
2
,
3
)
integral of 1/(sin(x)+1)
∫
1
sin
(
x
)
+
1
dx
(dy)/(dx)=(-2y^2)/(x^2)
dy
dx
=
−
2
y
2
x
2
integral of \sqrt[3]{x}
∫
3
√
x
dx
derivative of 3/4 x^{4/3}-3/8 x^{2/3}+7
d
dx
(
3
4
x
4
3
−
3
8
x
2
3
+
7
)
integral of 1/((x)^2)
∫
1
(
x
)
2
dx
d/(d{x)}(e^{{x}{y}{z}})
d
d
x
(
e
x
y
z
)
limit as x approaches 3 of 2x+2
lim
x
→
3
(
2
x
+
2
)
integral of (5-50x)/(sqrt(16-25x^2))
∫
5
−
5
0
x
√
1
6
−
2
5
x
2
dx
limit as θ approaches 0 of (1-cos(θ))/θ
lim
θ
→
0
(
1
−
cos
(
θ
)
θ
)
d/(dt)(9sin(t)-sin(9t))
d
dt
(
9
sin
(
t
)
−
sin
(
9
t
)
)
limit as x approaches 0 of (sin^8(x))/x
lim
x
→
0
(
sin
8
(
x
)
x
)
integral of (x-3)/((x-5)^2)
∫
x
−
3
(
x
−
5
)
2
dx
integral from 0 to x^2 of e^{-t^2}
∫
0
x
2
e
−
t
2
dt
integral from 0 to 3 of x^3sqrt(x^2+9)
∫
0
3
x
3
√
x
2
+
9
dx
derivative 1/2 e^x
derivative
1
2
e
x
integral of sin(t)e^{-st}
∫
sin
(
t
)
e
−
st
dt
(\partial)/(\partial x)(e^{xyz^9})
∂
∂
x
(
e
xyz
9
)
derivative ln(9-7x)
derivative
ln
(
9
−
7
x
)
integral of (3x^2+2x+1)/x
∫
3
x
2
+
2
x
+
1
x
dx
derivative of-3asin(3x+bcos(3x)*3)
d
dx
(
−
3
a
sin
(
3
x
)
+
b
cos
(
3
x
)
·
3
)
derivative of (sin(2x)/x)
d
dx
(
sin
(
2
x
)
x
)
limit as x approaches 2 of 9-x^2
lim
x
→
2
(
9
−
x
2
)
limit as x approaches-2 of (2x-1)/(x+2)
lim
x
→
−
2
(
2
x
−
1
x
+
2
)
3y^{''}+12y=0
3
y
′
′
+
1
2
y
=
0
x(dy)/(dx)+3y=(1+x)/(x^3)
x
dy
dx
+
3
y
=
1
+
x
x
3
integral of 8/(1-cos(4x))
∫
8
1
−
cos
(
4
x
)
dx
integral of sin^2(4θ)
∫
sin
2
(
4
θ
)
d
θ
integral of (7x^2+3x+7)/((x^2+1)^2)
∫
7
x
2
+
3
x
+
7
(
x
2
+
1
)
2
dx
laplace변환 f(t)=5cos(8t)+3e^{-4}sin(3t)
laplacetransform
f
(
t
)
=
5
cos
(
8
t
)
+
3
e
−
4
sin
(
3
t
)
limit as x approaches 0 of ln(x)-sqrt(x)
lim
x
→
0
(
ln
(
x
)
−
√
x
)
(\partial)/(\partial x)(y+z)
∂
∂
x
(
y
+
z
)
derivative of cot(x+arctan(x+1))
d
dx
(
cot
(
x
)
+
arctan
(
x
+
1
)
)
derivative of (x^3+1^4)
d
dx
(
(
x
3
+
1
)
4
)
integral of x^2-7x+2
∫
x
2
−
7
x
+
2
dx
1
..
1377
1378
1379
1380
1381
..
2459