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Functions & Graphing
幾何学
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前微積分
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統計
人気の高い微分積分問題
sum from n=1 to infinity of (n!)/(2n-1)
∑
n
=
1
∞
n
!
2
n
−
1
y^'= 5/(y+2)
y
′
=
5
y
+
2
derivative of (5x^6+8x^3^4)
d
dx
(
(
5
x
6
+
8
x
3
)
4
)
integral of csc(3x)cot(3x)
∫
csc
(
3
x
)
cot
(
3
x
)
dx
integral of (3y^2)
∫
(
3
y
2
)
dy
tangent y=x+sqrt(x),(49,56)
tangent
y
=
x
+
√
x
,
(
4
9
,
5
6
)
integral from 1 to 25 of 2/x
∫
1
2
5
2
x
dx
limit as x approaches+0 of (x^2)/(1-cos(x))
lim
x
→
+
0
(
x
2
1
−
cos
(
x
)
)
(dy)/(dx)=(5x)/(7y)
dy
dx
=
5
x
7
y
integral of 1/2 xcos(4x^2)
∫
1
2
x
cos
(
4
x
2
)
dx
integral of-2x+6x^2-4x^3+C
∫
−
2
x
+
6
x
2
−
4
x
3
+
Cdx
(\partial)/(\partial y)(ln(1+xy))
∂
∂
y
(
ln
(
1
+
xy
)
)
sum from n=1 to infinity of 1/n-1/(2n+1)
∑
n
=
1
∞
1
n
−
1
2
n
+
1
テイラー sqrt(1-x^2),0
taylor
√
1
−
x
2
,
0
derivative of sqrt(2-3x^2)
d
dx
(
√
2
−
3
x
2
)
derivative f(x)=(x^2)/(1+4x)
derivative
f
(
x
)
=
x
2
1
+
4
x
integral of 1/((arcsin(x))^3sqrt(1-x^2))
∫
1
(
arcsin
(
x
)
)
3
√
1
−
x
2
dx
laplacetransform e^{4(t-3)}
laplacetransform
e
4
(
t
−
3
)
limit as x approaches 1-of (-1)/(x^2-1)
lim
x
→
1
−
(
−
1
x
2
−
1
)
integral of 1/(1-5x)
∫
1
1
−
5
x
dx
(dr)/(dθ)r=(7+sec(θ))sin(θ)
dr
d
θ
r
=
(
7
+
sec
(
θ
)
)
sin
(
θ
)
derivative x^2sqrt(3x+5)
derivative
x
2
√
3
x
+
5
integral of x/((x^2+7)^2)
∫
x
(
x
2
+
7
)
2
dx
derivative f(x)=(-3x^3+3x^2)^3
derivative
f
(
x
)
=
(
−
3
x
3
+
3
x
2
)
3
limit as x approaches-1 of arccos(x)
lim
x
→
−
1
(
arccos
(
x
)
)
integral from 0 to pi of 3sin^2(xco)s^4x
∫
0
π
3
sin
2
(
xco
)
s
4
xdx
limit as x approaches 7 of ((1/x-1/7))/(x-7)
lim
x
→
7
(
(
1
x
−
1
7
)
x
−
7
)
integral of (x^3)/(x^8+16)
∫
x
3
x
8
+
1
6
dx
derivative of x^2(1-x^2)
d
dx
(
x
2
(
1
−
x
)
2
)
derivative 4sin(θ)-θ
derivative
4
sin
(
θ
)
−
θ
integral from-1 to 2 of xe^{6x}
∫
−
1
2
xe
6
x
dx
derivative 3x^{5/2}+8x^2
derivative
3
x
5
2
+
8
x
2
integral of 1/(sqrt(2pi))e^{(x^2)/2}
∫
1
√
2
π
e
x
2
2
dx
limit as x approaches 3-of ln(x^2-9)
lim
x
→
3
−
(
ln
(
x
2
−
9
)
)
derivative of sin(x+x*cos(x))
d
dx
(
sin
(
x
)
+
x
·
cos
(
x
)
)
derivative of x^2y-x
d
dx
(
x
2
y
−
x
)
integral of (cos(5x)cos(3x))
∫
(
cos
(
5
x
)
cos
(
3
x
)
)
dx
integral from 0 to 1 of x-x^3
∫
0
1
x
−
x
3
dx
(\partial)/(\partial x)(e^{-x^3-y^3})
∂
∂
x
(
e
−
x
3
−
y
3
)
derivative 5^t
derivative
5
t
f(x)=sin(x^5)
f
(
x
)
=
sin
(
x
5
)
derivative of (-5/(x^2))
d
dx
(
−
5
x
2
)
integral of (2x-4)/((x^2-4x+20)^2)
∫
2
x
−
4
(
x
2
−
4
x
+
2
0
)
2
dx
integral of x^2sqrt(ax^3-b)
∫
x
2
√
ax
3
−
b
dx
laplacetransform sin(5pit)
laplacetransform
sin
(
5
π
t
)
integral of (7x^2+9x+7)/((x^2+1)^2)
∫
7
x
2
+
9
x
+
7
(
x
2
+
1
)
2
dx
integral from 4 to 5 of x/(x^2+4x+20)
∫
4
5
x
x
2
+
4
x
+
2
0
dx
integral of (-5csc^2(x))
∫
(
−
5
csc
2
(
x
)
)
dx
テイラー xcos(2x),1
taylor
x
cos
(
2
x
)
,
1
limit as x approaches+1 of e^{4x^3-4x}
lim
x
→
+
1
(
e
4
x
3
−
4
x
)
derivative of (3x^4-x/x)
d
dx
(
3
x
4
−
x
x
)
integral of 30sin^3(x)cos^2(x)
∫
3
0
sin
3
(
x
)
cos
2
(
x
)
dx
integral of 5x*e^{10x}
∫
5
x
·
e
1
0
x
dx
integral from 2 to 3 of (x-4)sqrt(5-x)
∫
2
3
(
x
−
4
)
√
5
−
x
dx
derivative (x^2-49)/(x+7)
derivative
x
2
−
4
9
x
+
7
integral of (3x)/(sqrt(9-25x^4))
∫
3
x
√
9
−
2
5
x
4
dx
derivative f(x)=(x^2+3)^3(x^3+3)^2
derivative
f
(
x
)
=
(
x
2
+
3
)
3
(
x
3
+
3
)
2
derivative of 5x^2cos(7x)
d
dx
(
5
x
2
cos
(
7
x
)
)
f^{''}(x)=x^3-4x+1,f^'(0)=2,f(1)=-2
f
′
′
(
x
)
=
x
3
−
4
x
+
1
,
f
′
(
0
)
=
2
,
f
(
1
)
=
−
2
limit as x approaches 2 of x^2-5x+6x^2-4
lim
x
→
2
(
x
2
−
5
x
+
6
x
2
−
4
)
limit as x approaches 7 of (x+7)/(x-7)
lim
x
→
7
(
x
+
7
x
−
7
)
integral of cos(8x)cos(3x)
∫
cos
(
8
x
)
cos
(
3
x
)
dx
integral of 3/(sqrt(t))
∫
3
√
t
dt
derivative of ln(3x+x^2)
d
dx
(
ln
(
3
x
+
x
2
)
)
derivative of-(4x/y)
d
dx
(
−
4
x
y
)
(\partial)/(\partial z)(xsin(yz))
∂
∂
z
(
x
sin
(
yz
)
)
integral of xarcsin(6x)
∫
x
arcsin
(
6
x
)
dx
derivative of e^{(3x/2})
d
dx
(
e
3
x
2
)
limit as x approaches pi of ln(sin(x))
lim
x
→
π
(
ln
(
sin
(
x
)
)
)
integral of (sec(z)tan(z))/(sqrt(sec(z)))
∫
sec
(
z
)
tan
(
z
)
√
sec
(
z
)
dz
derivative (1-25x^2)^2arcsin(5x)
derivative
(
1
−
2
5
x
2
)
2
arcsin
(
5
x
)
tangent (64)/(x^2+16),\at x=3
tangent
6
4
x
2
+
1
6
,
at
x
=
3
integral from 2 to 3 of (x^2-4)
∫
2
3
(
x
2
−
4
)
dx
tangent f(x)=(6x)/(2+x^2),(2,2)
tangent
f
(
x
)
=
6
x
2
+
x
2
,
(
2
,
2
)
integral of (sqrt(3x+2))
∫
(
√
3
x
+
2
)
dx
derivative y=19cos(x/b-2.5)+19
derivative
y
=
1
9
cos
(
x
b
−
2
.
5
)
+
1
9
(\partial)/(\partial x)(sin^2(2x+3y))
∂
∂
x
(
sin
2
(
2
x
+
3
y
)
)
integral from 0 to 1 of x^2(x^3-2)^3
∫
0
1
x
2
(
x
3
−
2
)
3
dx
(\partial)/(\partial x)(t/x)
∂
∂
x
(
t
x
)
(dy)/(dx)+(3/x)y=-4x-10
dy
dx
+
(
3
x
)
y
=
−
4
x
−
1
0
integral of 1/(sqrt(x^2-4))
∫
1
√
x
2
−
4
dx
(dy)/(dx)= 2/x
dy
dx
=
2
x
derivative of a/(1+\frac{b{x+c}})
d
dx
(
a
1
+
b
x
+
c
)
integral of 6x^2
∫
6
x
2
dx
limit as x approaches 0 of x-1/(ln|x|)
lim
x
→
0
(
x
−
1
ln
|
x
|
)
x^2y^'+2xy=ln(x),y(1)=6
x
2
y
′
+
2
xy
=
ln
(
x
)
,
y
(
1
)
=
6
limit as x approaches-2-of x/(x^2-4)
lim
x
→
−
2
−
(
x
x
2
−
4
)
derivative sqrt(y/2)
derivative
√
y
2
derivative of-(48x/((x^2+12)^2))
d
dx
(
−
4
8
x
(
x
2
+
1
2
)
2
)
integral of e^{ix}
∫
e
ix
dx
derivative 1/(sin(x))
derivative
1
sin
(
x
)
integral of sin(2θ)sin(6θ)
∫
sin
(
2
θ
)
sin
(
6
θ
)
d
θ
laplacetransform 2sin(3t)cos(3t)
laplacetransform
2
sin
(
3
t
)
cos
(
3
t
)
integral of (z+3)^4
∫
(
z
+
3
)
4
dz
derivative (3x-2)^3(8x^2+7)^3
derivative
(
3
x
−
2
)
3
(
8
x
2
+
7
)
3
面積-1/2 x^3+2x^2+15/2 x-9,[1,6]
area
−
1
2
x
3
+
2
x
2
+
1
5
2
x
−
9
,
[
1
,
6
]
integral from-1 to 1 of 4-4x^2
∫
−
1
1
4
−
4
x
2
dx
derivative of (4-2x-x^2/(x^2-6))
d
dx
(
4
−
2
x
−
x
2
x
2
−
6
)
xv'+v=((1+2v))/(1-v)
xv
′
+
v
=
(
1
+
2
v
)
1
−
v
derivative x^4ln(x)
derivative
x
4
ln
(
x
)
1
..
5
6
7
8
9
..
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