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통계
일반적인 미적분학 문제
integral of tan^5(pix)sec^4(pix)
∫
tan
5
(
π
x
)
sec
4
(
π
x
)
dx
derivative x^4+7x^2-x
derivative
x
4
+
7
x
2
−
x
integral of 2x^3(3x^4-5)
∫
2
x
3
(
3
x
4
−
5
)
dx
integral from 0 to 2pi of sin^2(2x)
∫
0
2
π
sin
2
(
2
x
)
dx
integral of (1+3t^5)/(2t)
∫
1
+
3
t
5
2
t
dt
integral of ((2x^4)/(\sqrt[3]{x^2)})
∫
(
2
x
4
3
√
x
2
)
dx
y^{''}+36y=-36sec^2(6x)
y
′
′
+
3
6
y
=
−
3
6
sec
2
(
6
x
)
f(x)=sqrt(x+6)
f
(
x
)
=
√
x
+
6
지역 x=7y, 1/3 y=x, 1/7 y=x
area
x
=
7
y
,
1
3
y
=
x
,
1
7
y
=
x
derivative of ln(sqrt(1+sin^2(x)))
d
dx
(
ln
(
√
1
+
sin
2
(
x
)
)
)
limit as x approaches-7 of (x^2-8)/(7-x)
lim
x
→
−
7
(
x
2
−
8
7
−
x
)
derivative of-cos(xsin(x))
d
dx
(
−
cos
(
x
)
sin
(
x
)
)
(\partial)/(\partial x)(4xy)
∂
∂
x
(
4
xy
)
integral of e^{2x}cos(2x)
∫
e
2
x
cos
(
2
x
)
dx
derivative of arctanh(sin(x))
d
dx
(
arctanh
(
sin
(
x
)
)
)
integral of x/((3x^2-4)^4)
∫
x
(
3
x
2
−
4
)
4
dx
integral of (4x^2-3cos(x))
∫
(
4
x
2
−
3
cos
(
x
)
)
dx
integral from-1 to 1 of e^{x+1}
∫
−
1
1
e
x
+
1
dx
integral of sin(10x)cos(5x)
∫
sin
(
1
0
x
)
cos
(
5
x
)
dx
(\partial)/(\partial y)(x^4-3x^2y^2+y^4)
∂
∂
y
(
x
4
−
3
x
2
y
2
+
y
4
)
integral of (cos(x))/(sin(x)+1)
∫
cos
(
x
)
sin
(
x
)
+
1
dx
derivative of (sin(x)/(sqrt(2)))
d
dx
(
sin
(
x
)
√
2
)
tangent y=(4x)/(x^2+1)
tangent
y
=
4
x
x
2
+
1
derivative f(x)=x^{2.4}+e^{2.4}
derivative
f
(
x
)
=
x
2
.
4
+
e
2
.
4
(\partial)/(\partial x)(5x^4y-3ysin(x))
∂
∂
x
(
5
x
4
y
−
3
y
sin
(
x
)
)
경사지 (4.4,8997.96),(107.3,21421.44)
slope
(
4
.
4
,
8
9
9
7
.
9
6
)
,
(
1
0
7
.
3
,
2
1
4
2
1
.
4
4
)
f(x)=e^{ln(sin(x^2))}sqrt(2x+1)
f
(
x
)
=
e
ln
(
sin
(
x
2
)
)
√
2
x
+
1
y^{''}-(3/x)y^'-(5/(x^2))y=0
y
′
′
−
(
3
x
)
y
′
−
(
5
x
2
)
y
=
0
integral of (25)/((x-3)(x^2+16))
∫
2
5
(
x
−
3
)
(
x
2
+
1
6
)
dx
integral of e^{4x}cos(6x)
∫
e
4
x
cos
(
6
x
)
dx
derivative x^2-4x
derivative
x
2
−
4
x
(dx)/(dt)=3xt^2
dx
dt
=
3
xt
2
laplace변환 3sin(2t)
laplacetransform
3
sin
(
2
t
)
derivative of x^xsin(x)
d
dx
(
x
x
sin
(
x
)
)
y(1+x^2)((dy)/(dx))-x(1+y^2)=0
y
(
1
+
x
2
)
(
dy
dx
)
−
x
(
1
+
y
2
)
=
0
y^'=-(csc(y))/(sec^2(x))
y
′
=
−
csc
(
y
)
sec
2
(
x
)
tangent f(x)=((x-2)/(x+2))^2,\at x=-1
tangent
f
(
x
)
=
(
x
−
2
x
+
2
)
2
,
at
x
=
−
1
integral of 1+cos(x)
∫
1
+
cos
(
x
)
dx
(cos(x))^{sin(x)}
(
cos
(
x
)
)
sin
(
x
)
derivative of 2xcos(5x^2)
d
dx
(
2
x
cos
(
5
)
x
2
)
limit as x approaches-3 of-6/(x+3)
lim
x
→
−
3
(
−
6
x
+
3
)
integral of 4/(x^2)cos(4/x)
∫
4
x
2
cos
(
4
x
)
dx
derivative (-x^3-x^2+x)cos(x)
derivative
(
−
x
3
−
x
2
+
x
)
cos
(
x
)
d/(dt)(At^2e^{-t})
d
dt
(
At
2
e
−
t
)
integral from-2 to-1 of u-1/(u^2)
∫
−
2
−
1
u
−
1
u
2
du
integral of e^{tan(x)}*sec^2(x)
∫
e
tan
(
x
)
·
sec
2
(
x
)
dx
integral from 0 to pi of sin(x)sin(nx)
∫
0
π
sin
(
x
)
sin
(
nx
)
dx
integral of (y-1)/((4+y^2)^2)
∫
y
−
1
(
4
+
y
2
)
2
dy
integral of (4x-3)^6
∫
(
4
x
−
3
)
6
dx
limit as x approaches 2+of (x+3)/(x-2)
lim
x
→
2
+
(
x
+
3
x
−
2
)
tangent f(x)= 6/x ,\at x=1
tangent
f
(
x
)
=
6
x
,
at
x
=
1
limit as x approaches 2 of x^2-1/x
lim
x
→
2
(
x
2
−
1
x
)
inverse라플라스 1/(s^2(s+1)^2)
inverselaplace
1
s
2
(
s
+
1
)
2
integral of (x^5)/((3-x^6)^2)
∫
x
5
(
3
−
x
6
)
2
dx
limit as x approaches 4-of (x-4)/(x-1)
lim
x
→
4
−
(
x
−
4
x
−
1
)
derivative y= 1/(sqrt(x))
derivative
y
=
1
√
x
integral of 7x^2-3x+8+1/x+2/(x^2)
∫
7
x
2
−
3
x
+
8
+
1
x
+
2
x
2
dx
integral from 0 to 3 of 10-x-y^2
∫
0
3
1
0
−
x
−
y
2
dx
f(x)=x^2e^{3x}
f
(
x
)
=
x
2
e
3
x
limit as x approaches 2+of 2x-3
lim
x
→
2
+
(
2
x
−
3
)
derivative of e^{-x}-x^2
d
dx
(
e
−
x
−
x
2
)
integral from 0 to 0.6 of 400x
∫
0
0
.
6
4
0
0
xdx
integral of (x^2+x-3)/(3x^3-2x^2+6x-4)
∫
x
2
+
x
−
3
3
x
3
−
2
x
2
+
6
x
−
4
dx
inverse라플라스 e^{-5s}
inverselaplace
e
−
5
s
integral of (a^x)/(1+a^{2x)}
∫
a
x
1
+
a
2
x
dx
(dy)/(dx)=3y-5
dy
dx
=
3
y
−
5
(\partial)/(\partial x)(y/(2x+3y))
∂
∂
x
(
y
2
x
+
3
y
)
sum from n=1 to infinity}((\sqrt{n of+4))/(n^2)
∑
n
=
1
∞
(
√
n
+
4
)
n
2
limit as x approaches 3 of sqrt(2x^2-2)
lim
x
→
3
(
√
2
x
2
−
2
)
(dy)/(dx)+y^7x+y=0
dy
dx
+
y
7
x
+
y
=
0
derivative of (3cos(x)/(1-2sin(x)))
d
dx
(
3
cos
(
x
)
1
−
2
sin
(
x
)
)
(\partial}{\partial v}(\frac{u-v)/3)
∂
∂
v
(
u
−
v
3
)
integral of (e^x)/(e^x+1)
∫
e
x
e
x
+
1
dx
지역 3cos(2x),(3-3cos(2x))x=0x= pi/2
area
3
cos
(
2
x
)
,
(
3
−
3
cos
(
2
x
)
)
x
=
0
x
=
π
2
integral from 0 to 1 of pi(5x)^2
∫
0
1
π
(
5
x
)
2
dx
derivative of 5-5x^2
d
dx
(
5
−
5
x
2
)
6y^{''}-6y^'+75y=0
6
y
′
′
−
6
y
′
+
7
5
y
=
0
y^'=(2x)/(1+2y),y(2)=0
y
′
=
2
x
1
+
2
y
,
y
(
2
)
=
0
derivative ln(ln(7x))
derivative
ln
(
ln
(
7
x
)
)
integral of (cos(6x))/(sin(6x))
∫
cos
(
6
x
)
sin
(
6
x
)
dx
(\partial)/(\partial x)(-2e^{-x^2}x)
∂
∂
x
(
−
2
e
−
x
2
x
)
integral of 2x-6x^3
∫
2
x
−
6
x
3
dx
inverse라플라스-5
inverselaplace
−
5
지역 x^2,3-2x
area
x
2
,
3
−
2
x
(dy)/(dx)=xy,y(0)=1,y(1)=2
dy
dx
=
xy
,
y
(
0
)
=
1
,
y
(
1
)
=
2
derivative of 2pi-xcos(x)
d
dx
(
2
π
−
x
cos
(
x
)
)
cos^2(x)sin(x)(dy)/(dx)cos^3(x)y=1
cos
2
(
x
)
sin
(
x
)
dy
dx
cos
3
(
x
)
y
=
1
laplace변환 \H(t-2pi)sin(t-2pi)
laplacetransform
H
(
t
−
2
π
)
sin
(
t
−
2
π
)
derivative of (2+x/((2-x)^5))
d
dx
(
2
+
x
(
2
−
x
)
5
)
tangent f(x)=7sqrt(3)sin(x)+7cos(x)
tangent
f
(
x
)
=
7
√
3
sin
(
x
)
+
7
cos
(
x
)
integral from 1 to 5 of M/(e^M)
∫
1
5
M
e
M
dM
integral of 1/(x(a+bx))
∫
1
x
(
a
+
bx
)
dx
(dy)/(dt)+e^ty=-20e^t
dy
dt
+
e
t
y
=
−
2
0
e
t
limit as x approaches 1 of (sqrt(x)-8)/(\sqrt[3]{x)-4}
lim
x
→
1
(
√
x
−
8
3
√
x
−
4
)
integral of (x^2-5x)e^x
∫
(
x
2
−
5
x
)
e
x
dx
지역 2sqrt(x),(x^2)/4
area
2
√
x
,
x
2
4
derivative of cot(x^2+1)
d
dx
(
cot
(
x
2
+
1
)
)
integral from 1 to t of (27)/(x^3)
∫
1
t
2
7
x
3
dx
5x-4ysqrt(x^2+1)(dy)/(dx)=0
5
x
−
4
y
√
x
2
+
1
dy
dx
=
0
(\partial)/(\partial x)(2x^2yz)
∂
∂
x
(
2
x
2
yz
)
1
..
1410
1411
1412
1413
1414
..
2459