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일반적인 미적분학 문제
integral of (x^3+1)/(x^2+1)
∫
x
3
+
1
x
2
+
1
dx
derivative y=(sqrt(x))/(x+1)
derivative
y
=
√
x
x
+
1
derivative of sqrt(x^2-m^2)
d
dx
(
√
x
2
−
m
2
)
derivative ((3x^2))/((5-3x)^4)
derivative
(
3
x
2
)
(
5
−
3
x
)
4
derivative of-x^2+2
d
dx
(
−
x
2
+
2
)
integral of (8+x)
∫
(
8
+
x
)
dx
implicit (dy)/(dx),x^2y+xy^2=6
implicit
dy
dx
,
x
2
y
+
xy
2
=
6
integral of 1/(3-4x)
∫
1
3
−
4
x
dx
derivative of sqrt(x/(9.8))
d
dx
(
√
x
9
.
8
)
derivative f(x)=(ln(7))e^x
derivative
f
(
x
)
=
(
ln
(
7
)
)
e
x
tangent f(x)= 1/(x^3),(-2,-1/8)
tangent
f
(
x
)
=
1
x
3
,
(
−
2
,
−
1
8
)
integral of xe^{x/3}
∫
xe
x
3
dx
implicit (dy)/(dx),sin(x+y)=3x-2y
implicit
dy
dx
,
sin
(
x
+
y
)
=
3
x
−
2
y
integral of 4/(4x+1)
∫
4
4
x
+
1
dx
e^x(dy)/(dx)=2x
e
x
dy
dx
=
2
x
laplace변환 (t-1)cos(4(t-1))+t^2
laplacetransform
(
t
−
1
)
cos
(
4
(
t
−
1
)
)
+
t
2
f(x)=(x^2)/(4-cos(x))
f
(
x
)
=
x
2
4
−
cos
(
x
)
integral of sin^2(x/2)cos^2(x/2)
∫
sin
2
(
x
2
)
cos
2
(
x
2
)
dx
f(x)=sqrt((1-x)/(1+x))
f
(
x
)
=
√
1
−
x
1
+
x
integral of 7sin^3(xco)s^2x
∫
7
sin
3
(
xco
)
s
2
xdx
지역 y=2x^3-x^2-5x,y=3x-x^2
area
y
=
2
x
3
−
x
2
−
5
x
,
y
=
3
x
−
x
2
integral of 3(2x-2)ln(x-2)
∫
3
(
2
x
−
2
)
ln
(
x
−
2
)
dx
integral of sqrt(3x+1)
∫
√
3
x
+
1
dx
sum from n=0 to infinity of (-2/7)^n
∑
n
=
0
∞
(
−
2
7
)
n
지역 x^2-4x+1,-x+5
area
x
2
−
4
x
+
1
,
−
x
+
5
limit as x approaches sqrt(2) of 15
lim
x
→
√
2
(
1
5
)
integral of e^{-6t}
∫
e
−
6
t
dt
sqrt(x)+sqrt(y)*y^'=0
√
x
+
√
y
·
y
′
=
0
tangent f(x)=(3x-1)^2,\at x=1
tangent
f
(
x
)
=
(
3
x
−
1
)
2
,
at
x
=
1
limit as x approaches 2 of x^2-x-6
lim
x
→
2
(
x
2
−
x
−
6
)
(\partial)/(\partial x)(2x^3-10y)
∂
∂
x
(
2
x
3
−
1
0
y
)
경사지 (-7.2)(9.6)
slope
(
−
7
.
2
)
(
9
.
6
)
limit as x approaches 2+of e^{3/((2-x))}
lim
x
→
2
+
(
e
3
(
2
−
x
)
)
integral from 6 to 8 of y/(y^2-2y-3)
∫
6
8
y
y
2
−
2
y
−
3
dy
integral of (x^3-1)^4x^2
∫
(
x
3
−
1
)
4
x
2
dx
integral of 1/(u^2+a^2)
∫
1
u
2
+
a
2
du
sum from n=1 to infinity of 1/(n(n+2))
∑
n
=
1
∞
1
n
(
n
+
2
)
tangent sqrt(1-4x)
tangent
√
1
−
4
x
sum from n=1 to infinity of ((1))/(n^2)
∑
n
=
1
∞
(
1
)
n
2
(d^2)/(dx^2)(ln(1+e^x))
d
2
dx
2
(
ln
(
1
+
e
x
)
)
(\partial)/(\partial x)(7x+8y^2)
∂
∂
x
(
7
x
+
8
y
2
)
inverse라플라스 (s+11)/((s-10)(s+4))
inverselaplace
s
+
1
1
(
s
−
1
0
)
(
s
+
4
)
laplace변환 2e^{-2t}cos(7t)-5e^{-2t}sin(7t)
laplacetransform
2
e
−
2
t
cos
(
7
t
)
−
5
e
−
2
t
sin
(
7
t
)
derivative of (e^x/x)
d
dx
(
e
x
x
)
sum from n=0 to infinity of n+3
∑
n
=
0
∞
n
+
3
derivative 4sec^7(2-4x)
derivative
4
sec
7
(
2
−
4
x
)
limit as x approaches 0+of arcsin(2x-1)
lim
x
→
0
+
(
arcsin
(
2
x
−
1
)
)
implicit (dy)/(dx),3x^3y=6
implicit
dy
dx
,
3
x
3
y
=
6
limit as x approaches pi of cos(x/6)
lim
x
→
π
(
cos
(
x
6
)
)
derivative f(x)=-1/4 x^4+27/2 x^2
derivative
f
(
x
)
=
−
1
4
x
4
+
2
7
2
x
2
integral of (m^2)/(m+1)
∫
m
2
m
+
1
dm
derivative (64x)/(x^2+64)
derivative
6
4
x
x
2
+
6
4
integral of x^2ln(x)
∫
x
2
ln
(
x
)
dx
derivative of x^4-5x^3
d
dx
(
x
4
−
5
x
3
)
derivative of (x+10/(x-10))
d
dx
(
x
+
1
0
x
−
1
0
)
integral of xsqrt(1+x)
∫
x
√
1
+
x
dx
derivative ln(8x+5)
derivative
ln
(
8
x
+
5
)
xy^'+9y=12y^2,y(1)=-1
xy
′
+
9
y
=
1
2
y
2
,
y
(
1
)
=
−
1
derivative of x*a
d
dx
(
x
·
a
)
integral of 1/((x^2+1)^4)
∫
1
(
x
2
+
1
)
4
dx
integral of (2x+1)/(x^2-x)
∫
2
x
+
1
x
2
−
x
dx
d/(dt)((3y^2-t^2)/(y^5))
d
dt
(
3
y
2
−
t
2
y
5
)
derivative of ln(4/(xsqrt(x+1)))
d
dx
(
ln
(
4
x
√
x
+
1
)
)
(e^{x^2-1})^'
(
e
x
2
−
1
)
′
(\partial)/(\partial x)(-2xy)
∂
∂
x
(
−
2
xy
)
derivative of (x^3-4x+1e^x)
d
dx
(
(
x
3
−
4
x
+
1
)
e
x
)
derivative of arcsec^2(x)
d
dx
(
arcsec
2
(
x
)
)
limit as x approaches 0 of 5/(tan(3x))
lim
x
→
0
(
5
tan
(
3
x
)
)
8(dy)/(dx)+7e^{x+y}=0
8
dy
dx
+
7
e
x
+
y
=
0
y^'=tsqrt(y)
y
′
=
t
√
y
limit as z approaches 0 of 1/(1+z^2)
lim
z
→
0
(
1
1
+
z
2
)
derivative of (ln(x^2)/x)
d
dx
(
ln
(
x
2
)
x
)
(t^2+1)f^'(t)+[f(t)]^2+1=0
(
t
2
+
1
)
f
′
(
t
)
+
[
f
(
t
)
]
2
+
1
=
0
integral from 2 to 3 of 6/(sqrt(3-x))
∫
2
3
6
√
3
−
x
dx
derivative of ((x+8/(x-8))^5)
d
dx
(
(
x
+
8
x
−
8
)
5
)
integral from 2 to 5 of x^2-6x+9
∫
2
5
x
2
−
6
x
+
9
dx
d/(da)(cos(3a)cos(2a)+sin(4a)sin(a))
d
da
(
cos
(
3
a
)
cos
(
2
a
)
+
sin
(
4
a
)
sin
(
a
)
)
integral from 0 to 9 of x^2sqrt(81-x^2)
∫
0
9
x
2
√
8
1
−
x
2
dx
integral from 0.1 to x of x
∫
0
.
1
x
xdx
지역 0,5x,x^2-6
area
0
,
5
x
,
x
2
−
6
integral of 100x^{3/2}
∫
1
0
0
x
3
2
dx
(\partial)/(\partial x)((4pi^2y)/(x^2))
∂
∂
x
(
4
π
2
y
x
2
)
derivative of 1/(ax^2+bx+c)
d
dx
(
1
ax
2
+
bx
+
c
)
integral of 3/((x^2-1)^2)
∫
3
(
x
2
−
1
)
2
dx
(\partial)/(\partial x)(x+6y-37)
∂
∂
x
(
x
+
6
y
−
3
7
)
y^{''}=-a^2y
y
′
′
=
−
a
2
y
limit as x approaches 3-of cx^2+6x
lim
x
→
3
−
(
cx
2
+
6
x
)
integral of (4x^3+x^2)
∫
(
4
x
3
+
x
2
)
dx
integral of 1/(xsqrt(25-4x^2))
∫
1
x
√
2
5
−
4
x
2
dx
integral from 0 to 4 of x(sqrt(x)-1)
∫
0
4
x
(
√
x
−
1
)
dx
xy^'+y=6xy^2
xy
′
+
y
=
6
xy
2
derivative 100+2/x+(x^2)/5
derivative
1
0
0
+
2
x
+
x
2
5
(\partial)/(\partial t)(s+2t)
∂
∂
t
(
s
+
2
t
)
integral from 0 to 7 of x
∫
0
7
xdx
derivative e^{-3t}
derivative
e
−
3
t
derivative of log_{10}(x^2+1)
d
dx
(
log
1
0
(
x
2
+
1
)
)
tangent x/(1+x^2),\at x=-1
tangent
x
1
+
x
2
,
at
x
=
−
1
지역 y=2-x,y=4-x^2
area
y
=
2
−
x
,
y
=
4
−
x
2
integral of (x^2+e^{1-x})
∫
(
x
2
+
e
1
−
x
)
dx
y^{''}+2y+y=xe^{-x}
y
′
′
+
2
y
+
y
=
xe
−
x
1
..
1527
1528
1529
1530
1531
..
2459