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일반적인 미적분학 문제
integral of 5/(3+x^2)
∫
5
3
+
x
2
dx
derivative f(x)=x^2-5x+5
derivative
f
(
x
)
=
x
2
−
5
x
+
5
경사지intercept (6,5),(-3,-4)
slopeintercept
(
6
,
5
)
,
(
−
3
,
−
4
)
d/(dt)(3sin(t))
d
dt
(
3
sin
(
t
)
)
integral of tan(x)
∫
tan
(
x
)
dx
경사지 y=9+5x^2-2x^3
slope
y
=
9
+
5
x
2
−
2
x
3
integral from-1 to 2 of (x-4|x|)
∫
−
1
2
(
x
−
4
|
x
|
)
dx
(\partial)/(\partial x)(x/(1+x^2+y^2))
∂
∂
x
(
x
1
+
x
2
+
y
2
)
limit as x approaches 1 of-2x^2+2k
lim
x
→
1
(
−
2
x
2
+
2
k
)
integral of 2^{cos(x)}*sin(x)
∫
2
cos
(
x
)
·
sin
(
x
)
dx
integral of ln(x/2)
∫
ln
(
x
2
)
dx
integral of xe^{3x+1}
∫
xe
3
x
+
1
dx
지역 y=4x^2,y=4
area
y
=
4
x
2
,
y
=
4
limit as x approaches 2 of-x^2+4x-2
lim
x
→
2
(
−
x
2
+
4
x
−
2
)
integral of (9x^3)/(sqrt(x^2+1))
∫
9
x
3
√
x
2
+
1
dx
integral of (2x-3)/(sqrt(x^2+6x+4))
∫
2
x
−
3
√
x
2
+
6
x
+
4
dx
derivative of 13e^x
d
dx
(
1
3
e
x
)
tangent f(x)=((x^2))/(x-5),\at x=-3
tangent
f
(
x
)
=
(
x
2
)
x
−
5
,
at
x
=
−
3
laplace변환 0.001t
laplacetransform
0
.
0
0
1
t
ty^'=4y
ty
′
=
4
y
(x^2+1)y^'+4x(y-1)=0,y(0)=3
(
x
2
+
1
)
y
′
+
4
x
(
y
−
1
)
=
0
,
y
(
0
)
=
3
(dy)/(dx)+y^3x+8y=0
dy
dx
+
y
3
x
+
8
y
=
0
integral of sin^5(9x)
∫
sin
5
(
9
x
)
dx
derivative of-2/((x-1^2))
d
dx
(
−
2
(
x
−
1
)
2
)
sum from n=1 to infinity of 1/(8^n)
∑
n
=
1
∞
1
8
n
(dy)/(dt)=y(7-y)-49/4
dy
dt
=
y
(
7
−
y
)
−
4
9
4
derivative f(x)=x^2+6x
derivative
f
(
x
)
=
x
2
+
6
x
integral of 1/(sqrt(1-16x^2))
∫
1
√
1
−
1
6
x
2
dx
integral from 0 to 1 of e^{5x}-e^x
∫
0
1
e
5
x
−
e
x
dx
derivative e^{cot(4x)}
derivative
e
cot
(
4
x
)
integral of ((1+cos^2(x)))/(cos^2(x))
∫
(
1
+
cos
2
(
x
)
)
cos
2
(
x
)
dx
derivative (6x^2+8x+8x)/(sqrt(x))
derivative
6
x
2
+
8
x
+
8
x
√
x
(x^2)/(y^2-2)y^'= 1/(2y),y(1)=sqrt(3)
x
2
y
2
−
2
y
′
=
1
2
y
,
y
(
1
)
=
√
3
integral of (2x^4+3x^2-2x^{-3})/(x^2)
∫
2
x
4
+
3
x
2
−
2
x
−
3
x
2
dx
sum from n=1 to infinity of 1/(6n+5)
∑
n
=
1
∞
1
6
n
+
5
y^'=((y^2+2xy))/(x^2)
y
′
=
(
y
2
+
2
xy
)
x
2
integral of e^{3x}sin(3x)
∫
e
3
x
sin
(
3
x
)
dx
y^'= x/y ,y(0)=3
y
′
=
x
y
,
y
(
0
)
=
3
limit as x approaches-2 of 3x^2+7-1/x
lim
x
→
−
2
(
3
x
2
+
7
−
1
x
)
integral of 1/(1+(cos(x))^2)
∫
1
1
+
(
cos
(
x
)
)
2
dx
derivative of (18x+4x^2/((9+4x)^2))
d
dx
(
1
8
x
+
4
x
2
(
9
+
4
x
)
2
)
integral from 0 to 1 of 2+sqrt(1-x^2)
∫
0
1
2
+
√
1
−
x
2
dx
derivative of (1+x^{1/x})
d
dx
(
(
1
+
x
)
1
x
)
integral of sin(t^2)
∫
sin
(
t
2
)
dt
tangent f(x)=4x^2-5x,\at x=3
tangent
f
(
x
)
=
4
x
2
−
5
x
,
at
x
=
3
derivative f(x)=-4x
derivative
f
(
x
)
=
−
4
x
(\partial)/(\partial y)(t/(2y^4))
∂
∂
y
(
t
2
y
4
)
integral of xsin(5x^2)cos(6x^2)
∫
x
sin
(
5
x
2
)
cos
(
6
x
2
)
dx
(dy)/(dx)=x^2+y
dy
dx
=
x
2
+
y
derivative f(x)=x^3+2x^2+3x
derivative
f
(
x
)
=
x
3
+
2
x
2
+
3
x
integral of (x-1)/(x^2+2)
∫
x
−
1
x
2
+
2
dx
limit as x approaches 0 of ((7x^2-2x))/x
lim
x
→
0
(
(
7
x
2
−
2
x
)
x
)
laplace변환 1-cos(2t)
laplacetransform
1
−
cos
(
2
t
)
뿌리 xsin(y)
roots
x
sin
(
y
)
f^'(x)= x/8-1
f
′
(
x
)
=
x
8
−
1
경사지 y=2-x^3,P(1,1)
slope
y
=
2
−
x
3
,
P
(
1
,
1
)
(\partial}{\partial x}(\frac{xe^x)/y)
∂
∂
x
(
xe
x
y
)
implicit (dy)/(dx),e x/y =8x-y
implicit
dy
dx
,
e
x
y
=
8
x
−
y
25y^{'''}+40y^{''}+16y^'=0
2
5
y
′
′
′
+
4
0
y
′
′
+
1
6
y
′
=
0
derivative of 3arcsin(x^3)
d
dx
(
3
arcsin
(
x
3
)
)
derivative of e^{2x}(2-x)
d
dx
(
e
2
x
(
2
−
x
)
)
integral of (3x^2-2)/(x^2-4x-12)
∫
3
x
2
−
2
x
2
−
4
x
−
1
2
dx
derivative of arcsin(x^{100})
d
dx
(
arcsin
(
x
1
0
0
)
)
inverse라플라스 (20)/(2x^2+9x+30)
inverselaplace
2
0
2
x
2
+
9
x
+
3
0
laplace변환 e^{3t}sin(6t)
laplacetransform
e
3
t
sin
(
6
t
)
경사지 y=sqrt(x)
slope
y
=
√
x
(\partial)/(\partial w)(xe^w)
∂
∂
w
(
xe
w
)
derivative (log_{2}(x))/x
derivative
log
2
(
x
)
x
integral from 0 to 6 of xsqrt(36-x^2)
∫
0
6
x
√
3
6
−
x
2
dx
integral of-x^4ln(x)
∫
−
x
4
ln
(
x
)
dx
t^2y^{''}-ty^'+y=0
t
2
y
′
′
−
ty
′
+
y
=
0
(d^2)/(dx^2)((x^3)/(x^2-4))
d
2
dx
2
(
x
3
x
2
−
4
)
integral of cos(1)
∫
cos
(
1
)
dx
integral of (18x^3-36x^2+5)/(x^2-2x)
∫
1
8
x
3
−
3
6
x
2
+
5
x
2
−
2
x
dx
(d^3)/(dx^3)(xe^x)
d
3
dx
3
(
xe
x
)
integral of x(3x+8)^5
∫
x
(
3
x
+
8
)
5
dx
integral of 4tan(x)sec^5(x)
∫
4
tan
(
x
)
sec
5
(
x
)
dx
derivative of-5x^4+4x^3-20x-20
d
dx
(
−
5
x
4
+
4
x
3
−
2
0
x
−
2
0
)
sum from n=1 to infinity of cos((10)/n)
∑
n
=
1
∞
cos
(
1
0
n
)
tangent y=x^2-6x,(5,-5)
tangent
y
=
x
2
−
6
x
,
(
5
,
−
5
)
integral of (x^2-2)^3
∫
(
x
2
−
2
)
3
dx
integral of tan^3(x)cos(x)
∫
tan
3
(
x
)
cos
(
x
)
dx
동등성 (tan^3(x))/(2x+1)
parity
tan
3
(
x
)
2
x
+
1
(\partial)/(\partial y)(xyzsqrt(x))
∂
∂
y
(
xyz
√
x
)
maclaurin-ln(1-x^2)
maclaurin
−
ln
(
1
−
x
2
)
derivative of x/(753600x^2+900)
d
dx
(
x
7
5
3
6
0
0
x
2
+
9
0
0
)
지역 y=4x+4,y=5x+5,x=2
area
y
=
4
x
+
4
,
y
=
5
x
+
5
,
x
=
2
integral of (2x-1)/(x^2(x+3))
∫
2
x
−
1
x
2
(
x
+
3
)
dx
limit as x approaches 0 of ((2.7^x-1))/x
lim
x
→
0
(
(
2
.
7
x
−
1
)
x
)
d/(dt)(12t-40pisin(pit))
d
dt
(
1
2
t
−
4
0
π
sin
(
π
t
)
)
integral from 0 to 8pi of t^2sin(2t)
∫
0
8
π
t
2
sin
(
2
t
)
dt
integral of ax+b
∫
ax
+
bdx
integral of (e^x(x-1)-e^x)/((x-1)^2)
∫
e
x
(
x
−
1
)
−
e
x
(
x
−
1
)
2
dx
derivative tan(1/x)
derivative
tan
(
1
x
)
테일러 1/(2-x),1
taylor
1
2
−
x
,
1
derivative of (3x^3+x+2/(5x^2+1))
d
dx
(
3
x
3
+
x
+
2
5
x
2
+
1
)
(\partial)/(\partial x)(7ln(x^2+y^2))
∂
∂
x
(
7
ln
(
x
2
+
y
2
)
)
sum from n=5 to infinity of 1/n
∑
n
=
5
∞
1
n
x^{''}-5x^'+6x=e^t
x
′
′
−
5
x
′
+
6
x
=
e
t
derivative of-7/(x^8)
d
dx
(
−
7
x
8
)
1
..
1417
1418
1419
1420
1421
..
2459