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일반적인 미적분학 문제
y^'=3y+7,y(0)=4
y
′
=
3
y
+
7
,
y
(
0
)
=
4
laplace변환 t^2+2
laplacetransform
t
2
+
2
integral of 7xe^{4x}
∫
7
xe
4
x
dx
xyy^'+y^2=2x
xyy
′
+
y
2
=
2
x
integral of 3x^3+3x-3
∫
3
x
3
+
3
x
−
3
dx
integral from 0 to 8 of xsqrt(64-x^2)
∫
0
8
x
√
6
4
−
x
2
dx
integral of sin(pi)tcos(pi)t
∫
sin
(
π
)
t
cos
(
π
)
tdt
derivative (4x^2-5x+1)/x
derivative
4
x
2
−
5
x
+
1
x
integral of-4x^{-1}
∫
−
4
x
−
1
dx
laplace변환 5cos(2t-1)
laplacetransform
5
cos
(
2
t
−
1
)
derivative of (x^2/(x^3+1))
d
dx
(
x
2
x
3
+
1
)
derivative 1/(x^{10)}
derivative
1
x
1
0
derivative of 4/(x^7-e^{-8x})
d
dx
(
4
x
7
−
e
−
8
x
)
integral of x/((x+1)(x+2))
∫
x
(
x
+
1
)
(
x
+
2
)
dx
(\partial)/(\partial x)(1.015sqrt(E(m,x)bh^3m^{-1)L^{-4}})
∂
∂
x
(
1
.
0
1
5
√
E
(
m
,
x
)
bh
3
m
−
1
L
−
4
)
derivative of cot^4(x-csc^4(x))
d
dx
(
cot
4
(
x
)
−
csc
4
(
x
)
)
derivative y=2^{2x}
derivative
y
=
2
2
x
derivative y=e^{in(x^2+1)}
derivative
y
=
e
in
(
x
2
+
1
)
limit as x approaches 2 of (\sqrt[3]{3x^2-2x-8})/((x+2)^3)
lim
x
→
2
(
3
√
3
x
2
−
2
x
−
8
(
x
+
2
)
3
)
limit as x approaches 9 of x-7
lim
x
→
9
(
x
−
7
)
테일러 1/((1+x^2))
taylor
1
(
1
+
x
2
)
integral of (x^2)/(sqrt(9-x^2))
∫
x
2
√
9
−
x
2
dx
derivative of ln(sqrt(sin(3^{x^2)}))
d
dx
(
ln
(
√
sin
(
3
x
2
)
)
)
(x^2+y^2)dx-2xydy=0
(
x
2
+
y
2
)
dx
−
2
xydy
=
0
derivative 1-ln(3x)
derivative
1
−
ln
(
3
x
)
tangent f(x)=3x^2,\at x=1
tangent
f
(
x
)
=
3
x
2
,
at
x
=
1
derivative of x(4x+1^{1/3})
d
dx
(
x
(
4
x
+
1
)
1
3
)
integral of t/(t-2)
∫
t
t
−
2
dt
integral of 1/(x-c)
∫
1
x
−
c
dx
integral of (x^4-2x^2+1)/(x^3)
∫
x
4
−
2
x
2
+
1
x
3
dx
limit as x approaches 1-of 4x-5
lim
x
→
1
−
(
4
x
−
5
)
derivative 2/(3x)
derivative
2
3
x
integral of-(12)/(x^{13)}
∫
−
1
2
x
1
3
dx
tangent y=sqrt(x+3),(6,3)
tangent
y
=
√
x
+
3
,
(
6
,
3
)
(dy)/(dx)=2e^{x-y}
dy
dx
=
2
e
x
−
y
integral of (x^3)/(x^4-x^2+2)
∫
x
3
x
4
−
x
2
+
2
dx
derivative f(x)=(3x+7)e^x
derivative
f
(
x
)
=
(
3
x
+
7
)
e
x
derivative sqrt(x^2+10)
derivative
√
x
2
+
1
0
derivative of 1.394(1.006^x)
d
dx
(
1
.
3
9
4
(
1
.
0
0
6
)
x
)
integral of 1/((x^2-196)^{3/2)}
∫
1
(
x
2
−
1
9
6
)
3
2
dx
derivative of arccot(sqrt(4x))
d
dx
(
arccot
(
√
4
x
)
)
derivative of y^2(2-x-x^3)
d
dx
(
y
2
(
2
−
x
)
−
x
3
)
derivative x^2+2
derivative
x
2
+
2
y^'+3y=0,y(0)=0
y
′
+
3
y
=
0
,
y
(
0
)
=
0
(\partial)/(\partial x)(e^{(y+1)x})
∂
∂
x
(
e
(
y
+
1
)
x
)
derivative f(x)=(x^3+9x^2+x-8)/x
derivative
f
(
x
)
=
x
3
+
9
x
2
+
x
−
8
x
(\partial)/(\partial x)(sqrt(4ax))
∂
∂
x
(
√
4
ax
)
derivative of (x^2+6^9)
d
dx
(
(
x
2
+
6
)
9
)
derivative of cosh(4x)
d
dx
(
cosh
(
4
x
)
)
integral of (2x^2+7x-8)/(x-7)
∫
2
x
2
+
7
x
−
8
x
−
7
dx
(\partial)/(\partial y)(e^{2x+3y})
∂
∂
y
(
e
2
x
+
3
y
)
limit as x approaches 1+of x+2
lim
x
→
1
+
(
x
+
2
)
integral of x/((x-1)(x^2+2x+2))
∫
x
(
x
−
1
)
(
x
2
+
2
x
+
2
)
dx
derivative of x*e^{2x}
d
dx
(
x
·
e
2
x
)
sum from n=1 to infinity of-30n
∑
n
=
1
∞
−
3
0
n
(\partial)/(\partial t)(cos(xt)+3tx^2)
∂
∂
t
(
cos
(
xt
)
+
3
tx
2
)
integral of (sin(x))/(cos^2(x)+cos(x)-6)
∫
sin
(
x
)
cos
2
(
x
)
+
cos
(
x
)
−
6
dx
tangent f(x)=x^2-3x+5,\at x=1
tangent
f
(
x
)
=
x
2
−
3
x
+
5
,
at
x
=
1
sum from n=0 to infinity of n^3
∑
n
=
0
∞
n
3
tangent f(x)=-7x^3-8x^2-5x,\at x=-3
tangent
f
(
x
)
=
−
7
x
3
−
8
x
2
−
5
x
,
at
x
=
−
3
integral of (sin(2x))/(1+cos(2x))
∫
sin
(
2
x
)
1
+
cos
(
2
x
)
dx
integral of 1/((7x-1)sqrt(49x^2-14x))
∫
1
(
7
x
−
1
)
√
4
9
x
2
−
1
4
x
dx
integral from 1 to 2 of e^{1/x}
∫
1
2
e
1
x
dx
integral of ((2y)/((x^2+y^2)^2))
∫
(
2
y
(
x
2
+
y
2
)
2
)
dy
derivative f(x)=4x^{-3/8}
derivative
f
(
x
)
=
4
x
−
3
8
derivative of (x^7/7-x^3-3/x+1/(5x^5))
d
dx
(
x
7
7
−
x
3
−
3
x
+
1
5
x
5
)
limit as x approaches 0 of (sin(3x^2))/x
lim
x
→
0
(
sin
(
3
x
2
)
x
)
integral of sin(3x)sin(x)
∫
sin
(
3
x
)
sin
(
x
)
dx
integral from-2 to 3 of (4x^2+8)-(3x+2)
∫
−
2
3
(
4
x
2
+
8
)
−
(
3
x
+
2
)
dx
integral of 7sqrt(x^5)
∫
7
√
x
5
dx
derivative of 4*(sqrt(x^2+3x))
d
dx
(
4
·
(
√
x
2
+
3
x
)
)
derivative of 4sec^2(2x)
d
dx
(
4
sec
2
(
2
x
)
)
integral of ((1-sqrt(t))^2)/t
∫
(
1
−
√
t
)
2
t
dt
d/(dl)(2pisqrt(l/(9.8)))
d
dl
(
2
π
√
l
9
.
8
)
(dy)/(dx)+y/(x(x+1))=x+1
dy
dx
+
y
x
(
x
+
1
)
=
x
+
1
derivative of (x^2+3x^2)
d
dx
(
(
x
2
+
3
x
)
2
)
derivative (16x^3)/3-4x^2+6x-13
derivative
1
6
x
3
3
−
4
x
2
+
6
x
−
1
3
integral from 0 to 3 of (3x+2)
∫
0
3
(
3
x
+
2
)
dx
integral of tan(x
∫
tan
(
d
)
xdx
(\partial)/(\partial x)((x+1)^2+2(y-1)^2)
∂
∂
x
(
(
x
+
1
)
2
+
2
(
y
−
1
)
2
)
x^2y^'-3xy=4x^6
x
2
y
′
−
3
xy
=
4
x
6
integral of sqrt(16-x)
∫
√
1
6
−
x
dx
integral of (x^5)/(x^6-4)
∫
x
5
x
6
−
4
dx
derivative of csc(xtan(x))
d
dx
(
csc
(
x
)
tan
(
x
)
)
4sin(t)(dy)/(dt)+4ycos(t)=cos(t)sin^4(t)
4
sin
(
t
)
dy
dt
+
4
y
cos
(
t
)
=
cos
(
t
)
sin
4
(
t
)
y^{''}-3y^'+2y=e^{3x}+x^2
y
′
′
−
3
y
′
+
2
y
=
e
3
x
+
x
2
limit as x approaches 0 of x^2-2
lim
x
→
0
(
x
2
−
2
)
테일러 3/(x^2-x-2),1
taylor
3
x
2
−
x
−
2
,
1
(\partial)/(\partial y)(sqrt(4-x^2-6y^2))
∂
∂
y
(
√
4
−
x
2
−
6
y
2
)
(8t+y+2)dt-dy=0
(
8
t
+
y
+
2
)
dt
−
dy
=
0
derivative (csc(x))/(1+csc(x))
derivative
csc
(
x
)
1
+
csc
(
x
)
integral of x^2sqrt(1+2x)
∫
x
2
√
1
+
2
x
dx
integral of x^2e^{-ax}
∫
x
2
e
−
ax
dx
integral of cos(x/9)
∫
cos
(
x
9
)
dx
경사지intercept (3,-29),(-1,7)
slopeintercept
(
3
,
−
2
9
)
,
(
−
1
,
7
)
y^{''}+6y^'+9y=e^{-3t}
y
′
′
+
6
y
′
+
9
y
=
e
−
3
t
integral from 1 to 5 of (ln(x))/x
∫
1
5
ln
(
x
)
x
dx
integral from-infinity to 0 of 1/(5-9x)
∫
−
∞
0
1
5
−
9
x
dx
laplace변환 3e^{4t}
laplacetransform
3
e
4
t
4y^{''}-4y^'-3y=cos(2x)
4
y
′
′
−
4
y
′
−
3
y
=
cos
(
2
x
)
1
..
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1196
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..
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