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일반적인 미적분학 문제
integral from-1 to 1 of e^{u+1}
∫
−
1
1
e
u
+
1
du
limit as x approaches 2 of (x^2+1)/(x-2)
lim
x
→
2
(
x
2
+
1
x
−
2
)
(\partial)/(\partial x)(x-(2y+6x)/(13))
∂
∂
x
(
x
−
2
y
+
6
x
1
3
)
derivative y=ln(x/(1+x^2))
derivative
y
=
ln
(
x
1
+
x
2
)
4/10 x^2dy-13dx=0
4
1
0
x
2
dy
−
1
3
dx
=
0
inverse라플라스 3/((s-2)^2)
inverselaplace
3
(
s
−
2
)
2
(\partial)/(\partial x)(arctan(7xsqrt(t)))
∂
∂
x
(
arctan
(
7
x
√
t
)
)
integral of-2sin(2x)
∫
−
2
sin
(
2
x
)
dx
integral of (sin(sqrt(θ)))/(sqrt(θ))
∫
sin
(
√
θ
)
√
θ
d
θ
integral of (3e^{2x})/(e^{2x)+13e^x+40}
∫
3
e
2
x
e
2
x
+
1
3
e
x
+
4
0
dx
limit as x approaches 0 of-x^2+3x+a
lim
x
→
0
(
−
x
2
+
3
x
+
a
)
(dh)/(dt)=0.3(5-h)
dh
dt
=
0
.
3
(
5
−
h
)
integral of 36t(9t^2-7)^3
∫
3
6
t
(
9
t
2
−
7
)
3
dt
laplace변환 4sin(2t)
laplacetransform
4
sin
(
2
t
)
integral from-1 to 1 of e^{-x}cos(npix)
∫
−
1
1
e
−
x
cos
(
n
π
x
)
dx
integral of sin^7(xco)s^3x
∫
sin
7
(
xco
)
s
3
xdx
(2x+yx^{-1})dx+(xy-1)dy=0
(
2
x
+
yx
−
1
)
dx
+
(
xy
−
1
)
dy
=
0
derivative of ln|tan(x/2 |)
d
dx
(
ln
|
tan
(
x
2
)
|
)
derivative of (sqrt(9-x^2)/(32x))
d
dx
(
√
9
−
x
2
3
2
x
)
derivative s(t)=14t^2+840t
derivative
s
(
t
)
=
1
4
t
2
+
8
4
0
t
단순화 0
simplify
0
limit as x approaches 0 of (0*x^6)/(x^9)
lim
x
→
0
(
0
·
x
6
x
9
)
3y^{''}+75y=0
3
y
′
′
+
7
5
y
=
0
derivative f(x)=4-(20)/(x^3)+3/(x^5)
derivative
f
(
x
)
=
4
−
2
0
x
3
+
3
x
5
derivative of log_{6}(x^2-3x)
d
dx
(
log
6
(
x
2
−
3
x
)
)
derivative f(x)=-16x^{3/2}+6x^{1.7}+x
derivative
f
(
x
)
=
−
1
6
x
3
2
+
6
x
1
.
7
+
x
derivative of (cos(x)^x)
d
dx
(
(
cos
(
x
)
)
x
)
tangent ((x-1))/(x+1)
tangent
(
x
−
1
)
x
+
1
tangent-7x^4+11x^2-4
tangent
−
7
x
4
+
1
1
x
2
−
4
integral of (x^2)/((1+9x^2)^{3/2)}
∫
x
2
(
1
+
9
x
2
)
3
2
dx
limit as x approaches 6 of (x-2)^2
lim
x
→
6
(
(
x
−
2
)
2
)
4((dy)/(dx))-(y)-x=0
4
(
dy
dx
)
−
(
y
)
−
x
=
0
(dy)/(dx)x+xy=1-y
dy
dx
x
+
xy
=
1
−
y
tangent y=x^2+12x-3
tangent
y
=
x
2
+
1
2
x
−
3
integral of x^{2n-2}
∫
x
2
n
−
2
dx
derivative y=(8x^2+4x+8)/(sqrt(x))
derivative
y
=
8
x
2
+
4
x
+
8
√
x
integral from-1 to 1 of t^3(1+t^4)^3
∫
−
1
1
t
3
(
1
+
t
4
)
3
dt
derivative of (e^x/(ln(x)))
d
dx
(
e
x
ln
(
x
)
)
integral of 1-x/2
∫
1
−
x
2
dx
integral of (ln(x))/(2x^2)
∫
ln
(
x
)
2
x
2
dx
derivative 5(-csc^2(x)+sec^2(x))
derivative
5
(
−
csc
2
(
x
)
+
sec
2
(
x
)
)
derivative 4/(sqrt(u))
derivative
4
√
u
laplace변환 1-e^{-,\at}
laplacetransform
1
−
e
−
,
at
integral of 1/((x+2)^3)
∫
1
(
x
+
2
)
3
dx
derivative f(x)= x/(x+3)
derivative
f
(
x
)
=
x
x
+
3
(\partial)/(\partial x)(e^{ikx})
∂
∂
x
(
e
ikx
)
integral of (1+sin^2(x))
∫
(
1
+
sin
2
(
x
)
)
dx
derivative of ln((x-4^3))
d
dx
(
ln
(
(
x
−
4
)
3
)
)
integral of x*sqrt(x^2+5)
∫
x
·
√
x
2
+
5
dx
테일러 ln(4-x)
taylor
ln
(
4
−
x
)
(\partial)/(\partial z)(ln(1+x^2+e^y+z))
∂
∂
z
(
ln
(
1
+
x
2
+
e
y
+
z
)
)
limit as x approaches 0 of 1/(1-e^{-x)}
lim
x
→
0
(
1
1
−
e
−
x
)
inverse라플라스 s+3
inverselaplace
s
+
3
derivative f(x)=(x 1/9)/2
derivative
f
(
x
)
=
x
1
9
2
integral of (2cos(x)+4sin(x)+6)
∫
(
2
cos
(
x
)
+
4
sin
(
x
)
+
6
)
dx
integral from 1 to 2 of (x^3+3x^6)/(x^4)
∫
1
2
x
3
+
3
x
6
x
4
dx
integral from 0 to 2 of 5x
∫
0
2
5
xdx
integral of 1/(sin(x)+cos(x)-1)
∫
1
sin
(
x
)
+
cos
(
x
)
−
1
dx
limit as x approaches-infinity of a+1/x
lim
x
→
−
∞
(
a
+
1
x
)
derivative (7x^2+6x)(7x-8)
derivative
(
7
x
2
+
6
x
)
(
7
x
−
8
)
derivative f(x)=x^2+2x
derivative
f
(
x
)
=
x
2
+
2
x
derivative of (x^2+6x+9/(x-3))
d
dx
(
x
2
+
6
x
+
9
x
−
3
)
derivative f(x)=(2sqrt(x)-5)(3x+1)
derivative
f
(
x
)
=
(
2
√
x
−
5
)
(
3
x
+
1
)
y^'=(xy^3)/(sqrt(1+x^2)),y(0)=1
y
′
=
xy
3
√
1
+
x
2
,
y
(
0
)
=
1
(\partial)/(\partial x)(((3x-4y))/(-x+6y))
∂
∂
x
(
(
3
x
−
4
y
)
−
x
+
6
y
)
derivative-x/(9y)
derivative
−
x
9
y
경사지 (8,1),(0,-3)
slope
(
8
,
1
)
,
(
0
,
−
3
)
limit as x approaches-infinity of 1/(-x)
lim
x
→
−
∞
(
1
−
x
)
d/(dθ)(θ+cos(θ))
d
d
θ
(
θ
+
cos
(
θ
)
)
limit as x approaches 2 of x/(x^2-2x)
lim
x
→
2
(
x
x
2
−
2
x
)
(\partial)/(\partial x)((-x^4+7x^2+3y)^6)
∂
∂
x
(
(
−
x
4
+
7
x
2
+
3
y
)
6
)
(y-xy+x-1)dx+x^2dy=0
(
y
−
xy
+
x
−
1
)
dx
+
x
2
dy
=
0
integral of (sqrt(x+49))/x
∫
√
x
+
4
9
x
dx
integral of (x^3(1))/(sqrt(1-x^8))
∫
x
3
(
1
)
√
1
−
x
8
dx
d/(dt)(-e^{-t}sin(t)+e^{-t}cos(t))
d
dt
(
−
e
−
t
sin
(
t
)
+
e
−
t
cos
(
t
)
)
derivative (2x^2)/5
derivative
2
x
2
5
limit as x approaches 0 of (a^x-1)/x
lim
x
→
0
(
a
x
−
1
x
)
integral of 2x(x^2+4)^3
∫
2
x
(
x
2
+
4
)
3
dx
derivative of (x-1^{-1})
d
dx
(
(
x
−
1
)
−
1
)
integral of 1/(e^xsqrt(1-e^{2x))}
∫
1
e
x
√
1
−
e
2
x
dx
f(x)=sin^2(x/2)
f
(
x
)
=
sin
2
(
x
2
)
x*(dy)/(dx)+(11+x)y=e^{-x}
x
·
dy
dx
+
(
1
1
+
x
)
y
=
e
−
x
integral from 0 to x^2 of sin(t)
∫
0
x
2
sin
(
t
)
dt
derivative of (x^{3/2}/3-x^{1/2})
d
dx
(
x
3
2
3
−
x
1
2
)
derivative 7/(r^3)
derivative
7
r
3
derivative f(t)=8tsin(pit)
derivative
f
(
t
)
=
8
t
sin
(
π
t
)
derivative of x^{2n}
d
dx
(
x
2
n
)
derivative of 1/(9-x^2)
d
dx
(
1
9
−
x
2
)
integral from 0 to t of e^{-2x}
∫
0
t
e
−
2
x
dx
integral of e^{-st}(t-2)^2
∫
e
−
st
(
t
−
2
)
2
dt
integral from x to y of (t^2-1)
∫
x
y
(
t
2
−
1
)
dt
f^'(x)=x^{-3}+pix^2-sqrt(2)
f
′
(
x
)
=
x
−
3
+
π
x
2
−
√
2
derivative f(2)=10-3x
derivative
f
(
2
)
=
1
0
−
3
x
limit as x approaches 2+of 2x
lim
x
→
2
+
(
2
x
)
integral of e^{x^3}(3x^2)
∫
e
x
3
(
3
x
2
)
dx
integral of sqrt(cos(x))sin^3(x)
∫
√
cos
(
x
)
sin
3
(
x
)
dx
(3y^2+2xy)dx-(2xy+x^2)dy=0
(
3
y
2
+
2
xy
)
dx
−
(
2
xy
+
x
2
)
dy
=
0
(\partial)/(\partial x)(|4x^2-6yx|)
∂
∂
x
(
|
4
x
2
−
6
yx
|
)
limit as x approaches 2-of 3ln(x)
lim
x
→
2
−
(
3
ln
(
x
)
)
integral of 4/(x^2-16)
∫
4
x
2
−
1
6
dx
1
..
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1162
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