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일반적인 미적분학 문제
derivative of 12arccot(ax^2)
d
dx
(
1
2
arccot
(
ax
2
)
)
integral of sin(2t)
∫
sin
(
2
t
)
dt
integral from 0 to pi/4 of tan^5(x)
∫
0
π
4
tan
5
(
x
)
dx
integral from 0 to pi of 19sin^2(4x)
∫
0
π
1
9
sin
2
(
4
x
)
dx
integral of t+4
∫
t
+
4
dt
tangent f(x)=sin(sin(x)),\at x=3pi,0
tangent
f
(
x
)
=
sin
(
sin
(
x
)
)
,
at
x
=
3
π
,
0
derivative a^x
derivative
a
x
(3x^2y^2+y)dx+(2x^3y+x)dy=0
(
3
x
2
y
2
+
y
)
dx
+
(
2
x
3
y
+
x
)
dy
=
0
지역 y=e^x,y=e^{-4x},x=ln(3)
area
y
=
e
x
,
y
=
e
−
4
x
,
x
=
ln
(
3
)
integral of xsqrt(x+4)
∫
x
√
x
+
4
dx
integral from 0 to pi/6 of cos^3(x)
∫
0
π
6
cos
3
(
x
)
dx
integral of (5x^4+3x^2+2x)
∫
(
5
x
4
+
3
x
2
+
2
x
)
dx
integral of 16xln(7x)
∫
1
6
x
ln
(
7
x
)
dx
integral from 0 to pi/2 of 11sin^2(2x)
∫
0
π
2
1
1
sin
2
(
2
x
)
dx
integral of (sqrt(a^2-x^2))/x
∫
√
a
2
−
x
2
x
dx
xy^'+2y=4x^2
xy
′
+
2
y
=
4
x
2
derivative of (-e^{1/x}/(x^2))
d
dx
(
−
e
1
x
x
2
)
y^{''}+5y^'+6y=2x
y
′
′
+
5
y
′
+
6
y
=
2
x
derivative of x^3*sin^2(5x)
d
dx
(
x
3
·
sin
2
(
5
x
)
)
limit as x approaches 1 of 1/(sqrt(1-x))
lim
x
→
1
(
1
√
1
−
x
)
integral of (x+1/x)^2(x-1/x)^2-x+1/x
∫
(
x
+
1
x
)
2
(
x
−
1
x
)
2
−
x
+
1
x
dx
(\partial)/(\partial y)(arctan(xsqrt(t)))
∂
∂
y
(
arctan
(
x
√
t
)
)
(\partial)/(\partial x)((sin(x))/(sin(y)))
∂
∂
x
(
sin
(
x
)
sin
(
y
)
)
integral from 0 to 4 of (4-x)sqrt(x)
∫
0
4
(
4
−
x
)
√
x
dx
integral from 0 to 4 of pi(1/(x+3))^2
∫
0
4
π
(
1
x
+
3
)
2
dx
integral from 0 to x of t^2cos(t)
∫
0
x
t
2
cos
(
t
)
dt
integral of 3x-x^2
∫
3
x
−
x
2
dx
derivative (2x-sqrt(x))(5x+2)
derivative
(
2
x
−
√
x
)
(
5
x
+
2
)
tangent f(x)=x^3-2x+1,(2,5)
tangent
f
(
x
)
=
x
3
−
2
x
+
1
,
(
2
,
5
)
d/(dt)(sqrt(3t))
d
dt
(
√
3
t
)
단순화 16ln(x^2)-x^2
simplify
1
6
ln
(
x
2
)
−
x
2
(\partial)/(\partial x)(e^{4xy}*4y)
∂
∂
x
(
e
4
xy
·
4
y
)
derivative of (x^n/n)
d
dx
(
x
n
n
)
derivative of e^{-x}arcsin(4e^x)
d
dx
(
e
−
x
arcsin
(
4
e
x
)
)
derivative of e^{xcos(x})
d
dx
(
e
x
cos
(
x
)
)
y^'+y^{1/2}=0
y
′
+
y
1
2
=
0
(sin^2(t))^'
(
sin
2
(
t
)
)
′
derivative of-18sin(3x)
d
dx
(
−
1
8
sin
(
3
x
)
)
limit as x approaches 0+of x^4
lim
x
→
0
+
(
x
4
)
limit as x approaches-3 of (x+1)/(x+3)
lim
x
→
−
3
(
x
+
1
x
+
3
)
경사지 (19,3),(20,3)
slope
(
1
9
,
3
)
,
(
2
0
,
3
)
integral of (x-2/x)^2
∫
(
x
−
2
x
)
2
dx
derivative of 14sin(x)
d
dx
(
1
4
sin
(
x
)
)
limit as x approaches-2 of (x^3)/(x-2)
lim
x
→
−
2
(
x
3
x
−
2
)
integral of 4y^3
∫
4
y
3
dy
derivative f(x)=2x-1
derivative
f
(
x
)
=
2
x
−
1
integral of 12e^{3x}
∫
1
2
e
3
x
dx
integral of (1-t)(2+t^2)
∫
(
1
−
t
)
(
2
+
t
2
)
dt
(d^2)/(dx^2)(cot(2x)+3x^2)
d
2
dx
2
(
cot
(
2
x
)
+
3
x
2
)
derivative of log_{2}(2x)
d
dx
(
log
2
(
2
x
)
)
derivative of arccot(x/2)
d
dx
(
arccot
(
x
2
)
)
tangent f(x)=7-x^2
tangent
f
(
x
)
=
7
−
x
2
integral from 0 to 20 of 1
∫
0
2
0
1
integral of 5x^2sin(pix)
∫
5
x
2
sin
(
π
x
)
dx
derivative of ln|x+1|
d
dx
(
ln
|
x
+
1
|
)
derivative of sqrt(x^2-\sqrt{2x)}
d
dx
(
√
x
2
−
√
2
x
)
derivative of (x-4/(3x-x^2))
d
dx
(
x
−
4
3
x
−
x
2
)
integral of sqrt(2+2cos(x))
∫
√
2
+
2
cos
(
x
)
dx
integral of (u^2)/(1+u^2)
∫
u
2
1
+
u
2
du
지역 y=2x^2,y=8x^2,5x+y=3
area
y
=
2
x
2
,
y
=
8
x
2
,
5
x
+
y
=
3
derivative of 2e^x+xe^x
d
dx
(
2
e
x
+
xe
x
)
tangent f(x)=8+5x^2-2x^3,(2,12)
tangent
f
(
x
)
=
8
+
5
x
2
−
2
x
3
,
(
2
,
1
2
)
integral from 7 to 9 of 7/((x-8)^{10)}
∫
7
9
7
(
x
−
8
)
1
0
dx
integral of ((x^2-x+42))/(x^3+7x)
∫
(
x
2
−
x
+
4
2
)
x
3
+
7
x
dx
derivative of-(x+1(x-1)^2)
d
dx
(
−
(
x
+
1
)
(
x
−
1
)
2
)
derivative f(x)=((x+3)/(x-3))^5
derivative
f
(
x
)
=
(
x
+
3
x
−
3
)
5
integral of (x+1/(x^3))
∫
(
x
+
1
x
3
)
dx
sum from n=1 to infinity of 1/2 (0.3)^n
∑
n
=
1
∞
1
2
(
0
.
3
)
n
tangent f(x)= 3/x ,\at x=-5
tangent
f
(
x
)
=
3
x
,
at
x
=
−
5
inverse라플라스 ((s^2))/(s^2+1)
inverselaplace
(
s
2
)
s
2
+
1
integral of (1-x^2)/(1-2x)
∫
1
−
x
2
1
−
2
x
dx
integral from 1/2 to 3 of 16xln(2x)
∫
1
2
3
1
6
x
ln
(
2
x
)
dx
(\partial)/(\partial x)(ln(r/(ro)))
∂
∂
x
(
ln
(
r
ro
)
)
(x^2+y)(dy)/(dx)-y-3x^2=2y
(
x
2
+
y
)
dy
dx
−
y
−
3
x
2
=
2
y
integral of sqrt(x+13)
∫
√
x
+
1
3
dx
limit as x approaches 2 of (5x+2)/(x-2)
lim
x
→
2
(
5
x
+
2
x
−
2
)
derivative of e^{jx}
d
dx
(
e
jx
)
y^'=sqrt(y^2-9)
y
′
=
√
y
2
−
9
테일러 1/(x^2+1)
taylor
1
x
2
+
1
integral of cos(x)(8+4sin^2(x))
∫
cos
(
x
)
(
8
+
4
sin
2
(
x
)
)
dx
derivative y=cos(x^3)
derivative
y
=
cos
(
x
3
)
limit as x approaches 5 of (x^2-3x-10)/(x-5)
lim
x
→
5
(
x
2
−
3
x
−
1
0
x
−
5
)
derivative of (7x-8^5)
d
dx
(
(
7
x
−
8
)
5
)
(\partial)/(\partial x)(ln(2ye^{xy}))
∂
∂
x
(
ln
(
2
ye
xy
)
)
derivative of (sqrt(x+1)/(sqrt(x-1)))
d
dx
(
√
x
+
1
√
x
−
1
)
derivative of x^{x^x}
d
dx
(
x
x
x
)
limit as x approaches infinity of (2^{-x}-2^x)/(2^{-x)+2^x}
lim
x
→
∞
(
2
−
x
−
2
x
2
−
x
+
2
x
)
integral of (2x)/(3x^2-4)
∫
2
x
3
x
2
−
4
dx
derivative 3/(5+x^2)
derivative
3
5
+
x
2
sum from n=1 to infinity of ((-2)/3)^n
∑
n
=
1
∞
(
−
2
3
)
n
integral of 9xln(x)
∫
9
x
ln
(
x
)
dx
limit as x approaches-2 of 4^xcos(pix)
lim
x
→
−
2
(
4
x
cos
(
π
x
)
)
테일러 e^{3x^3}
taylor
e
3
x
3
derivative y=sqrt(x)(x-8)
derivative
y
=
√
x
(
x
−
8
)
derivative 2^{3x+1}
derivative
2
3
x
+
1
d/(d{r)}(({r})/(sqrt({r)^2+1)})
d
d
r
(
r
√
r
2
+
1
)
normal f(x)=x*5^x,\at x=1
normal
f
(
x
)
=
x
·
5
x
,
at
x
=
1
integral of sqrt(1-x)
∫
√
1
−
x
dx
y^{''}-3y^'+2y=2e^3t
y
′
′
−
3
y
′
+
2
y
=
2
e
3
t
limit as x approaches infinity of 8/x
lim
x
→
∞
(
8
x
)
1
..
1380
1381
1382
1383
1384
..
2459