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일반적인 미적분학 문제
integral from 2 to 5 of t^4ln(2t)
∫
2
5
t
4
ln
(
2
t
)
dt
limit as x approaches 0 of (1+4/(x^4))^x
lim
x
→
0
(
(
1
+
4
x
4
)
x
)
((-9x^2+12x+24)/((x^2-5x-6)^2))^'
(
−
9
x
2
+
1
2
x
+
2
4
(
x
2
−
5
x
−
6
)
2
)
′
integral of ((x^3+36))/(x^2+36)
∫
(
x
3
+
3
6
)
x
2
+
3
6
dx
integral of 4cos(2θ)
∫
4
cos
(
2
θ
)
d
θ
derivative of 2^{(3x})
d
dx
(
2
(
3
x
)
)
integral of r^2cos(θ)
∫
r
2
cos
(
θ
)
dr
derivative of sqrt(9+\sqrt{6x)}
d
dx
(
√
9
+
√
6
x
)
derivative of 4-2x^2
d
dx
(
4
−
2
x
2
)
derivative x^2e^x-2xe^x+7e^x
derivative
x
2
e
x
−
2
xe
x
+
7
e
x
limit as x approaches-1 of x^2+3x+2
lim
x
→
−
1
(
x
2
+
3
x
+
2
)
3y^{''}-14y^'+8y=0
3
y
′
′
−
1
4
y
′
+
8
y
=
0
derivative of (x^3/(4-x^2))
d
dx
(
x
3
4
−
x
2
)
derivative of sec(xtan(x)sqrt(x)(x+1))
d
dx
(
sec
(
x
)
tan
(
x
)
√
x
(
x
+
1
)
)
x^3(dy)/(dx)+4x^2y=e^{-x}
x
3
dy
dx
+
4
x
2
y
=
e
−
x
integral of 5sin(3x)sin(6x)
∫
5
sin
(
3
x
)
sin
(
6
x
)
dx
inverse라플라스 (15)/(3s+sqrt(3))
inverselaplace
1
5
3
s
+
√
3
integral of (x^3+2x)/(x^4+4x^2+3)
∫
x
3
+
2
x
x
4
+
4
x
2
+
3
dx
(dy)/(dt)+0.7ty=7t,y(0)=7
dy
dt
+
0
.
7
ty
=
7
t
,
y
(
0
)
=
7
y^{''}+2y^'+2y=sin(2x)
y
′
′
+
2
y
′
+
2
y
=
sin
(
2
x
)
derivative of (50/(x^9))
d
dx
(
5
0
x
9
)
integral of 8/(sqrt(4-x^2))
∫
8
√
4
−
x
2
dx
integral of (x^2-1)/(x^3-3x+1)
∫
x
2
−
1
x
3
−
3
x
+
1
dx
derivative cos^{sin(x)}(x)
derivative
cos
sin
(
x
)
(
x
)
derivative f(x)=e^{-0.5x}(4-x)-2
derivative
f
(
x
)
=
e
−
0
.
5
x
(
4
−
x
)
−
2
sum from n=1 to infinity of 5/(4n^2-1)
∑
n
=
1
∞
5
4
n
2
−
1
derivative of-3sin(6x)
d
dx
(
−
3
sin
(
6
x
)
)
지역 3x,(6x)/7 ,55-x^2
area
3
x
,
6
x
7
,
5
5
−
x
2
(\partial)/(\partial t)(e^{-t}cos(t))
∂
∂
t
(
e
−
t
cos
(
t
)
)
integral of 1/(x^3+xy^2)
∫
1
x
3
+
xy
2
dy
derivative of-16sin(4x)
d
dx
(
−
1
6
sin
(
4
x
)
)
derivative of ln((1+sqrt(x)/(x^3)))
d
dx
(
ln
(
1
+
√
x
x
3
)
)
integral from 1/5 to 7 of 8xln(5x)
∫
1
5
7
8
x
ln
(
5
x
)
dx
y^'+2/x y=4x
y
′
+
2
x
y
=
4
x
derivative of sin^2(x/2)
d
dx
(
sin
2
(
x
2
)
)
derivative of ln(7x^2+5y^2)
d
dx
(
ln
(
7
x
2
+
5
y
2
)
)
derivative 4t^{(-1)/8}+5ln(t)+ln(5)
derivative
4
t
−
1
8
+
5
ln
(
t
)
+
ln
(
5
)
sum from n=1 to infinity of 3/(5^n)+2/n
∑
n
=
1
∞
3
5
n
+
2
n
tangent f(x)=3x^2-4x+1
tangent
f
(
x
)
=
3
x
2
−
4
x
+
1
지역 y=4,y=x^2
area
y
=
4
,
y
=
x
2
integral of 2e^{-x/2}
∫
2
e
−
x
2
dx
derivative of (9-sec(x)/(tan(x)))
d
dx
(
9
−
sec
(
x
)
tan
(
x
)
)
sum from n=1 to infinity of (2n)/(5n-8)
∑
n
=
1
∞
2
n
5
n
−
8
integral of (3x^2-1)^43x
∫
(
3
x
2
−
1
)
4
3
xdx
integral of (x^3+5)
∫
(
x
3
+
5
)
dx
derivative x^2-6(3)+9
derivative
x
2
−
6
(
3
)
+
9
derivative sqrt(3x^2+2)
derivative
√
3
x
2
+
2
integral of x/(4x^2+1)
∫
x
4
x
2
+
1
dx
integral of e^{t/5}
∫
e
t
5
dt
integral of ((x+3))/(x^2+8x-9)
∫
(
x
+
3
)
x
2
+
8
x
−
9
dx
limit as x approaches 2-of (x^2)/(x-2)
lim
x
→
2
−
(
x
2
x
−
2
)
sum from n=1 to infinity of n^3(1+n^4)
∑
n
=
1
∞
n
3
(
1
+
n
4
)
derivative f(x)=x*e^{2x-4},x=2
derivative
f
(
x
)
=
x
·
e
2
x
−
4
,
x
=
2
integral of ((sin(sqrt(x))))/(sqrt(x))
∫
(
sin
(
√
x
)
)
√
x
dx
경사지intercept (3,-1),(4,7)
slopeintercept
(
3
,
−
1
)
,
(
4
,
7
)
derivative y= 4/(7x^2)
derivative
y
=
4
7
x
2
(dy)/(dx)=(3x^2)/(y^2)
dy
dx
=
3
x
2
y
2
tangent 6x^2+5x+8,\at x=4
tangent
6
x
2
+
5
x
+
8
,
at
x
=
4
limit as x approaches 4 of sqrt(x^3+6x)
lim
x
→
4
(
√
x
3
+
6
x
)
limit as x approaches 2 of 3cos(x)
lim
x
→
2
(
3
cos
(
x
)
)
f(x)=x^2cos(1/x)
f
(
x
)
=
x
2
cos
(
1
x
)
maclaurin (1-2x)^{-2}
maclaurin
(
1
−
2
x
)
−
2
sum from n=2 to infinity of n/(3n^3+1)
∑
n
=
2
∞
n
3
n
3
+
1
derivative 8/(1-x)
derivative
8
1
−
x
d/(dt)(4t^2+2t+5)
d
dt
(
4
t
2
+
2
t
+
5
)
derivative of e^{cos(x}+e^{sin(y)})
d
dx
(
e
cos
(
x
)
+
e
sin
(
y
)
)
derivative of log_{3}(5x-1)
d
dx
(
log
3
(
5
x
−
1
)
)
tangent y= 5/x ,(4, 5/4)
tangent
y
=
5
x
,
(
4
,
5
4
)
derivative t^2*sqrt(t^3+2)
derivative
t
2
·
√
t
3
+
2
derivative 1/(2sqrt(r))+1/(9r^{8/9)}
derivative
1
2
√
r
+
1
9
r
8
9
derivative of 7/(1+x)
d
dx
(
7
1
+
x
)
sum from n=1 to infinity of 4/(n^2+1)
∑
n
=
1
∞
4
n
2
+
1
integral of-9.8
∫
−
9
.
8
dx
integral of 2e^{-0.2x}
∫
2
e
−
0
.
2
x
dx
(d^2)/(dx^2)y=(4x+3)(2x^2+7x-1)
d
2
dx
2
y
=
(
4
x
+
3
)
(
2
x
2
+
7
x
−
1
)
(\partial)/(\partial x)(11x^2y+8xy^3)
∂
∂
x
(
1
1
x
2
y
+
8
xy
3
)
derivative of 4-sqrt(x+7)
d
dx
(
4
−
√
x
+
7
)
derivative of 1/((4x^3))
d
dx
(
1
(
4
x
)
3
)
y^'=(x^8)/y
y
′
=
x
8
y
integral of x^3+5x-1
∫
x
3
+
5
x
−
1
dx
(\partial)/(\partial x)(3x^{2/3})
∂
∂
x
(
3
x
2
3
)
integral from 1 to 2 of 1/(8-3x)
∫
1
2
1
8
−
3
x
dx
inverse라플라스 sin(t)
inverselaplace
sin
(
t
)
derivative e^{1/x}
derivative
e
1
x
integral of 8x^3+12x+2
∫
8
x
3
+
1
2
x
+
2
dx
derivative of a{r}(xc,5x)
d
dx
(
a
r
(
x
)
c
,
5
x
)
(\partial)/(\partial x)(x^2y^2-3y)
∂
∂
x
(
x
2
y
2
−
3
y
)
integral of 3x+2
∫
3
x
+
2
dx
지역 f(x)=4x+8,0,8
area
f
(
x
)
=
4
x
+
8
,
0
,
8
sum from n=0 to infinity of (7n!)/(2^n)
∑
n
=
0
∞
7
n
!
2
n
tangent f(x)=1-x-x^2,\at x=0
tangent
f
(
x
)
=
1
−
x
−
x
2
,
at
x
=
0
derivative x(29-2x)(16-2x)
derivative
x
(
2
9
−
2
x
)
(
1
6
−
2
x
)
derivative log_{7}(x)
derivative
log
7
(
x
)
테일러 ln(x+2),-1
taylor
ln
(
x
+
2
)
,
−
1
2xy^'-y=3x^2
2
xy
′
−
y
=
3
x
2
integral of 9tan(x)sec(3)(x)
∫
9
tan
(
x
)
sec
(
3
)
(
x
)
dx
integral from-1 to 1 of 4/(1+x^2)
∫
−
1
1
4
1
+
x
2
dx
f(x)=x^6e^x
f
(
x
)
=
x
6
e
x
derivative sin(x)ln(8x)
derivative
sin
(
x
)
ln
(
8
x
)
derivative of e^x+4
d
dx
(
e
x
+
4
)
1
..
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