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Popolari Calcoli Problemi
(dy)/(dt)+1/t y= 6/t
dy
dt
+
1
t
y
=
6
t
integral of 1/(sin^2(x)cos(x))
∫
1
sin
2
(
x
)
cos
(
x
)
dx
area 2x,4x^2
area
2
x
,
4
x
2
integral of (sin(x))^4(cos(x))^2
∫
(
sin
(
x
)
)
4
(
cos
(
x
)
)
2
dx
(\partial)/(\partial x)(xln(x/y))
∂
∂
x
(
x
ln
(
x
y
)
)
integral of cos(2x)sin(x)
∫
cos
(
2
x
)
sin
(
x
)
dx
integral of (|x|+1)
∫
(
|
x
|
+
1
)
dx
taylor (x^2)/(1+x),0
taylor
x
2
1
+
x
,
0
8(sin(t)y^'+cos(t)y)=cos(t)sin^5(t)
8
(
sin
(
t
)
y
′
+
cos
(
t
)
y
)
=
cos
(
t
)
sin
5
(
t
)
derivative 1/(1+5x^2)
derivative
1
1
+
5
x
2
tangent f(x)=sqrt(5x+1),\at x=7
tangent
f
(
x
)
=
√
5
x
+
1
,
at
x
=
7
derivative e^{-3x}
derivative
e
−
3
x
derivative f(x)=x^2cot(x)
derivative
f
(
x
)
=
x
2
cot
(
x
)
integral of cos(ln(x))
∫
cos
(
ln
(
x
)
)
dx
integral of (x^2)/(sqrt(49+x^2))
∫
x
2
√
4
9
+
x
2
dx
integral of x(1+x^3)
∫
x
(
1
+
x
3
)
dx
y^'+y=2,y(0)=0
y
′
+
y
=
2
,
y
(
0
)
=
0
pendenza (-5.3)(7.9)
slope
(
−
5
.
3
)
(
7
.
9
)
integral from 0 to 1 of 5xe^{-x^2}
∫
0
1
5
xe
−
x
2
dx
x^2y^{''}=2xy^'+(y^')^2
x
2
y
′
′
=
2
xy
′
+
(
y
′
)
2
tangent f(x)=x^2+8,(1,9)
tangent
f
(
x
)
=
x
2
+
8
,
(
1
,
9
)
derivative of (4x^3/(x^4+27))
d
dx
(
4
x
3
x
4
+
2
7
)
derivative of arcsin(tan(sqrt(x^2+1)))
d
dx
(
arcsin
(
tan
(
√
x
2
+
1
)
)
)
(\partial)/(\partial x)(ln(x^8y))
∂
∂
x
(
ln
(
x
8
y
)
)
limit as x approaches 0 of-1/(x^2)
lim
x
→
0
(
−
1
x
2
)
derivative of 3sin^2(2x)
d
dx
(
3
sin
2
(
2
x
)
)
integral of (sin^2(x))/(1+cos^2(x))
∫
sin
2
(
x
)
1
+
cos
2
(
x
)
dx
integral of 15x^3e^x
∫
1
5
x
3
e
x
dx
limit as x approaches infinity of-x
lim
x
→
∞
(
−
x
)
derivative of 8xarcsin(x)
d
dx
(
8
x
arcsin
(
x
)
)
derivative of 3xln(9x^2)
d
dx
(
3
x
ln
(
9
x
2
)
)
limit as x approaches 0 of e^{(1/x)}
lim
x
→
0
(
e
(
1
x
)
)
integral of (1+(1/2)*2/((2*x+3)))
∫
(
1
+
(
1
2
)
·
2
(
2
·
x
+
3
)
)
dx
derivative of (sin(x^2)/(sin^2(x)))
d
dx
(
sin
(
x
2
)
sin
2
(
x
)
)
derivative y=6x^2e^{-x}
derivative
y
=
6
x
2
e
−
x
derivative f(x)=2^{20}
derivative
f
(
x
)
=
2
2
0
derivative f(x)=2-x
derivative
f
(
x
)
=
2
−
x
derivative of ((3x^2-5^4)/((4x^3+2)^5))
d
dx
(
(
3
x
2
−
5
)
4
(
4
x
3
+
2
)
5
)
derivative y=-x^2+4x
derivative
y
=
−
x
2
+
4
x
y^{''}+2y^'+y=sin(x)
y
′
′
+
2
y
′
+
y
=
sin
(
x
)
integral of (x^4+2x^2-1)/(sqrt(x))
∫
x
4
+
2
x
2
−
1
√
x
dx
derivative of (sin(x+cos(x))/(x^3+x-2))
d
dx
(
sin
(
x
)
+
cos
(
x
)
x
3
+
x
−
2
)
sum from n=21 to infinity of e^{-0.06n}
∑
n
=
2
1
∞
e
−
0
.
0
6
n
(x^2-9)(dy)/(dx)+xy=0
(
x
2
−
9
)
dy
dx
+
xy
=
0
integral of sqrt(16-4x^2)
∫
√
1
6
−
4
x
2
dx
derivative 1/2 sec(2x)
derivative
1
2
sec
(
2
x
)
(dy)/(dx)-y/x =2x^2ln(x)
dy
dx
−
y
x
=
2
x
2
ln
(
x
)
limit as x approaches 1 of 4x^2-2x+5
lim
x
→
1
(
4
x
2
−
2
x
+
5
)
derivative of (1+1/x /(1-1/x))
d
dx
(
1
+
1
x
1
−
1
x
)
(dy)/(dx)=e^{3x}*e^{2y}
dy
dx
=
e
3
x
·
e
2
y
limit as x approaches 3 of (x^2+3)/(x-1)
lim
x
→
3
(
x
2
+
3
x
−
1
)
integral of x^2sqrt(x^3+31)
∫
x
2
√
x
3
+
3
1
dx
area y= 3/x ,y= x/(12),1<= x<= 6
area
y
=
3
x
,
y
=
x
1
2
,
1
≤
x
≤
6
limit as x approaches 0 of-1+1/x
lim
x
→
0
(
−
1
+
1
x
)
integral from 2 to 3 of (16)/(sqrt(3-x))
∫
2
3
1
6
√
3
−
x
dx
maclaurin 1/(2x-5)
maclaurin
1
2
x
−
5
integral of 1+cot^2(x)
∫
1
+
cot
2
(
x
)
dx
derivative of (x^3/6-3x)
d
dx
(
x
3
6
−
3
x
)
integral of 1/36 x
∫
1
3
6
xdx
integral from 0 to 4 of 1/(x^2-2x-3)
∫
0
4
1
x
2
−
2
x
−
3
dx
(dy)/(dx)=(2x)/(x^2+3)(y-1)
dy
dx
=
2
x
x
2
+
3
(
y
−
1
)
derivative 1/(g^2(x))
derivative
1
g
2
(
x
)
derivative 10x(x^2+5)^4
derivative
1
0
x
(
x
2
+
5
)
4
derivative y=2e^3t
derivative
y
=
2
e
3
t
integral of (4x(sqrt(3x)-2))
∫
(
4
x
(
√
3
x
−
2
)
)
dx
derivative of 2aarccos(sqrt(2x))
d
dx
(
2
a
arccos
(
√
2
x
)
)
derivative sin^4(6x^2)
derivative
sin
4
(
6
x
2
)
integral of 11x^{4/7}+8x^{-6/7}
∫
1
1
x
4
7
+
8
x
−
6
7
dx
integral of (sec(θ))/(cos(θ)-sec(θ))
∫
sec
(
θ
)
cos
(
θ
)
−
sec
(
θ
)
d
θ
(dy)/(dx)=1-y^2
dy
dx
=
1
−
y
2
integral of e^x-1/x+4+5x^3
∫
e
x
−
1
x
+
4
+
5
x
3
dx
integral of (v^2)/(sqrt(-v^2+3))
∫
v
2
√
−
v
2
+
3
dv
integral of sin(3x+4)
∫
sin
(
3
x
+
4
)
dx
derivative of 2/((x-3t^2+1))
d
dx
(
2
(
x
−
3
t
)
2
+
1
)
limit as x approaches 1 of x(x-2)
lim
x
→
1
(
x
(
x
−
2
)
)
limit as x approaches 0+of x
lim
x
→
0
+
(
x
)
sum from n=0 to infinity of sin((npi)/7)
∑
n
=
0
∞
sin
(
n
π
7
)
derivative of sinh(9x)
d
dx
(
sinh
(
9
x
)
)
integral from 0 to 1 of (e^x+e^{-x})^2
∫
0
1
(
e
x
+
e
−
x
)
2
dx
integral of 2cos(2x)-2
∫
2
cos
(
2
x
)
−
2
dx
derivative of (x-7/(x+2))
d
dx
(
x
−
7
x
+
2
)
integral of 1/(sqrt(12-4x-x^2))
∫
1
√
1
2
−
4
x
−
x
2
dx
area x^2-2,e^x,[-1,1]
area
x
2
−
2
,
e
x
,
[
−
1
,
1
]
tangent ((4x^3))/((2-3x)^5)
tangent
(
4
x
3
)
(
2
−
3
x
)
5
integral of+sin^3(θ)cos^4(θ)
∫
+
sin
3
(
θ
)
cos
4
(
θ
)
d
θ
derivative (x+9)/(x^3+x-2)
derivative
x
+
9
x
3
+
x
−
2
integral of (24x)/((3x^2+7)^3)
∫
2
4
x
(
3
x
2
+
7
)
3
dx
integral of x^1cos(-5x)
∫
x
1
cos
(
−
5
x
)
dx
xy^'+(x+1)y=x,y(ln(2))=1
xy
′
+
(
x
+
1
)
y
=
x
,
y
(
ln
(
2
)
)
=
1
limit as x approaches 0 of 4x+tan(2x)
lim
x
→
0
(
4
x
+
tan
(
2
x
)
)
integral of 13tan^3(x)
∫
1
3
tan
3
(
x
)
dx
derivative of 4x-2y
d
dx
(
4
x
−
2
y
)
taylor 9-10^{-10}e^{40x}
taylor
9
−
1
0
−
1
0
e
4
0
x
(dy)/(dx)-2xy=6x,y(0)=-7
dy
dx
−
2
xy
=
6
x
,
y
(
0
)
=
−
7
derivative f(x)=(t+1)/(t^3+t-2)
derivative
f
(
x
)
=
t
+
1
t
3
+
t
−
2
derivative of 7-4/(x-8+(2x)/(3x+1))
d
dx
(
7
−
4
x
−
8
+
2
x
3
x
+
1
)
integral of v
∫
vdv
derivative of 1000(18^3-x^{1/3})
d
dx
(
1
0
0
0
(
1
8
3
−
x
)
1
3
)
limit as x approaches 6+of x^2-36
lim
x
→
6
+
(
x
2
−
3
6
)
derivative 8(e^xcos(x)-e^xsin(x))
derivative
8
(
e
x
cos
(
x
)
−
e
x
sin
(
x
)
)
1
..
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