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Popolari Calcoli Problemi
area y=x^2,y=x+2,x=-2
area
y
=
x
2
,
y
=
x
+
2
,
x
=
−
2
maclaurin ln(1/(x+5))+xcos(x)
maclaurin
ln
(
1
x
+
5
)
+
x
cos
(
x
)
integral of sin(6pit)
∫
sin
(
6
π
t
)
dt
tangent y=x-x^3,(1,0)
tangent
y
=
x
−
x
3
,
(
1
,
0
)
integral of 1+tan(x)
∫
1
+
tan
(
x
)
dx
derivative of 5-5cos(x)
d
dx
(
5
−
5
cos
(
x
)
)
integral of \sqrt[3]{2-3x}
∫
3
√
2
−
3
x
dx
derivative of 1/((x^2+1^4))
d
dx
(
1
(
x
2
+
1
)
4
)
(\partial)/(\partial y)(-2xy)
∂
∂
y
(
−
2
xy
)
derivative of ((2x^2+1/(3x^3+1))^2)
d
dx
(
(
2
x
2
+
1
3
x
3
+
1
)
2
)
derivative 7\sqrt[4]{-v}
derivative
7
4
√
−
v
sin(t)=y^'+y
sin
(
t
)
=
y
′
+
y
sum from n=1 to infinity of (-1)/(n+1)
∑
n
=
1
∞
−
1
n
+
1
integral of (1-6x)e^{3x-9x^2}
∫
(
1
−
6
x
)
e
3
x
−
9
x
2
dx
limit as n approaches infinity of 7^n
lim
n
→
∞
(
7
n
)
integral from 0 to 11 of 2piy(121-y^2)
∫
0
1
1
2
π
y
(
1
2
1
−
y
2
)
dy
(\partial)/(\partial y)(x^2+y-e^{x+y})
∂
∂
y
(
x
2
+
y
−
e
x
+
y
)
integral of x/(e^x)
∫
x
e
x
dx
integral of 2x*sec^2(3x)
∫
2
x
·
sec
2
(
3
x
)
dx
limit as x approaches 0 of e^{2pi}
lim
x
→
0
(
e
2
π
)
integral of e^xsqrt(x)
∫
e
x
√
x
dx
inversalaplace 1/((s-3)^2+3)
inverselaplace
1
(
s
−
3
)
2
+
3
integral of (35x^4-3)/(7x^5-3x)
∫
3
5
x
4
−
3
7
x
5
−
3
x
dx
pendenza (-7,-3),(-5,-8)
slope
(
−
7
,
−
3
)
,
(
−
5
,
−
8
)
integral of (x^2)/2+3x
∫
x
2
2
+
3
xdx
derivative of (x-2(x+1)(x+5))
d
dx
(
(
x
−
2
)
(
x
+
1
)
(
x
+
5
)
)
integral of (x^2-4x-15)
∫
(
x
2
−
4
x
−
1
5
)
dx
integral of x^2cos(4x)
∫
x
2
cos
(
4
x
)
dx
integral of sqrt(x+y)
∫
√
x
+
y
dx
derivative f(x)=sin(8e^x)
derivative
f
(
x
)
=
sin
(
8
e
x
)
integral of (3x^2y)
∫
(
3
x
2
y
)
dx
area sin^2(x),sin^3(x),[0,2pi]
area
sin
2
(
x
)
,
sin
3
(
x
)
,
[
0
,
2
π
]
y^'=(x^8-8y)/x
y
′
=
x
8
−
8
y
x
f(x)=x+sqrt(x)
f
(
x
)
=
x
+
√
x
integral of u^{-6}
∫
u
−
6
du
x(dy)/(dx)+2y=-3sin(x)
x
dy
dx
+
2
y
=
−
3
sin
(
x
)
y^{''}+2y^'+5y=10
y
′
′
+
2
y
′
+
5
y
=
1
0
derivative of ((x+1/(x-1))^2)
d
dx
(
(
x
+
1
x
−
1
)
2
)
taylor sqrt(2+x)
taylor
√
2
+
x
laplacetrasformazione f(t)=6t^3e^{-2t}
laplacetransform
f
(
t
)
=
6
t
3
e
−
2
t
limit as x approaches 4 of (x^2-9)/(x-3)
lim
x
→
4
(
x
2
−
9
x
−
3
)
area (sec^2(x))/2 ,2cos^2(x)
area
sec
2
(
x
)
2
,
2
cos
2
(
x
)
limit as x approaches 2 of 4x^2-11x-2
lim
x
→
2
(
4
x
2
−
1
1
x
−
2
)
integral from 0 to 1 of 1/((16+x^2)^2)
∫
0
1
1
(
1
6
+
x
2
)
2
dx
limit as x approaches 0 of 1/(sqrt(5)+\sqrt{5)}
lim
x
→
0
(
1
√
5
+
√
5
)
integral of 1/(1-(x/L))
∫
1
1
−
(
x
L
)
dx
(dy)/(dx)+2y=1
dy
dx
+
2
y
=
1
(dy)/(dx)+3x^2*y=6x^2
dy
dx
+
3
x
2
·
y
=
6
x
2
(\partial)/(\partial y)(arctan(xy))
∂
∂
y
(
arctan
(
xy
)
)
derivative of 2sin^3(sqrt(x))
d
dx
(
2
sin
3
(
√
x
)
)
derivative y=x^2sin^4(x)+xcos^{-2}(x)
derivative
y
=
x
2
sin
4
(
x
)
+
x
cos
−
2
(
x
)
integral of cos(x)tan^2(x)
∫
cos
(
x
)
tan
2
(
x
)
dx
y^'=-2y,y(0)=2
y
′
=
−
2
y
,
y
(
0
)
=
2
(\partial)/(\partial y)(xye^{5y})
∂
∂
y
(
xye
5
y
)
integral of \sqrt[4]{x^3}
∫
4
√
x
3
dx
derivative x=6.4cos(1.2^2t^2)
derivative
x
=
6
.
4
cos
(
1
.
2
2
t
2
)
integral of sin(4x)sin(3x)
∫
sin
(
4
x
)
sin
(
3
x
)
dx
limit as x approaches pi of ln(tan(x))
lim
x
→
π
(
ln
(
tan
(
x
)
)
)
limit as x approaches-infinity of e^{-x}+x-1
lim
x
→
−
∞
(
e
−
x
+
x
−
1
)
derivative of 13arctan(sqrt(x))
d
dx
(
1
3
arctan
(
√
x
)
)
derivative (3x^4+4)^2
derivative
(
3
x
4
+
4
)
2
y^{''}+4y^'+3y=6e^{-x}
y
′
′
+
4
y
′
+
3
y
=
6
e
−
x
integral of 1/(sqrt(ax+b))
∫
1
√
ax
+
b
dx
(d^2y)/(dx^2)-2(dy)/(dx)+y=(e^x)/(x^2+1)
d
2
y
dx
2
−
2
dy
dx
+
y
=
e
x
x
2
+
1
derivative y=ln(x^2+y^2)
derivative
y
=
ln
(
x
2
+
y
2
)
(\partial)/(\partial y)(e^{x^2-y^2})
∂
∂
y
(
e
x
2
−
y
2
)
derivative of 1.5(1/3+x/2-(x^3/6))
d
dx
(
1
.
5
(
1
3
+
x
2
−
x
3
6
)
)
integral of 1/(sqrt(-x^2-2x8))
∫
1
√
−
x
2
−
2
x
8
dx
integral of ((1))/(x^4)
∫
(
1
)
x
4
dx
(sqrt(x^2))^'
(
√
x
2
)
′
integral of 1/((x-1)^3sqrt(x^2-2x-1))
∫
1
(
x
−
1
)
3
√
x
2
−
2
x
−
1
dx
derivative of x*sqrt(9-x)
d
dx
(
x
·
√
9
−
x
)
integral from 4 to 4 of f(x)
∫
4
4
f
(
x
)
dx
integral of (3e^x)
∫
(
3
e
x
)
dx
derivative of ((x^2+1/(x^2-1))^7)
d
dx
(
(
x
2
+
1
x
2
−
1
)
7
)
derivative of sqrt(x^3+4)
d
dx
(
√
x
3
+
4
)
tangent 6/(x^2+4)
tangent
6
x
2
+
4
(\partial)/(\partial x)(4pi^2 y/(x^2))
∂
∂
x
(
4
π
2
y
x
2
)
derivative arctan(2x)
derivative
arctan
(
2
x
)
limit as x approaches 0 of (2x)/0
lim
x
→
0
(
2
x
0
)
area e^x,x,0,2
area
e
x
,
x
,
0
,
2
limit as x approaches-4 of-8/(x^2+8x+16)
lim
x
→
−
4
(
−
8
x
2
+
8
x
+
1
6
)
limit as x approaches 0 of (1-5x)^{4/x}
lim
x
→
0
(
(
1
−
5
x
)
4
x
)
integral of 2/(x^2sqrt(9+x^2))
∫
2
x
2
√
9
+
x
2
dx
limit as x approaches-2 of (x-1)/(3x+6)
lim
x
→
−
2
(
x
−
1
3
x
+
6
)
limit as x approaches 4 of \sqrt[3]{x+4}
lim
x
→
4
(
3
√
x
+
4
)
(y^4-x^2)*(dy)/(dx)=-xy
(
y
4
−
x
2
)
·
dy
dx
=
−
xy
integral of (x-1)^5
∫
(
x
−
1
)
5
dx
laplacetrasformazione e^{-t}cos(2t)
laplacetransform
e
−
t
cos
(
2
t
)
limit as x approaches 0+of (1/5)^{1/x}
lim
x
→
0
+
(
(
1
5
)
1
x
)
(\partial)/(\partial x)(x^{1/2}y^{1/2}z)
∂
∂
x
(
x
1
2
y
1
2
z
)
integral from 0 to 6 of sqrt(1+x)
∫
0
6
√
1
+
x
dx
limit as x approaches 3+of (x+9)/(x-3)
lim
x
→
3
+
(
x
+
9
x
−
3
)
integral of (ln(x+8))/(x+8)
∫
ln
(
x
+
8
)
x
+
8
dx
(\partial)/(\partial x)((2x-4y)/(2x+4y))
∂
∂
x
(
2
x
−
4
y
2
x
+
4
y
)
integral of e^xcos^2(x)
∫
e
x
cos
2
(
x
)
dx
(\partial)/(\partial y)(3x^2+2xy^3)
∂
∂
y
(
3
x
2
+
2
xy
3
)
sum from n=1 to infinity of (x^n)/(6^n)
∑
n
=
1
∞
x
n
6
n
integral of tan(x)y
∫
tan
(
x
)
ydy
derivative ln(14-9x^2+2x^4)
derivative
ln
(
1
4
−
9
x
2
+
2
x
4
)
1
..
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