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Popolari Calcoli Problemi
(d^2y)/(dx^2)+2/x (dy)/(dx)=3xx
d
2
y
dx
2
+
2
x
dy
dx
=
3
xx
tangent f(x)=(x^2+7)(5x+4),\at x=2
tangent
f
(
x
)
=
(
x
2
+
7
)
(
5
x
+
4
)
,
at
x
=
2
limit as x approaches 0 of 9
lim
x
→
0
(
9
)
integral of 1/(cos^2(3x))
∫
1
cos
2
(
3
x
)
dx
integral of e
∫
e
y^'=(2x^7e^{y/x}+x^5y^2)/(x^6y)
y
′
=
2
x
7
e
y
x
+
x
5
y
2
x
6
y
(dy)/(dt)=1y,y(1)=3
dy
dt
=
1
y
,
y
(
1
)
=
3
derivative of 3x^3+5x^2-4x+10
d
dx
(
3
x
3
+
5
x
2
−
4
x
+
1
0
)
integral of tan^2(6x)sec^4(6x)
∫
tan
2
(
6
x
)
sec
4
(
6
x
)
dx
area x^3,-x,8
area
x
3
,
−
x
,
8
derivative of sqrt((2x-y))
d
dx
(
√
(
2
x
−
y
)
)
d/(dt)(t^4)
d
dt
(
t
4
)
integral from 0 to 6 of 9sqrt(4x+1)
∫
0
6
9
√
4
x
+
1
dx
36y^{''}-y=0,y(-5)=1,y^'(-5)=-1
3
6
y
′
′
−
y
=
0
,
y
(
−
5
)
=
1
,
y
′
(
−
5
)
=
−
1
y^{''}-y^'=0
y
′
′
−
y
′
=
0
limit as x approaches 2+of tan((pix)/4)
lim
x
→
2
+
(
tan
(
π
x
4
)
)
integral from 1 to infinity of 2^{-x}
∫
1
∞
2
−
x
dx
tangent f(x)=(x^3+2)^5,\at x=-1
tangent
f
(
x
)
=
(
x
3
+
2
)
5
,
at
x
=
−
1
taylor sqrt(x),1
taylor
√
x
,
1
derivative of sqrt(4-3x^2)
d
dx
(
√
4
−
3
x
2
)
area y=x^3-6x^2+8x,y=x^2-4x
area
y
=
x
3
−
6
x
2
+
8
x
,
y
=
x
2
−
4
x
derivative ln(xe^{sqrt(x)}+2)
derivative
ln
(
xe
√
x
+
2
)
derivative of (2cot(x)/(csc(x)))
d
dx
(
2
cot
(
x
)
csc
(
x
)
)
derivative of In(-x^2+6x)
d
dx
(
In
(
−
x
2
+
6
x
)
)
limit as x approaches 1+of (x+9)/(x+2)
lim
x
→
1
+
(
x
+
9
x
+
2
)
(\partial)/(\partial x)(4yx^3-12y^2x^2)
∂
∂
x
(
4
yx
3
−
1
2
y
2
x
2
)
inversalaplace se^{-s}
inverselaplace
se
−
s
limit as x approaches 0+of x^{3/x}
lim
x
→
0
+
(
x
3
x
)
derivative of cos(6x^3-4)
d
dx
(
cos
(
6
x
3
−
4
)
)
laplacetrasformazione e^{-2((t-1))}*1((t-1))
laplacetransform
e
−
2
(
(
t
−
1
)
)
·
1
(
(
t
−
1
)
)
integral from 0 to 7 of e^xsin(x)
∫
0
7
e
x
sin
(
x
)
dx
derivative of 2x^3-48x^2
d
dx
(
2
x
3
−
4
8
x
2
)
integral of sqrt(2x-1)
∫
√
2
x
−
1
dx
integral of 16θsec^2(θ)
∫
1
6
θ
sec
2
(
θ
)
d
θ
y^{''}-6y^'+9y=0,y(0)=4,y^'(0)=0
y
′
′
−
6
y
′
+
9
y
=
0
,
y
(
0
)
=
4
,
y
′
(
0
)
=
0
integral from-1/3 to 0 of 3/4 (1-x^2)
∫
−
1
3
0
3
4
(
1
−
x
2
)
dx
derivative sqrt(x)+x^2+ln(x)
derivative
√
x
+
x
2
+
ln
(
x
)
limit as x approaches+2pi of f(x)
lim
x
→
+
2
π
(
f
(
x
)
)
derivative ln(x^3+3x)
derivative
ln
(
x
3
+
3
x
)
(dx)/(dy)=5x+y
dx
dy
=
5
x
+
y
(dy)/(dx)=y^2,y(1)=1
dy
dx
=
y
2
,
y
(
1
)
=
1
integral of (2x+1)/(x(x+1)^2)
∫
2
x
+
1
x
(
x
+
1
)
2
dx
integral of (x-2)
∫
(
x
−
2
)
dx
integral from 0 to 1 of xcos(2x^2+7)
∫
0
1
x
cos
(
2
x
2
+
7
)
dx
(\partial)/(\partial x)(sqrt(xy^2+y^2))
∂
∂
x
(
√
xy
2
+
y
2
)
integral from 1 to 3 of 2r^4ln(r)
∫
1
3
2
r
4
ln
(
r
)
dr
pendenza (-4,-4),(2,5)
slope
(
−
4
,
−
4
)
,
(
2
,
5
)
integral of (4x-3)(2x-1)
∫
(
4
x
−
3
)
(
2
x
−
1
)
dx
(\partial)/(\partial x)(x^3y+xy^2-2x^2-y^2)
∂
∂
x
(
x
3
y
+
xy
2
−
2
x
2
−
y
2
)
integral of (x-1)/(x+2)
∫
x
−
1
x
+
2
dx
integral of u*sec^2(u)
∫
u
·
sec
2
(
u
)
du
derivative f(x)=8x^3
derivative
f
(
x
)
=
8
x
3
derivative of (sec^2(x)dx)
d
dx
(
(
sec
2
(
x
)
)
dx
)
derivative f(t)=t^6sin(t)
derivative
f
(
t
)
=
t
6
sin
(
t
)
derivative cos(-x)
derivative
cos
(
−
x
)
(\partial)/(\partial y)(5x+4y)
∂
∂
y
(
5
x
+
4
y
)
integral of 2xe^{3x^2}
∫
2
xe
3
x
2
dx
limit as x approaches+(-1) of x-1
lim
x
→
+
(
−
1
)
(
x
−
1
)
integral from 0 to 2 of pi(4/(x^2+4))^2
∫
0
2
π
(
4
x
2
+
4
)
2
dx
limit as x approaches 0 of ((sin(x)))/x
lim
x
→
0
(
(
sin
(
x
)
)
x
)
(\partial)/(\partial x)(-x^3+6x^2y^3+5y^2)
∂
∂
x
(
−
x
3
+
6
x
2
y
3
+
5
y
2
)
integral of (2x+3)/((2x^2+6x)^4)
∫
2
x
+
3
(
2
x
2
+
6
x
)
4
dx
(dx)/(dt)= 1/(t(1-t))
dx
dt
=
1
t
(
1
−
t
)
d/(dt)(xy)
d
dt
(
xy
)
derivative 7xsin(pix)
derivative
7
x
sin
(
π
x
)
integral of (x-1/(x^2))
∫
(
x
−
1
x
2
)
dx
integral of ln(5^x)
∫
ln
(
5
x
)
dx
derivative 9t^2+sqrt(t^3)
derivative
9
t
2
+
√
t
3
integral of e^{-sx}x
∫
e
−
sx
xdx
laplacetrasformazione t^2cos(2t)
laplacetransform
t
2
cos
(
2
t
)
derivative of log_{10}(2x-3)
d
dx
(
log
1
0
(
2
x
−
3
)
)
integral of (x^2+12x-4)/(x^3-4x)
∫
x
2
+
1
2
x
−
4
x
3
−
4
x
dx
(\partial)/(\partial x)(4xln(y)+yln(z)-4x)
∂
∂
x
(
4
x
ln
(
y
)
+
y
ln
(
z
)
−
4
x
)
integral of (x^2)/(x-10)
∫
x
2
x
−
1
0
dx
(dy)/(dx)=(4x+y)^2
dy
dx
=
(
4
x
+
y
)
2
derivative of (x^3-1/(x-1))
d
dx
(
x
3
−
1
x
−
1
)
(\partial)/(\partial x)(ln(10x))
∂
∂
x
(
ln
(
1
0
x
)
)
derivative of x/(log_{e(x)})
d
dx
(
x
log
e
(
x
)
)
derivative of be^{-x}
d
dx
(
be
−
x
)
integral of (x^{3/2}+2x+1)
∫
(
x
3
2
+
2
x
+
1
)
dx
limit as h approaches 0 of (2/(1+h)-2)/h
lim
h
→
0
(
2
1
+
h
−
2
h
)
derivative-7x^4+7x^3-x^2+x
derivative
−
7
x
4
+
7
x
3
−
x
2
+
x
integral of (sec(3x))/(cot(3x))
∫
sec
(
3
x
)
cot
(
3
x
)
dx
(\partial)/(\partial y)(y/(2x+3y))
∂
∂
y
(
y
2
x
+
3
y
)
integral from 0 to 2pi of (cos(x))^2
∫
0
2
π
(
cos
(
x
)
)
2
dx
derivative (2x^2+6x+2)/(sqrt(x))
derivative
2
x
2
+
6
x
+
2
√
x
integral of sec^2(x)sqrt(tan(x))
∫
sec
2
(
x
)
√
tan
(
x
)
dx
(1/x+2y^2x)dx+(2yx^2-cos(y))dy=0,y(1)=pi
(
1
x
+
2
y
2
x
)
dx
+
(
2
yx
2
−
cos
(
y
)
)
dy
=
0
,
y
(
1
)
=
π
sum from n=1 to infinity of (sin(3))^n
∑
n
=
1
∞
(
sin
(
3
)
)
n
derivative of e^{x+y}-1
d
dx
(
e
x
+
y
−
1
)
integral of (sin^4(x))/(cos^6(x))
∫
sin
4
(
x
)
cos
6
(
x
)
dx
tangent f(x)=7sqrt(x),\at x=4
tangent
f
(
x
)
=
7
√
x
,
at
x
=
4
sum from n=5 to infinity of (n^3)/(2^n)
∑
n
=
5
∞
n
3
2
n
f^{''}(x)=2
f
′
′
(
x
)
=
2
limit as x approaches-infinity of x+1/x
lim
x
→
−
∞
(
x
+
1
x
)
integral from 0 to pi/4 of sec(x)
∫
0
π
4
sec
(
x
)
dx
integral of 24x^5
∫
2
4
x
5
dx
integral of 2sqrt(x)ln(x)
∫
2
√
x
ln
(
x
)
dx
derivative of cos(4e^{-8x})
d
dx
(
cos
(
4
e
−
8
x
)
)
tangent f(x)=x+2/x ,(2,3)
tangent
f
(
x
)
=
x
+
2
x
,
(
2
,
3
)
1
..
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500
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