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Popular Calculus Problems
limit as x approaches-1 of 1/(x^3-x)
lim
x
→
−
1
(
1
x
3
−
x
)
y^8-(sqrt(y^9+4))/(sqrt(x^34)y^')=0
y
8
−
√
y
9
+
4
√
x
3
4
y
′
=
0
integral of (-xsqrt(x^4))
∫
(
−
x
√
x
4
)
dx
integral of (x^2)/(sqrt(5+x^3))
∫
x
2
√
5
+
x
3
dx
(\partial}{\partial t}(\frac{(s-2r))/t)
∂
∂
t
(
(
s
−
2
r
)
t
)
y^'+y+4sin(x)=0
y
′
+
y
+
4
sin
(
x
)
=
0
integral of (31)/((1-x^2)^{3/2)}
∫
3
1
(
1
−
x
2
)
3
2
dx
integral of tan(6x+1)
∫
tan
(
6
x
+
1
)
dx
integral of (8x^2-7x+12)/(x^3+4x)
∫
8
x
2
−
7
x
+
1
2
x
3
+
4
x
dx
derivative of (-2x+3x^{-2}ln(x))
d
dx
(
(
−
2
x
+
3
x
−
2
)
ln
(
x
)
)
derivative of (x^7/(x^4))
d
dx
(
x
7
x
4
)
limit as x approaches 0 of 1+1/(x^2)
lim
x
→
0
(
1
+
1
x
2
)
derivative of x^3-2x^2y-2y^2-1
derivative
x
3
−
2
x
2
y
−
2
y
2
−
1
derivative of arcsin(x/7)
derivative
arcsin
(
x
7
)
derivative of y=4^{-x}sin(x)
derivative
y
=
4
−
x
sin
(
x
)
integral of (9-x^2)/(7x^3+x)
∫
9
−
x
2
7
x
3
+
x
dx
limit as x approaches 2 of (x^7-128)/(x-2)
lim
x
→
2
(
x
7
−
1
2
8
x
−
2
)
derivative of ee^x
d
dx
(
ee
x
)
integral of-2xy
∫
−
2
xydx
integral of y-2
∫
y
−
2
dy
sum from n=1 to infinity of 1/(n^{0.9)}
∑
n
=
1
∞
1
n
0
.
9
integral of kx
∫
kxdx
derivative of x+y^3
d
dx
(
x
+
y
3
)
limit as x approaches 0 of (tan(7x))^x
lim
x
→
0
(
(
tan
(
7
x
)
)
x
)
integral of (20x)/(sqrt(5x^2-6))
∫
2
0
x
√
5
x
2
−
6
dx
tangent of f(x)= 1/(sqrt(5x))
tangent
f
(
x
)
=
1
√
5
x
derivative of 5e^{20}
derivative
5
e
2
0
integral of (x-2)^3ln(x-2)
∫
(
x
−
2
)
3
ln
(
x
−
2
)
dx
derivative of (4/5 x)^3
derivative
(
4
5
x
)
3
slope of 1-2x^2
slope
1
−
2
x
2
y^'=((x^2+1))/(3y^2)
y
′
=
(
x
2
+
1
)
3
y
2
derivative of e^{x^3}
derivative
e
x
3
y^{''}+y^'=a*x^2+b*x^3
y
′
′
+
y
′
=
a
·
x
2
+
b
·
x
3
integral of 6y
∫
6
ydy
integral of ((sqrt(x)+2)^3)/(sqrt(x))
∫
(
√
x
+
2
)
3
√
x
dx
(\partial)/(\partial s)(rcos(s))
∂
∂
s
(
r
cos
(
s
)
)
(x(11-x))/(1100)dx=dt,x(0)=3
x
(
1
1
−
x
)
1
1
0
0
dx
=
dt
,
x
(
0
)
=
3
derivative of f(x)=sqrt(8)
derivative
f
(
x
)
=
√
8
derivative of 2-x^{2/3}
d
dx
(
2
−
x
2
3
)
integral of (x^4+1)/(2x^2)
∫
x
4
+
1
2
x
2
dx
integral of x/(x^4+2)
∫
x
x
4
+
2
dx
tangent of f(x)= 5/x ,\at x=1
tangent
f
(
x
)
=
5
x
,
at
x
=
1
integral of te^t
∫
te
t
dt
integral of x/(x^4+1)
∫
x
x
4
+
1
dx
tangent of y= 1/(x^6),(1,1)
tangent
y
=
1
x
6
,
(
1
,
1
)
integral of (4x)/((2x^2-7)^{10)}
∫
4
x
(
2
x
2
−
7
)
1
0
dx
laplacetransform 3t^3
laplacetransform
3
t
3
integral of 1/(sqrt(a^2+u^2))
∫
1
√
a
2
+
u
2
du
slope of (9,1),(-1,1)
slope
(
9
,
1
)
,
(
−
1
,
1
)
integral of-2/(x^3)
∫
−
2
x
3
dx
integral of sqrt(4-x)
∫
√
4
−
x
dx
derivative of 8/(x^2+1)
d
dx
(
8
x
2
+
1
)
derivative of x(x^2+1)^3
derivative
x
(
x
2
+
1
)
3
tangent of f(x)=x^4-4x^2,\at x=1
tangent
f
(
x
)
=
x
4
−
4
x
2
,
at
x
=
1
integral of sqrt(25-y^2)
∫
√
2
5
−
y
2
dy
area 3x-6,-2x+10,2,5
area
3
x
−
6
,
−
2
x
+
1
0
,
2
,
5
(dy)/(dx)+xy=0
dy
dx
+
xy
=
0
integral of x/(x^2-5x+6)
∫
x
x
2
−
5
x
+
6
dx
derivative of sqrt(1+xln(2))
d
dx
(
√
1
+
x
ln
(
2
)
)
integral from 1 to 4 of (x-1)
∫
1
4
(
x
−
1
)
dx
limit as x approaches c of f(x)g(x)
lim
x
→
c
(
f
(
x
)
g
(
x
)
)
integral from 0 to 1 of 6/(1+x^2)
∫
0
1
6
1
+
x
2
dx
tangent of f(x)=3cot^4(x),\at x= pi/4
tangent
f
(
x
)
=
3
cot
4
(
x
)
,
at
x
=
π
4
integral of 3/(x^2sqrt(x^2+9))
∫
3
x
2
√
x
2
+
9
dx
derivative of x^{e^2}
d
dx
(
x
e
2
)
integral of (e^x)/(1+64e^{2x)}
∫
e
x
1
+
6
4
e
2
x
dx
tangent of e^{3x}*ln(4x)
tangent
e
3
x
·
ln
(
4
x
)
limit as x approaches 2 of 5-3x
lim
x
→
2
(
5
−
3
x
)
derivative of 1/(\sqrt[3]{2x+1})
d
dx
(
1
3
√
2
x
+
1
)
derivative of cos(2x-1*tan(1-2x))
d
dx
(
cos
(
2
x
−
1
)
·
tan
(
1
−
2
x
)
)
integral of 3x(2-3x^2)
∫
3
x
(
2
−
3
x
2
)
dx
integral of tan(x/2)sec^2(x/2)
∫
tan
(
x
2
)
sec
2
(
x
2
)
dx
y^{'''}+4y^{''}=3x-1
y
′
′
′
+
4
y
′
′
=
3
x
−
1
integral of e^{(x+3)}
∫
e
(
x
+
3
)
dx
integral of x^2cos(9x)
∫
x
2
cos
(
9
x
)
dx
inverse oflaplace 1/(5s)
inverselaplace
1
5
s
(\partial)/(\partial x)(xyze^{x^2+y^2+z^2})
∂
∂
x
(
xyze
x
2
+
y
2
+
z
2
)
integral of xsqrt(4a^2-x^2)
∫
x
√
4
a
2
−
x
2
dx
(\partial)/(\partial y)(x^2+y^2+z^2+xy)
∂
∂
y
(
x
2
+
y
2
+
z
2
+
xy
)
limit as x approaches infinity of-1x
lim
x
→
∞
(
−
1
x
)
area y=x,y=0.2x^2-1.2x+3
area
y
=
x
,
y
=
0
.
2
x
2
−
1
.
2
x
+
3
derivative of sqrt(25+16t^2)
derivative
√
2
5
+
1
6
t
2
derivative of (x+y)^2
derivative
(
x
+
y
)
2
derivative of xsqrt(2-x^2)
derivative
x
√
2
−
x
2
laplacetransform e^{-3t}sin(4t)
laplacetransform
e
−
3
t
sin
(
4
t
)
integral of 1/(y(y^2+1))
∫
1
y
(
y
2
+
1
)
dy
derivative of f(x)=6\sqrt[3]{x}
derivative
f
(
x
)
=
6
3
√
x
integral of (sqrt(25-4x^2))/x
∫
√
2
5
−
4
x
2
x
dx
integral from 2 to infinity of 1/(x^2+4)
∫
2
∞
1
x
2
+
4
dx
derivative of (y^3)/(18)+3/(2y)
derivative
y
3
1
8
+
3
2
y
(\partial)/(\partial x)(x^y+y)
∂
∂
x
(
x
y
+
y
)
derivative of 4/x
derivative
4
x
integral of (3x^2+6x)(x^3+3x^2+1)^{2/3}
∫
(
3
x
2
+
6
x
)
(
x
3
+
3
x
2
+
1
)
2
3
dx
integral of (x+3)/(sqrt(x^2+4x+5))
∫
x
+
3
√
x
2
+
4
x
+
5
dx
derivative of ln(7x^2+3y^2)
derivative
ln
(
7
x
2
+
3
y
2
)
integral of cot^3(3x)csc^5(3x)
∫
cot
3
(
3
x
)
csc
5
(
3
x
)
dx
(\partial)/(\partial x)(sin(xy)ln(x+y))
∂
∂
x
(
sin
(
xy
)
ln
(
x
+
y
)
)
integral of (1-y^2)^2
∫
(
1
−
y
2
)
2
dy
derivative of y= 1/((7x+12)^3)
derivative
y
=
1
(
7
x
+
1
2
)
3
derivative of \sqrt[4]{(e^{5x}/(x^2+1)})
d
dx
(
4
√
e
5
x
x
2
+
1
)
1
..
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