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Popular Calculus Problems
integral of 1/(x^2+11x+28)
∫
1
x
2
+
1
1
x
+
2
8
dx
y^'=5x^4e^{-x^5}+e^x
y
′
=
5
x
4
e
−
x
5
+
e
x
sum from n=0 to infinity of n!2^nn^{-n}
∑
n
=
0
∞
n
!
2
n
n
−
n
tangent of f(x)=2x^3+3x^2-12x+8
tangent
f
(
x
)
=
2
x
3
+
3
x
2
−
1
2
x
+
8
parity y=(x^x)/(sin(x))
parity
y
=
x
x
sin
(
x
)
limit as x approaches 2 of (x^3+8)/(x-2)
lim
x
→
2
(
x
3
+
8
x
−
2
)
(\partial)/(\partial y)(e^{x-1}cos(y))
∂
∂
y
(
e
x
−
1
cos
(
y
)
)
(\partial)/(\partial x)(72y^7x^7-56y^6x^6)
∂
∂
x
(
7
2
y
7
x
7
−
5
6
y
6
x
6
)
derivative of (sqrt(1-x))/(sqrt(1+x))
derivative
√
1
−
x
√
1
+
x
limit as x approaches 0 of (5x+6)/x
lim
x
→
0
(
5
x
+
6
x
)
limit as x approaches 3+of (x^2)/(9-x^2)
lim
x
→
3
+
(
x
2
9
−
x
2
)
integral of 1x(4-2(x-3))
∫
1
x
(
4
−
2
(
x
−
3
)
)
dx
slope of (-5,-1),(-1,5)
slope
(
−
5
,
−
1
)
,
(
−
1
,
5
)
limit as x approaches 3-of 2/(3-x)
lim
x
→
3
−
(
2
3
−
x
)
derivative of 2sqrt(x)+\sqrt[3]{x}
d
dx
(
2
√
x
+
3
√
x
)
integral of 7sin(x/3)
∫
7
sin
(
x
3
)
dx
y^'=(x^4y^3+2x^4)/(y^2)
y
′
=
x
4
y
3
+
2
x
4
y
2
derivative of-1/8 cos(x/2)
d
dx
(
−
1
8
cos
(
x
2
)
)
integral of x/6 e^{x^2}
∫
x
6
e
x
2
dx
(\partial)/(\partial x)(sin(7y^2-7xy))
∂
∂
x
(
sin
(
7
y
2
−
7
xy
)
)
integral of e^{2x}(x+1)
∫
e
2
x
(
x
+
1
)
dx
inverse oflaplace (s+2)/(s(s^2+9))
inverselaplace
s
+
2
s
(
s
2
+
9
)
integral of 2x(x^2+6)^4
∫
2
x
(
x
2
+
6
)
4
dx
laplacetransform 6*e^{5t}*cos(2t)-e^{7t}
laplacetransform
6
·
e
5
t
·
cos
(
2
t
)
−
e
7
t
integral of ae^{3x}
∫
ae
3
x
dx
limit as x approaches-2 of x^2+2x+4
lim
x
→
−
2
(
x
2
+
2
x
+
4
)
f(x)=x^6-4x^4+x+1
f
(
x
)
=
x
6
−
4
x
4
+
x
+
1
(dy)/(dx)= 1/x (y^2+0.6y)
dy
dx
=
1
x
(
y
2
+
0
.
6
y
)
integral from-1 to 3 of-x^2+2x+3
∫
−
1
3
−
x
2
+
2
x
+
3
dx
f^'(x)=sqrt(x)(3+5x),f(1)=7
f
′
(
x
)
=
√
x
(
3
+
5
x
)
,
f
(
1
)
=
7
integral of (sin(x))/(sin(x)+cos(x))
∫
sin
(
x
)
sin
(
x
)
+
cos
(
x
)
dx
solvefor f,tan(f)(x)=7x^4+4 x/2 sqrt(x^3+1)
solvefor
f
,
tan
(
f
)
(
x
)
=
7
x
4
+
4
x
2
√
x
3
+
1
integral of (1/(x^3)+7/(x^2))
∫
(
1
x
3
+
7
x
2
)
dx
tangent of f(x)=x^2+5,(2,9)
tangent
f
(
x
)
=
x
2
+
5
,
(
2
,
9
)
taylor 10sqrt(1+x)
taylor
1
0
√
1
+
x
integral of 1/(x^2(1-x))
∫
1
x
2
(
1
−
x
)
dx
(\partial)/(\partial t)(e^{-7t}cos(pix))
∂
∂
t
(
e
−
7
t
cos
(
π
x
)
)
limit as x approaches pi/4 of (sin(x-pi/4))/(4x-pi)
lim
x
→
π
4
(
sin
(
x
−
π
4
)
4
x
−
π
)
x^'+x=0
x
′
+
x
=
0
1/x (dy)/(dx)= 1/(x^2+1)
1
x
dy
dx
=
1
x
2
+
1
derivative of f(x)=5cos(x)
derivative
f
(
x
)
=
5
cos
(
x
)
limit as x approaches 0 of (xe^x)/(sin(x))
lim
x
→
0
(
xe
x
sin
(
x
)
)
sum from n=1 to infinity of 1(5/6)^n
∑
n
=
1
∞
1
(
5
6
)
n
derivative of 1/(5x-2)
d
dx
(
1
5
x
−
2
)
sum from k=1 to infinity of cos(1/k)-cos(1/(k+1))
∑
k
=
1
∞
cos
(
1
k
)
−
cos
(
1
k
+
1
)
sum from n=0 to infinity of ((3^n))/2
∑
n
=
0
∞
(
3
n
)
2
integral of 9/(x^2(x^2+25))
∫
9
x
2
(
x
2
+
2
5
)
dx
tangent of 1/x
tangent
1
x
(dx)/(dt)=6-(3x)/(500)
dx
dt
=
6
−
3
x
5
0
0
inverse oflaplace ((6s-4))/(s^2-4s+20)
inverselaplace
(
6
s
−
4
)
s
2
−
4
s
+
2
0
(\partial)/(\partial x)(x^{2/3})
∂
∂
x
(
x
2
3
)
limit as x approaches 0+of e^x+ln(x)
lim
x
→
0
+
(
e
x
+
ln
(
x
)
)
integral of (18)/((x+3)(x^2-9))
∫
1
8
(
x
+
3
)
(
x
2
−
9
)
dx
y^{''}+2y^'+y=(-4e^{-t})/(t^2+1)
y
′
′
+
2
y
′
+
y
=
−
4
e
−
t
t
2
+
1
(\partial)/(\partial x)((y^2-x^2)/(xy))
∂
∂
x
(
y
2
−
x
2
xy
)
sum from n=1 to infinity of 4/(7n+2)
∑
n
=
1
∞
4
7
n
+
2
derivative of x^5e^{-3x}
d
dx
(
x
5
e
−
3
x
)
d/(dt)(7e^tsin(t))
d
dt
(
7
e
t
sin
(
t
)
)
derivative of (2x^2/(x^2+1))
d
dx
(
2
x
2
x
2
+
1
)
derivative of 1+4/x
d
dx
(
1
+
4
x
)
integral of (ln(3x+1))/(6x+2)
∫
ln
(
3
x
+
1
)
6
x
+
2
dx
derivative of 6+1/8 (t-4)^2
derivative
6
+
1
8
(
t
−
4
)
2
integral of pitcos(nt)
∫
π
t
cos
(
nt
)
dt
limit as x approaches 0 of (2x)/(e^x-1)
lim
x
→
0
(
2
x
e
x
−
1
)
integral of 1/(x^3-216)
∫
1
x
3
−
2
1
6
dx
area x=-2,x=1,y=10x,y=x^2-11
area
x
=
−
2
,
x
=
1
,
y
=
1
0
x
,
y
=
x
2
−
1
1
derivative of (x^4-x^3-8/((x-3)(x+2)))
d
dx
(
x
4
−
x
3
−
8
(
x
−
3
)
(
x
+
2
)
)
tangent of y=x^3-4,(2,0)
tangent
y
=
x
3
−
4
,
(
2
,
0
)
integral from 0 to 2 of (3-x^3)
∫
0
2
(
3
−
x
3
)
dx
integral of (sqrt(36+(ln(4x))^2))/x
∫
√
3
6
+
(
ln
(
4
x
)
)
2
x
dx
integral of (5tsqrt(t))/(1+t^5)
∫
5
t
√
t
1
+
t
5
dt
derivative of y=sin(x)*cos(x)
derivative
y
=
sin
(
x
)
·
cos
(
x
)
derivative of f(x)=x-2ln(1-1/x)
derivative
f
(
x
)
=
x
−
2
ln
(
1
−
1
x
)
laplacetransform 27t^2sin(6t-60)
laplacetransform
2
7
t
2
sin
(
6
t
−
6
0
◦
)
derivative of sqrt(x^2+y^2-5)
d
dx
(
√
x
2
+
y
2
−
5
)
derivative of 3x-1/x
d
dx
(
3
x
−
1
x
)
integral from 2 to 6 of x/(x^2+4x+13)
∫
2
6
x
x
2
+
4
x
+
1
3
dx
derivative of f(x)=(2+3x)(6-5x)
derivative
f
(
x
)
=
(
2
+
3
x
)
(
6
−
5
x
)
area x^2+6x+8,0
area
x
2
+
6
x
+
8
,
0
derivative of f(x)=3sin(x)
derivative
f
(
x
)
=
3
sin
(
x
)
(\partial)/(\partial x)(1/y)
∂
∂
x
(
1
y
)
derivative of y=2x^6
derivative
y
=
2
x
6
integral of 1/(1-t^2)
∫
1
1
−
t
2
dt
integral of 1/(sqrt(225+x^2))
∫
1
√
2
2
5
+
x
2
dx
integral of (e^x)/(81-e^{2x)}
∫
e
x
8
1
−
e
2
x
dx
integral of x^2sqrt(16-x^2)
∫
x
2
√
1
6
−
x
2
dx
integral of 6sinh(x/2-ln(3))
∫
6
sinh
(
x
2
−
ln
(
3
)
)
dx
area y=e^x,y=3,x=0
area
y
=
e
x
,
y
=
3
,
x
=
0
derivative of 5e^{-x}
derivative
5
e
−
x
integral of (3e^x)/(e^{2x)+10e^x+25}
∫
3
e
x
e
2
x
+
1
0
e
x
+
2
5
dx
integral of ((e^x+9))/((e^{2x)-6e^x+9)}
∫
(
e
x
+
9
)
(
e
2
x
−
6
e
x
+
9
)
dx
tangent of f(x)= 8/x ,\at x=4
tangent
f
(
x
)
=
8
x
,
at
x
=
4
area y=sqrt(2x),2sqrt(x-4),y=0
area
y
=
√
2
x
,
2
√
x
−
4
,
y
=
0
derivative of sqrt(5x^3-10x^2-3/x)
derivative
√
5
x
3
−
1
0
x
2
−
3
x
derivative of sin(x^3+2x-1)
d
dx
(
sin
(
x
3
+
2
x
−
1
)
)
(dy)/(dt)=5y+y^4,y(0)=1
dy
dt
=
5
y
+
y
4
,
y
(
0
)
=
1
derivative of 1-cos^2(17x)
derivative
1
−
cos
2
(
1
7
x
)
derivative of f(x)=6x^2-20x^3
derivative
f
(
x
)
=
6
x
2
−
2
0
x
3
derivative of 5-|x-2|
d
dx
(
5
−
|
x
−
2
|
)
area 8-x^2,x^2,-3,3
area
8
−
x
2
,
x
2
,
−
3
,
3
1
..
1207
1208
1209
1210
1211
..
2459