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Popular Calculus Problems
limit as x approaches 1 of 7e^{x-1}
lim
x
→
1
(
7
e
x
−
1
)
integral of (2-2x)
∫
(
2
−
2
x
)
dx
(\partial)/(\partial x)(2x^3)
∂
∂
x
(
2
x
3
)
integral from 1 to 8 of 9\sqrt[3]{x}
∫
1
8
9
3
√
x
dx
integral of-10ln(x^2-1)
∫
−
1
0
ln
(
x
2
−
1
)
dx
integral of (1-sqrt(x))/(1+\sqrt[4]{x)}
∫
1
−
√
x
1
+
4
√
x
dx
derivative of cos(pix)
d
dx
(
cos
(
π
x
)
)
inverse oflaplace s/(s^2+1)
inverselaplace
s
s
2
+
1
integral of 1/(sqrt(36-6t^2))
∫
1
√
3
6
−
6
t
2
dt
derivative of f(x)=2-x^2
derivative
f
(
x
)
=
2
−
x
2
inverse oflaplace {1/(S^3)}
inverselaplace
{
1
S
3
}
integral of In(x)
∫
In
(
x
)
dx
taylor ln(1-2x)
taylor
ln
(
1
−
2
x
)
derivative of y=sqrt(x+4)
derivative
y
=
√
x
+
4
integral of (x+1)/(x^2-x-6)
∫
x
+
1
x
2
−
x
−
6
dx
derivative of (e^x+1^7)
d
dx
(
(
e
x
+
1
)
7
)
integral of (x-3)/(-x^2+4x-5)
∫
x
−
3
−
x
2
+
4
x
−
5
dx
(\partial)/(\partial y)(ye^{xy}-1/y)
∂
∂
y
(
ye
xy
−
1
y
)
derivative of 4x^3-66x^2+216x
d
dx
(
4
x
3
−
6
6
x
2
+
2
1
6
x
)
derivative of cos^2(x^3-ln(x^2-1))
d
dx
(
cos
2
(
x
3
)
−
ln
(
x
2
−
1
)
)
tangent of (x^3)/6-3x^2+((77x))/6-8,\at x=5
tangent
x
3
6
−
3
x
2
+
(
7
7
x
)
6
−
8
,
at
x
=
5
derivative of t^3ln(t)
derivative
t
3
ln
(
t
)
(dy)/(dx)= y/(2+x^2)
dy
dx
=
y
2
+
x
2
limit as x approaches 0 of (e^x-2)/x
lim
x
→
0
(
e
x
−
2
x
)
limit as x approaches-8 of (8+x)/(8+x)
lim
x
→
−
8
(
8
+
x
8
+
x
)
integral of (x^4+x^3)^{12}(4x^3+3x^2)
∫
(
x
4
+
x
3
)
1
2
(
4
x
3
+
3
x
2
)
dx
laplacetransform cos(2t)
laplacetransform
cos
(
2
t
)
laplacetransform s^2+4s+13s^2+4s+13
laplacetransform
s
2
+
4
s
+
1
3
s
2
+
4
s
+
1
3
sum from n=0 to infinity of (n+1)x^n
∑
n
=
0
∞
(
n
+
1
)
x
n
derivative of (x^2-x+1/(x^2+1))
d
dx
(
x
2
−
x
+
1
x
2
+
1
)
(dy)/(dx)+3/(3.5)y=9.8
dy
dx
+
3
3
.
5
y
=
9
.
8
(\partial)/(\partial z)(zln(x^2ycos(z)))
∂
∂
z
(
z
ln
(
x
2
y
cos
(
z
)
)
)
(\partial)/(\partial x)(sin(x)+xcos(x))
∂
∂
x
(
sin
(
x
)
+
x
cos
(
x
)
)
(dy)/(dt)=4-(1.5y)/(10+2.5t)
dy
dt
=
4
−
1
.
5
y
1
0
+
2
.
5
t
integral of 6tan^4(x)
∫
6
tan
4
(
x
)
dx
(\partial)/(\partial x)(2x+y+1)
∂
∂
x
(
2
x
+
y
+
1
)
integral of (3x^2-7)/(x^3-7x+6)
∫
3
x
2
−
7
x
3
−
7
x
+
6
dx
integral from 0 to 1 of (tsqrt(4+9t^2))
∫
0
1
(
t
√
4
+
9
t
2
)
dt
slope ofintercept x+2y=x+2y=8
slopeintercept
x
+
2
y
=
x
+
2
y
=
8
y^'=5x(x-3)
y
′
=
5
x
(
x
−
3
)
(dy)/(dx)= 1/3 (x^2+2)^{3/2}
dy
dx
=
1
3
(
x
2
+
2
)
3
2
(\partial)/(\partial x)(e^{ye^x})
∂
∂
x
(
e
ye
x
)
integral of (e^{-5x}+2e^x)
∫
(
e
−
5
x
+
2
e
x
)
dx
integral of 8/(7x)
∫
8
7
x
dx
derivative of f(x)=(34x-2pi*x^3)/2
derivative
f
(
x
)
=
3
4
x
−
2
π
·
x
3
2
(\partial)/(\partial x)(e^{4y-x^2-y^2})
∂
∂
x
(
e
4
y
−
x
2
−
y
2
)
integral of (8x^7-7/(x^7))
∫
(
8
x
7
−
7
x
7
)
dx
derivative of y=x^{10}
derivative
y
=
x
1
0
derivative of f(x)=-(16)/(x^3)
derivative
f
(
x
)
=
−
1
6
x
3
derivative of ax^2(x-3+bx^4(ln(x/3)))
d
dx
(
ax
2
(
x
−
3
)
+
bx
4
(
ln
(
x
3
)
)
)
integral of (2t)/(1-t^2)
∫
2
t
1
−
t
2
dt
sum from n=1 to infinity of n*2^{-n}
∑
n
=
1
∞
n
·
2
−
n
-5t^2y^{''}-2ty^'+14y=0
−
5
t
2
y
′
′
−
2
ty
′
+
1
4
y
=
0
derivative of f(x)=pix
derivative
f
(
x
)
=
π
x
derivative of x^2e^x-2xe^x+5e^x
derivative
x
2
e
x
−
2
xe
x
+
5
e
x
limit as x approaches 0 of (x^2+5x)/x
lim
x
→
0
(
x
2
+
5
x
x
)
xy^'=y+x
xy
′
=
y
+
x
integral of |2x-3|
∫
|
2
x
−
3
|
dx
y^{''}+6y^'=-108cos(6x)
y
′
′
+
6
y
′
=
−
1
0
8
cos
(
6
x
)
integral of ((5sin^3(x)))/(cos(x))
∫
(
5
sin
3
(
x
)
)
cos
(
x
)
dx
integral of 5e^{9x}
∫
5
e
9
x
dx
tangent of f(x)=x^4,(2,16)
tangent
f
(
x
)
=
x
4
,
(
2
,
1
6
)
limit as x approaches 0 of+(x)
lim
x
→
0
(
+
(
x
)
)
integral of 1/((x/2)^2+1)
∫
1
(
x
2
)
2
+
1
dx
derivative of \sqrt[3]{8}
d
dx
(
3
√
8
)
derivative of (e^{2x}-1/x)
d
dx
(
e
2
x
−
1
x
)
derivative of ay(x)
d
dx
(
ay
(
x
)
)
derivative of 6/(x^5)
d
dx
(
6
x
5
)
integral of e^{-x/2}x
∫
e
−
x
2
xdx
(dy)/(dx)-2y=e^{3x}
dy
dx
−
2
y
=
e
3
x
integral of xcos(x/2)
∫
x
cos
(
x
2
)
dx
((x-y))/((x+2y))=(dy)/(dx)
(
x
−
y
)
(
x
+
2
y
)
=
dy
dx
y'=y^2-4
y
′
=
y
2
−
4
(x^2+4)((dy)/(dx))=xy
(
x
2
+
4
)
(
dy
dx
)
=
xy
integral of x^3sqrt(x^2+40)
∫
x
3
√
x
2
+
4
0
dx
derivative of 4/(x^2)
derivative
4
x
2
integral of ((x-95))/(x^2(x+5))
∫
(
x
−
9
5
)
x
2
(
x
+
5
)
dx
y^'=(x-3)(y+1)^{(2/3)}
y
′
=
(
x
−
3
)
(
y
+
1
)
(
2
3
)
limit as x approaches 2+of e^{3/(2-x)}
lim
x
→
2
+
(
e
3
2
−
x
)
derivative of (x^3+y^3/(x^2+y^2))
d
dx
(
x
3
+
y
3
x
2
+
y
2
)
integral of 23
∫
2
3
integral of (x+2)/(x^2(x^2+1))
∫
x
+
2
x
2
(
x
2
+
1
)
dx
sum from n=1 to infinity of 1/((2n-1)2n)
∑
n
=
1
∞
1
(
2
n
−
1
)
2
n
limit as h approaches 0 of 4(h+2)
lim
h
→
0
(
4
(
h
+
2
)
)
y^'+3y=1
y
′
+
3
y
=
1
(dy)/(dx)=x^2y^3
dy
dx
=
x
2
y
3
y^{''}+6y^'+9y=3x+5,y(0)=1,y^'(0)=-1
y
′
′
+
6
y
′
+
9
y
=
3
x
+
5
,
y
(
0
)
=
1
,
y
′
(
0
)
=
−
1
integral from 0 to 1 of (x^3+x)
∫
0
1
(
x
3
+
x
)
dx
integral of 2xyz
∫
2
xyzdy
(\partial)/(\partial y)(y-1/x)
∂
∂
y
(
y
−
1
x
)
limit as x approaches 2+of 3
lim
x
→
2
+
(
3
)
laplacetransform t^3e^{-,\at}
laplacetransform
t
3
e
−
,
at
integral of x/(sqrt(6x+1))
∫
x
√
6
x
+
1
dx
derivative of arctan((2x)/5)
derivative
arctan
(
2
x
5
)
derivative of 4xsqrt(3x^2+2)
derivative
4
x
√
3
x
2
+
2
derivative of (x^5)/(10)+1/(6x^3)
derivative
x
5
1
0
+
1
6
x
3
t*(dy)/(dt)=t^3+14t^3y
t
·
dy
dt
=
t
3
+
1
4
t
3
y
integral of (cos(t))/(sin^4(t)-16)
∫
cos
(
t
)
sin
4
(
t
)
−
1
6
dt
derivative of (x+5/(x+1))
d
dx
(
x
+
5
x
+
1
)
limit as x approaches 1 of (4-x^2)/(x+2)
lim
x
→
1
(
4
−
x
2
x
+
2
)
1
..
557
558
559
560
561
..
2459