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الهندسة
علم المثلثات
قبل التفاضل والتكامل
حساب التفاضل والتكامل
إحصائيات
مسائل حساب التفاضل والتكامل مشهورة
integral of 1/(sin(x)cos(x)+cos^2(x))
∫
1
sin
(
x
)
cos
(
x
)
+
cos
2
(
x
)
dx
integral of (cos(x))/(1-sin(x))
∫
cos
(
x
)
1
−
sin
(
x
)
dx
sum from n=0 to infinity of 1/((4n^2-1))
∑
n
=
0
∞
1
(
4
n
2
−
1
)
integral from 8 to infinity of xe^{-2x}
∫
8
∞
xe
−
2
x
dx
derivative of sin^3(x+sin(3x))
d
dx
(
sin
3
(
x
)
+
sin
(
3
x
)
)
d/(dy)(sqrt(tan(x)+y))
d
dy
(
√
tan
(
x
)
+
y
)
derivative of x^{(-1/2})
d
dx
(
x
−
1
2
)
integral of ((arctan(x))^2)/(x^2+1)
∫
(
arctan
(
x
)
)
2
x
2
+
1
dx
inverselaplace 1/((s-4))
inverselaplace
1
(
s
−
4
)
(\partial)/(\partial y)(x^2yz+1/(xyz^2))
∂
∂
y
(
x
2
yz
+
1
xyz
2
)
sum from n=0 to infinity of (-1)^nx^n
∑
n
=
0
∞
(
−
1
)
n
x
n
(dy)/(dx)=5y^2,y(0)=3
dy
dx
=
5
y
2
,
y
(
0
)
=
3
tangent f(x)=x^3-15x,(1,-14)
tangent
f
(
x
)
=
x
3
−
1
5
x
,
(
1
,
−
1
4
)
derivative of (10/x)
d
dx
(
1
0
x
)
integral of (yln(x))/x
∫
y
ln
(
x
)
x
dx
tangent 1/(sqrt(5x)),\at x=9
tangent
1
√
5
x
,
at
x
=
9
taylor 1/((sqrt((3-2x))))
taylor
1
(
√
(
3
−
2
x
)
)
tangent (5x+2)/(6x-4)
tangent
5
x
+
2
6
x
−
4
area y=x,(0,6)
area
y
=
x
,
(
0
,
6
)
integral from 0 to 4 of 2t+4
∫
0
4
2
t
+
4
dt
sum from n=0 to infinity of 1/((n(n+2)))
∑
n
=
0
∞
1
(
n
(
n
+
2
)
)
area x+y=4,x-y=0,y+3x=4
area
x
+
y
=
4
,
x
−
y
=
0
,
y
+
3
x
=
4
derivative of (4x/(x^2-4))
d
dx
(
4
x
x
2
−
4
)
(dy)/(dx)+y=e^x
dy
dx
+
y
=
e
x
derivative f(x)=-(6x^2)/((x^3-1)^2)
derivative
f
(
x
)
=
−
6
x
2
(
x
3
−
1
)
2
derivative of (x+1^{2/3}(2x^2-1)^3)
d
dx
(
(
x
+
1
)
2
3
(
2
x
2
−
1
)
3
)
derivative of sin(kx)
d
dx
(
sin
(
kx
)
)
derivative of 2/((4-x^2))
d
dx
(
2
(
4
−
x
)
2
)
integral of 2u^2
∫
2
u
2
du
limit as x approaches-1 of (x-1)/(x+1)
lim
x
→
−
1
(
x
−
1
x
+
1
)
integral of sin^5(x/2)
∫
sin
5
(
x
2
)
dx
derivative of x^2sin(ln(x))
d
dx
(
x
2
sin
(
ln
(
x
)
)
)
limit as x approaches 0 of sqrt(5-2x^2)
lim
x
→
0
(
√
5
−
2
x
2
)
limit as x approaches 3 of 2x^{-1}
lim
x
→
3
(
2
x
−
1
)
(dy)/(dx)= 1/4 sqrt(y)cos^2(sqrt(y))
dy
dx
=
1
4
√
y
cos
2
(
√
y
)
integral of csc(x)tan(x)
∫
csc
(
x
)
tan
(
x
)
dx
derivative of cos(xln(x^2+1))
d
dx
(
cos
(
x
)
ln
(
x
2
+
1
)
)
integral of sqrt(25-x^2)(-2x)
∫
√
2
5
−
x
2
(
−
2
x
)
dx
limit as x approaches 1+of (1-x)/(x^2-1)
lim
x
→
1
+
(
1
−
x
x
2
−
1
)
integral of (2x-5)^7
∫
(
2
x
−
5
)
7
dx
integral of (18)/(x^2-x-20)
∫
1
8
x
2
−
x
−
2
0
dx
integral of (6e^x+7/x)
∫
(
6
e
x
+
7
x
)
dx
integral of y^3+1.8y^2-2.4y
∫
y
3
+
1
.
8
y
2
−
2
.
4
ydy
derivative y= x/(sqrt(x^2+4))
derivative
y
=
x
√
x
2
+
4
(\partial)/(\partial y)((xy)/(x+y+z))
∂
∂
y
(
xy
x
+
y
+
z
)
(\partial)/(\partial y)(2xy-y)
∂
∂
y
(
2
xy
−
y
)
derivative f(x)= 7/(sqrt(x))
derivative
f
(
x
)
=
7
√
x
derivative (sin(x))/(cos(x))
derivative
sin
(
x
)
cos
(
x
)
d/(dt)(sin(3ln(t)-e^{t^2}))
d
dt
(
sin
(
3
ln
(
t
)
−
e
t
2
)
)
tangent y=x^2-3,(-2,1)
tangent
y
=
x
2
−
3
,
(
−
2
,
1
)
integral of (x^5+1)/(x^3-3x^2-10x)
∫
x
5
+
1
x
3
−
3
x
2
−
1
0
x
dx
derivative of e^xx+7e^x
d
dx
(
e
x
x
+
7
e
x
)
integral of (e^x-3)^2
∫
(
e
x
−
3
)
2
dx
area 10x^4-10x^2,9x^2
area
1
0
x
4
−
1
0
x
2
,
9
x
2
(\partial)/(\partial y)((2-x)(y-2)(3-x-y))
∂
∂
y
(
(
2
−
x
)
(
y
−
2
)
(
3
−
x
−
y
)
)
integral of 2/(x^2+x)
∫
2
x
2
+
x
dx
derivative of 30(4e^{x^2}x^3+6e^{x^2}x)
d
dx
(
3
0
(
4
e
x
2
x
3
+
6
e
x
2
x
)
)
derivative of (6x^2+8x+4/(sqrt(x)))
d
dx
(
6
x
2
+
8
x
+
4
√
x
)
integral of sin(6x)cos(3x)
∫
sin
(
6
x
)
cos
(
3
x
)
dx
derivative of (x^{x+1})
d
dx
(
(
x
)
x
+
1
)
(dx)/(dy)=sin(x+y)
dx
dy
=
sin
(
x
+
y
)
derivative (2x-1)^2*ln(2x-1)
derivative
(
2
x
−
1
)
2
·
ln
(
2
x
−
1
)
slope (0.4)(6.8)
slope
(
0
.
4
)
(
6
.
8
)
y^'=-ay
y
′
=
−
ay
derivative of x^ay^{1-a}
d
dx
(
x
a
y
1
−
a
)
limit as x approaches 0 of arctan(5x)
lim
x
→
0
(
arctan
(
5
x
)
)
d/(dt)((ln(t))^2)
d
dt
(
(
ln
(
t
)
)
2
)
slope (1,-1),(6,-1)
slope
(
1
,
−
1
)
,
(
6
,
−
1
)
integral from 6 to 8 of (92)/((x-6)^3)
∫
6
8
9
2
(
x
−
6
)
3
dx
derivative of sin^4(cos(8x))
d
dx
(
sin
4
(
cos
(
8
x
)
)
)
limit as x approaches 4 of x^4-5x^2+2
lim
x
→
4
(
x
4
−
5
x
2
+
2
)
area f(x)= 1/x ,[1,2]
area
f
(
x
)
=
1
x
,
[
1
,
2
]
integral from-5 to 0 of 2^{1-x}
∫
−
5
0
2
1
−
x
dx
tangent y=(6x)/(x^2+1)
tangent
y
=
6
x
x
2
+
1
(\partial)/(\partial x)(xsin(2y))
∂
∂
x
(
x
sin
(
2
y
)
)
derivative f(x)=(x^2+3)(x^2-4x)
derivative
f
(
x
)
=
(
x
2
+
3
)
(
x
2
−
4
x
)
integral of (5x^2+7x-11)/(x^2)
∫
5
x
2
+
7
x
−
1
1
x
2
dx
integral of (2x+6)e^{-4x}
∫
(
2
x
+
6
)
e
−
4
x
dx
(\partial)/(\partial x)(cos(5x))
∂
∂
x
(
cos
(
5
x
)
)
derivative f(x)=(8x+9)(9x-10)
derivative
f
(
x
)
=
(
8
x
+
9
)
(
9
x
−
1
0
)
derivative of 7(cos(x^2-2x^2sin(x^2)))
d
dx
(
7
(
cos
(
x
2
)
−
2
x
2
sin
(
x
2
)
)
)
derivative f(x)=x^22^x
derivative
f
(
x
)
=
x
2
2
x
integral of 5/(x^2+4x-1)
∫
5
x
2
+
4
x
−
1
dx
integral of 1/(x(x^2+1))
∫
1
x
(
x
2
+
1
)
dx
derivative cos(e^{-t^2})
derivative
cos
(
e
−
t
2
)
integral from 0 to pi of sin(6x)cos(3x)
∫
0
π
sin
(
6
x
)
cos
(
3
x
)
dx
integral of-2e^x(e^x-1)^3
∫
−
2
e
x
(
e
x
−
1
)
3
dx
derivative 9arctan(x-sqrt(1+x^2))
derivative
9
arctan
(
x
−
√
1
+
x
2
)
slope (19,-16),(-7,-15)
slope
(
1
9
,
−
1
6
)
,
(
−
7
,
−
1
5
)
limit as x approaches 2 of x^3
lim
x
→
2
(
x
3
)
derivative 7xe^x
derivative
7
xe
x
(\partial)/(\partial y)(-y/((x+2)^2))
∂
∂
y
(
−
y
(
x
+
2
)
2
)
derivative of (arctan(x)dx)
d
dx
(
(
arctan
(
x
)
)
dx
)
derivative of (x^2+1/(3x^3+4x))
d
dx
(
x
2
+
1
3
x
3
+
4
x
)
integral of (e^{sqrt(x)})
∫
(
e
√
x
)
dx
derivative of (x-4/(x+2))
d
dx
(
x
−
4
x
+
2
)
limit as x approaches 3 of 4x^2-2x+10
lim
x
→
3
(
4
x
2
−
2
x
+
1
0
)
integral of 8e^x
∫
8
e
x
dx
derivative of (x+2/(x-4))
d
dx
(
x
+
2
x
−
4
)
derivative-2ab^2e^{-b^2x^2}x
derivative
−
2
ab
2
e
−
b
2
x
2
x
1
..
442
443
444
445
446
..
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