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الهندسة
علم المثلثات
قبل التفاضل والتكامل
حساب التفاضل والتكامل
إحصائيات
مسائل حساب التفاضل والتكامل مشهورة
integral from 0 to 1 of sqrt(1+(6\sqrt{x))^2}
∫
0
1
√
1
+
(
6
√
x
)
2
dx
integral of (x^2-4x+3)/(x^3+2x^2+x)
∫
x
2
−
4
x
+
3
x
3
+
2
x
2
+
x
dx
(\partial)/(\partial x)(x+y+xy)
∂
∂
x
(
x
+
y
+
xy
)
limit as z approaches 2 of sqrt(7z^2+14z-7)
lim
z
→
2
(
√
7
z
2
+
1
4
z
−
7
)
integral of 1/((x^2+3x-4))
∫
1
(
x
2
+
3
x
−
4
)
dx
derivative y=(3x^2+2)(4x-3)
derivative
y
=
(
3
x
2
+
2
)
(
4
x
−
3
)
inverselaplace 5/(s-3)-4/(s+6)
inverselaplace
5
s
−
3
−
4
s
+
6
derivative of (2x+1/(3-x))
d
dx
(
2
x
+
1
3
−
x
)
inverselaplace 1/(s^2(s+1))
inverselaplace
1
s
2
(
s
+
1
)
(d^4)/(dx^4)(arctan(x))
d
4
dx
4
(
arctan
(
x
)
)
integral of (x^3-10x-3)
∫
(
x
3
−
1
0
x
−
3
)
dx
integral from 2 to 4 of ((6+x^2)/(x^3))
∫
2
4
(
6
+
x
2
x
3
)
dx
limit as x approaches 0+of ln(x^2)
lim
x
→
0
+
(
ln
(
x
2
)
)
derivative of ax^2+by(x^2)
d
dx
(
ax
2
+
by
(
x
)
2
)
integral of (x^3+2x-1)
∫
(
x
3
+
2
x
−
1
)
dx
derivative a^3+cos^3(x)
derivative
a
3
+
cos
3
(
x
)
area y=|5x|,y=x^2-6
area
y
=
|
5
x
|
,
y
=
x
2
−
6
derivative of ln(1-2x)
d
dx
(
ln
(
1
−
2
x
)
)
(\partial)/(\partial θ)(-e^{-3r}sin(θ))
∂
∂
θ
(
−
e
−
3
r
sin
(
θ
)
)
limit as x approaches infinity of 10
lim
x
→
∞
(
1
0
)
integral of 1/5-6/x
∫
1
5
−
6
x
dx
sum from n=1 to infinity of (n!)/(106^n)
∑
n
=
1
∞
n
!
1
0
6
n
d/(dt)(e^{3tsin(2t)})
d
dt
(
e
3
t
sin
(
2
t
)
)
x^2y^{''}-3xy^'+5y=0,y(1)=-1,y^'(1)=4
x
2
y
′
′
−
3
xy
′
+
5
y
=
0
,
y
(
1
)
=
−
1
,
y
′
(
1
)
=
4
integral of sin(2x)*sin(x)
∫
sin
(
2
x
)
·
sin
(
x
)
dx
derivative of-(11/(sqrt(x)))
d
dx
(
−
1
1
√
x
)
integral of (5e^x)/(e^{2x)+8e^x+16}
∫
5
e
x
e
2
x
+
8
e
x
+
1
6
dx
integral of (7/(x^4))
∫
(
7
x
4
)
dx
(\partial)/(\partial x)(ln(e^x+y))
∂
∂
x
(
ln
(
e
x
+
y
)
)
integral of (x+1)/((x-3)^2)
∫
x
+
1
(
x
−
3
)
2
dx
integral from t to 1 of 1/(x^2)
∫
t
1
1
x
2
dx
limit as x approaches 8 of cos((pix)/3)
lim
x
→
8
(
cos
(
π
x
3
)
)
derivative y=(x^4)/(f(x))
derivative
y
=
x
4
f
(
x
)
derivative f(x)=3x^2-4x
derivative
f
(
x
)
=
3
x
2
−
4
x
y^{''}+2y^'+26y=0,y(0)=4,y^'(0)=-2
y
′
′
+
2
y
′
+
2
6
y
=
0
,
y
(
0
)
=
4
,
y
′
(
0
)
=
−
2
derivative of sqrt(x)*ln(x)
d
dx
(
√
x
·
ln
(
x
)
)
(\partial)/(\partial x)(x^{2+y^2})
∂
∂
x
(
x
2
+
y
2
)
integral of (15x^4)
∫
(
1
5
x
4
)
dx
derivative of (-7x^2/(2x^2-5))
d
dx
(
−
7
x
2
2
x
2
−
5
)
derivative of-cos(5x)
d
dx
(
−
cos
(
5
x
)
)
integral of 7e^4
∫
7
e
4
dx
derivative f(h)=x^2+2x+7
derivative
f
(
h
)
=
x
2
+
2
x
+
7
2y^{''}+8y^'+8y=0
2
y
′
′
+
8
y
′
+
8
y
=
0
derivative 5x^4e^x+e^xx^5
derivative
5
x
4
e
x
+
e
x
x
5
derivative of x^4-2x^2-8
d
dx
(
x
4
−
2
x
2
−
8
)
implicit (dy)/(dx),y=2^x
implicit
dy
dx
,
y
=
2
x
limit as x approaches 0 of (2x)/(3x)
lim
x
→
0
(
2
x
3
x
)
integral from 0 to 1 of 5^x
∫
0
1
5
x
dx
tangent sqrt(sin(6x))
tangent
√
sin
(
6
x
)
derivative y= 1/((t^4+1)^3)
derivative
y
=
1
(
t
4
+
1
)
3
(\partial)/(\partial y)((2x^2y)/(2+x^2y^2))
∂
∂
y
(
2
x
2
y
2
+
x
2
y
2
)
sum from n=0 to infinity of 1/(ln(n+2))
∑
n
=
0
∞
1
ln
(
n
+
2
)
integral of x/(3x^2+4)
∫
x
3
x
2
+
4
dx
limit as x approaches+3 of 2x^2-3x+4
lim
x
→
+
3
(
2
x
2
−
3
x
+
4
)
integral of 1/(x^{5/3)}
∫
1
x
5
3
dx
(\partial)/(\partial x)(200(x-y^2))
∂
∂
x
(
2
0
0
(
x
−
y
2
)
)
integral of tan(x)+3/2-3sin^2(x)
∫
tan
(
x
)
+
3
2
−
3
sin
2
(
x
)
dx
derivative of x-cos(sqrt(x))
d
dx
(
x
−
cos
(
√
x
)
)
derivative of (x+1(x^3+x-2))
d
dx
(
(
x
+
1
)
(
x
3
+
x
−
2
)
)
integral of 5/((x-1)(x^2+4))
∫
5
(
x
−
1
)
(
x
2
+
4
)
dx
area 2x+1,(1,3)
area
2
x
+
1
,
(
1
,
3
)
8x^7y+x^8y^'=-5sec^2(x)tan(x)
8
x
7
y
+
x
8
y
′
=
−
5
sec
2
(
x
)
tan
(
x
)
derivative of-x+y+2
d
dx
(
−
x
+
y
+
2
)
limit as x approaches pi/6 of (sin(x)-sin(pi/6))/(x-pi/6)
lim
x
→
π
6
(
sin
(
x
)
−
sin
(
π
6
)
x
−
π
6
)
integral of 20tan(2x)sec^2(2x)
∫
2
0
tan
(
2
x
)
sec
2
(
2
x
)
dx
derivative of sin(ln(4x))
d
dx
(
sin
(
ln
(
4
x
)
)
)
derivative e^{-4x^2}
derivative
e
−
4
x
2
limit as x approaches-1 of sqrt(16-4x)
lim
x
→
−
1
(
√
1
6
−
4
x
)
integral of ((y)ln(1+y))
∫
(
(
y
)
ln
(
1
+
y
)
)
dy
integral of (2+5/7 x-6x^2)
∫
(
2
+
5
7
x
−
6
x
2
)
dx
derivative of (x-5sqrt(x-5))
d
dx
(
(
x
−
5
)
√
x
−
5
)
limit as x approaches 0 of ((x-1)^3-1)/x
lim
x
→
0
(
(
x
−
1
)
3
−
1
x
)
integral of (2/x-1/(x^2))
∫
(
2
x
−
1
x
2
)
dx
integral of 1/(x^2+10x-6)
∫
1
x
2
+
1
0
x
−
6
dx
integral of tan^4(5x)
∫
tan
4
(
5
x
)
dx
derivative x^4+2e^x
derivative
x
4
+
2
e
x
limit as x approaches 2i of (x^2)/2
lim
x
→
2
i
(
x
2
2
)
integral of 6xsin(x)
∫
6
x
sin
(
x
)
dx
integral of ((e^3)/(e^{x-1)})^2
∫
(
e
3
e
x
−
1
)
2
dx
derivative of ((8x^2/(4-x))^3)
d
dx
(
(
8
x
2
4
−
x
)
3
)
integral of csc^2(x)cot(x)
∫
csc
2
(
x
)
cot
(
x
)
dx
derivative of 2xcos(2x)
d
dx
(
2
x
cos
(
2
x
)
)
derivative of 4x^3+3x^2-6x
d
dx
(
4
x
3
+
3
x
2
−
6
x
)
y-x(dy)/(dx)=a(1+x^2(dy)/(dx))
y
−
x
dy
dx
=
a
(
1
+
x
2
dy
dx
)
tangent f(x)=(5x-9)(x+5),(2,7)
tangent
f
(
x
)
=
(
5
x
−
9
)
(
x
+
5
)
,
(
2
,
7
)
x^{''}+10x^'+21x=0
x
′
′
+
1
0
x
′
+
2
1
x
=
0
integral of (x+10)/(x^2-x-2)
∫
x
+
1
0
x
2
−
x
−
2
dx
integral from-3 to 0 of (sqrt(9-x^2))
∫
−
3
0
(
√
9
−
x
2
)
dx
(\partial)/(\partial x)(7y^6x^6-6y^5x^5)
∂
∂
x
(
7
y
6
x
6
−
6
y
5
x
5
)
sqrt(y)dx+(x-4)dy=0
√
y
dx
+
(
x
−
4
)
dy
=
0
derivative of e^{x^{-2}}
d
dx
(
e
x
−
2
)
(\partial)/(\partial x)(-(4x)/((x^2-1)^2))
∂
∂
x
(
−
4
x
(
x
2
−
1
)
2
)
inverselaplace 4/((s^2+4))
inverselaplace
4
(
s
2
+
4
)
limit as x approaches infinity of csc(x)
lim
x
→
∞
(
csc
(
x
)
)
3(dy)/(dx)=x^2
3
dy
dx
=
x
2
integral of (x+8)/(3x^2-12)
∫
x
+
8
3
x
2
−
1
2
dx
integral of (1/(x(ln(x)-1)))
∫
(
1
x
(
ln
(
x
)
−
1
)
)
dx
integral of (log_{3}(x))/(3x)
∫
log
3
(
x
)
3
x
dx
integral of sin(4x)cos^2(2x)sin(x)
∫
sin
(
4
x
)
cos
2
(
2
x
)
sin
(
x
)
dx
derivative tan(3)x^2
derivative
tan
(
3
)
x
2
1
..
253
254
255
256
257
..
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