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Question: Cannot find integration

Question:Cannot find integration

Jameel123 20 Maple 15
integration
April 06 2020
0

Cannot find integration proplem_in_maple.mw

> 

restart
> 

with(LinearAlgebra)
> 

with(orthopoly)
> 

``
> 

with(student)
> 

Digits := 32

32

 (1)
> 

interface(rtablesize = 100)

10

 (2)
> 

a := 0; b := 1; N := 5; h := (b-a)/N; B[0] := 1; B[1] := x; n := 2; B[2] := x^2+2; alpha := 1/2

0

  

1

  

5

  

1/5

  

1

  

x

  

2

  

x^2+2

  

1/2

 (3)
> 

NULL
> 

for j from 3 to N do B[j] := expand(x*B[j-1]-B[j-2]) end do

x^3+x

  

x^4-2

  

x^5-3*x-x^3

 (4)
> 

for i from 0 to N do x[i] := h*i+a end do

0

  

1/5

  

2/5

  

3/5

  

4/5

  

1

 (5)
> 

y := sum(c[s]*B[s], s = 0 .. N)

c[0]+c[1]*x+c[2]*(x^2+2)+c[3]*(x^3+x)+c[4]*(x^4-2)+c[5]*(x^5-3*x-x^3)

 (6)
> 

yt := subs(x = t, y)

c[0]+c[1]*t+c[2]*(t^2+2)+c[3]*(t^3+t)+c[4]*(t^4-2)+c[5]*(t^5-3*t-t^3)

 (7)
> 

k := expand(int(yt*sin(t)*x, t = 0 .. x))

x*c[0]+22*x*c[4]-c[1]*cos(x)*x^2-c[2]*cos(x)*x^3+2*c[2]*sin(x)*x^2-c[3]*cos(x)*x^4+3*c[3]*sin(x)*x^3+5*c[3]*cos(x)*x^2-c[4]*cos(x)*x^5+4*c[4]*sin(x)*x^4+12*c[4]*cos(x)*x^3-24*c[4]*sin(x)*x^2-c[5]*cos(x)*x^6+5*c[5]*sin(x)*x^5+21*c[5]*cos(x)*x^4-63*c[5]*sin(x)*x^3-123*c[5]*cos(x)*x^2-x*cos(x)*c[0]-22*x*cos(x)*c[4]+x*c[1]*sin(x)-5*x*c[3]*sin(x)+123*x*c[5]*sin(x)

 (8)
> 

k4 := k*y

(x*c[0]+22*x*c[4]-c[1]*cos(x)*x^2-c[2]*cos(x)*x^3+2*c[2]*sin(x)*x^2-c[3]*cos(x)*x^4+3*c[3]*sin(x)*x^3+5*c[3]*cos(x)*x^2-c[4]*cos(x)*x^5+4*c[4]*sin(x)*x^4+12*c[4]*cos(x)*x^3-24*c[4]*sin(x)*x^2-c[5]*cos(x)*x^6+5*c[5]*sin(x)*x^5+21*c[5]*cos(x)*x^4-63*c[5]*sin(x)*x^3-123*c[5]*cos(x)*x^2-x*cos(x)*c[0]-22*x*cos(x)*c[4]+x*c[1]*sin(x)-5*x*c[3]*sin(x)+123*x*c[5]*sin(x))*(c[0]+c[1]*x+c[2]*(x^2+2)+c[3]*(x^3+x)+c[4]*(x^4-2)+c[5]*(x^5-3*x-x^3))

 (9)
> 

f := (8*x^3*(1/3)-2*x^(1/2))*y/GAMMA(1/2)+(1/1260)*x+k4

((8/3)*x^3-2*x^(1/2))*(c[0]+c[1]*x+c[2]*(x^2+2)+c[3]*(x^3+x)+c[4]*(x^4-2)+c[5]*(x^5-3*x-x^3))/Pi^(1/2)+(1/1260)*x+(x*c[0]+22*x*c[4]-c[1]*cos(x)*x^2-c[2]*cos(x)*x^3+2*c[2]*sin(x)*x^2-c[3]*cos(x)*x^4+3*c[3]*sin(x)*x^3+5*c[3]*cos(x)*x^2-c[4]*cos(x)*x^5+4*c[4]*sin(x)*x^4+12*c[4]*cos(x)*x^3-24*c[4]*sin(x)*x^2-c[5]*cos(x)*x^6+5*c[5]*sin(x)*x^5+21*c[5]*cos(x)*x^4-63*c[5]*sin(x)*x^3-123*c[5]*cos(x)*x^2-x*cos(x)*c[0]-22*x*cos(x)*c[4]+x*c[1]*sin(x)-5*x*c[3]*sin(x)+123*x*c[5]*sin(x))*(c[0]+c[1]*x+c[2]*(x^2+2)+c[3]*(x^3+x)+c[4]*(x^4-2)+c[5]*(x^5-3*x-x^3))

 (10)
> 

"f(x):=((8/3 x^3-2 sqrt(x)) (c[0]+c[1] x+c[2] (x^2+2)+c[3] (x^3+x)+c[4] (x^4-2)+c[5] (x^5-3 x-x^3)))/(sqrt(Pi))+1/1260 x+(x c[0]+22 x c[4]+x c[1] sin(x)-5 x c[3] sin(x)+123 x c[5] sin(x)-x cos(x) c[0]-22 x cos(x) c[4]-c[1] cos(x) x^2-c[2] cos(x) x^3+2 c[2] sin(x) x^2-c[3] cos(x) x^4+3 c[3] sin(x) x^3+5 c[3] cos(x) x^2-c[4] cos(x) x^5+4 c[4] sin(x) x^4+12 c[4] cos(x) x^3-24 c[4] sin(x) x^2-c[5] cos(x) x^6+5 c[5] sin(x) x^5+21 c[5] cos(x) x^4-63 c[5] sin(x) x^3-123 c[5] cos(x) x^2) (c[0]+c[1] x+c[2] (x^2+2)+c[3] (x^3+x)+c[4] (x^4-2)+c[5] (x^5-3 x-x^3))"

proc (x) options operator, arrow; ((8/3)*x^3-2*sqrt(x))*(c[0]+Typesetting:-delayDotProduct(c[1], x, true)+c[2]*(x^2+2)+c[3]*(x^3+x)+c[4]*(x^4-2)+c[5]*(x^5-3*x-x^3))/sqrt(Pi)+Typesetting:-delayDotProduct(1/1260, x, true)+(Typesetting:-delayDotProduct(x, c[0], true)+22*x*c[4]+Typesetting:-delayDotProduct(x, c[1], true)*sin(x)-5*x*c[3]*sin(x)+123*x*c[5]*sin(x)-Typesetting:-delayDotProduct(x, cos(x), true)*c[0]-22*x*cos(x)*c[4]-c[1]*cos(x)*x^2-c[2]*cos(x)*x^3+2*c[2]*sin(x)*x^2-c[3]*cos(x)*x^4+3*c[3]*sin(x)*x^3+5*c[3]*cos(x)*x^2-c[4]*cos(x)*x^5+4*c[4]*sin(x)*x^4+12*c[4]*cos(x)*x^3-24*c[4]*sin(x)*x^2-c[5]*cos(x)*x^6+5*c[5]*sin(x)*x^5+21*c[5]*cos(x)*x^4-63*c[5]*sin(x)*x^3-123*c[5]*cos(x)*x^2)*(c[0]+Typesetting:-delayDotProduct(c[1], x, true)+c[2]*(x^2+2)+c[3]*(x^3+x)+c[4]*(x^4-2)+c[5]*(x^5-3*x-x^3)) end proc

 (11)
> 

NULL
> 

"H(f,alpha,x):=Int((x-s)^(alpha-1)*f(s)/GAMMA(alpha), s = 0 .. x)"

proc (f, alpha, x) options operator, arrow; Int((x-s)^(alpha-1)*f(s)/GAMMA(alpha), s = 0 .. x) end proc

 (12)
> 

`assuming`([value(%)], [x > 0])

proc (f, alpha, x) options operator, arrow; Int((x-s)^(alpha-1)*f(s)/GAMMA(alpha), s = 0 .. x) end proc

 (13)
> 

H(f, alpha, x)

Int((((8/3)*s^3-2*s^(1/2))*(c[0]+c[1]*s+c[2]*(s^2+2)+c[3]*(s^3+s)+c[4]*(s^4-2)+c[5]*(s^5-3*s-s^3))/Pi^(1/2)+(1/1260)*s+(s*c[0]+22*s*c[4]+c[1]*s*sin(s)-5*s*c[3]*sin(s)+123*s*c[5]*sin(s)-s*cos(s)*c[0]-22*s*cos(s)*c[4]-c[1]*cos(s)*s^2-c[2]*cos(s)*s^3+2*c[2]*sin(s)*s^2-c[3]*cos(s)*s^4+3*c[3]*sin(s)*s^3+5*c[3]*cos(s)*s^2-c[4]*cos(s)*s^5+4*c[4]*sin(s)*s^4+12*c[4]*cos(s)*s^3-24*c[4]*sin(s)*s^2-c[5]*cos(s)*s^6+5*c[5]*sin(s)*s^5+21*c[5]*cos(s)*s^4-63*c[5]*sin(s)*s^3-123*c[5]*cos(s)*s^2)*(c[0]+c[1]*s+c[2]*(s^2+2)+c[3]*(s^3+s)+c[4]*(s^4-2)+c[5]*(s^5-3*s-s^3)))/((x-s)^(1/2)*Pi^(1/2)), s = 0 .. x)

 (14)
> 

z := value(%)

int((((8/3)*s^3-2*s^(1/2))*(c[0]+c[1]*s+c[2]*(s^2+2)+c[3]*(s^3+s)+c[4]*(s^4-2)+c[5]*(s^5-3*s-s^3))/Pi^(1/2)+(1/1260)*s+(s*c[0]+22*s*c[4]+c[1]*s*sin(s)-5*s*c[3]*sin(s)+123*s*c[5]*sin(s)-s*cos(s)*c[0]-22*s*cos(s)*c[4]-c[1]*cos(s)*s^2-c[2]*cos(s)*s^3+2*c[2]*sin(s)*s^2-c[3]*cos(s)*s^4+3*c[3]*sin(s)*s^3+5*c[3]*cos(s)*s^2-c[4]*cos(s)*s^5+4*c[4]*sin(s)*s^4+12*c[4]*cos(s)*s^3-24*c[4]*sin(s)*s^2-c[5]*cos(s)*s^6+5*c[5]*sin(s)*s^5+21*c[5]*cos(s)*s^4-63*c[5]*sin(s)*s^3-123*c[5]*cos(s)*s^2)*(c[0]+c[1]*s+c[2]*(s^2+2)+c[3]*(s^3+s)+c[4]*(s^4-2)+c[5]*(s^5-3*s-s^3)))/((x-s)^(1/2)*Pi^(1/2)), s = 0 .. x)

 (15)
> 

`assuming`([value(%)], [x > 0])

int((((8/3)*s^3-2*s^(1/2))*(c[0]+c[1]*s+c[2]*(s^2+2)+c[3]*(s^3+s)+c[4]*(s^4-2)+c[5]*(s^5-3*s-s^3))/Pi^(1/2)+(1/1260)*s+(s*c[0]+22*s*c[4]+c[1]*s*sin(s)-5*s*c[3]*sin(s)+123*s*c[5]*sin(s)-s*cos(s)*c[0]-22*s*cos(s)*c[4]-c[1]*cos(s)*s^2-c[2]*cos(s)*s^3+2*c[2]*sin(s)*s^2-c[3]*cos(s)*s^4+3*c[3]*sin(s)*s^3+5*c[3]*cos(s)*s^2-c[4]*cos(s)*s^5+4*c[4]*sin(s)*s^4+12*c[4]*cos(s)*s^3-24*c[4]*sin(s)*s^2-c[5]*cos(s)*s^6+5*c[5]*sin(s)*s^5+21*c[5]*cos(s)*s^4-63*c[5]*sin(s)*s^3-123*c[5]*cos(s)*s^2)*(c[0]+c[1]*s+c[2]*(s^2+2)+c[3]*(s^3+s)+c[4]*(s^4-2)+c[5]*(s^5-3*s-s^3)))/((x-s)^(1/2)*Pi^(1/2)), s = 0 .. x)

 (16)
> 

``


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