Advanced Search

Question: Maple unable to evaluate integral but upon simple substitution is able to.

Question:Maple unable to evaluate integral but upon simple substitution is able to.

markweitzman 100 Maple 2019
integration
May 11 2021
2

So Maple 2019 seems to be unable to evaluate a relatively easy integeral for a positive integer, but when the obvious substitution u=cos(x) is made it is able to evaluate the integral.  Is there some setting I am using that is causing Maple to give up without much effort?  
 

> 

restart
> 

assume(n::integer, n > 0)
> 

about(n)

Originally n, renamed n~:
  is assumed to be: AndProp(integer,RealRange(1,infinity))

  
> 

int(sin(x)^(2*n+1), x = 0 .. Pi)

int(sin(x)^(2*n+1), x = 0 .. Pi)

 (1)
> 

for j to 5 do int(sin(x)^(2*j+1), x = 0 .. Pi) end do

4/3

  

16/15

  

32/35

  

256/315

  

512/693

 (2)
> 

int((-u^2+1)^n, u = -1 .. 1)

GAMMA(n+1)*Pi^(1/2)/GAMMA(n+3/2)

 (3)
> 

for j to 5 do int((-u^2+1)^j, u = -1 .. 1) end do

4/3

  

16/15

  

32/35

  

256/315

  

512/693

 (4)
> 

``


 

Download walter.mw
Please Wait...