how to get a value using integral

hello, I have a trouble to get value using integral.

My question is

so, I use

syms x

double(int(x^3.5/(x-1)^(1/2),0,1)) % vpa(int(x^3.5/(x-1)^(1/2),0,1))

but I got error or numeric::int even though the real solution is -0.859029i. So Do you have any ideas to solve this problem???

Answer 1

[David Goodmanson]

Hello Jongnam, try

format long
fun = @(x) x.^(7/2)./(sqrt(x-1))
integral(fun,0,1)

 ans =  0.000000000000000 - 0.859029241215738i

As a check, with the substitution x = sin(theta)^2 you can arrive at (-i) *

2*Integral{0,pi/2} sin(theta)^8 dtheta
= (7*5*3*1)/(8*6*4*2)*pi
ans = 0.859029241215959