Making a proper integral equation

Hello I'm having trouble computing this function

I've tried doing it in this format but I'm struggling on actually making the equation itself.

syms x
f = x^-1*(sin*(x^-1*log(x))) ;
Fint = int(f,x,[0 1])

Fvpa = vpa(Fint)

However its giving me an "Error using sin"

How would I find the integral of this function?

Answer 1

[VBBV]

f = x^-1*(sin(x^-1*log(x))) ;  % 

[VBBV]

As sin is builtin function it expects input within ( ) . If you include * between sin and ( then it violates the syntax of sin function provided here

[Howie]

Why doesn't it compute my integral?

syms x
f = x^-1*(sin(x^-1*log(x))) ; 
Fint = int(f,x,[0 1])

Fint = 

Fvpa = vpa(Fint)

Fvpa = 

[VBBV]

syms x
f = x^-1*(sin(x^-1*log(x))) ; 
Fint = int(f,x,[0 1])  % symbolic integration 

Fint = 

f = @(x) x.^-1.*(sin(x.^-1.*log(x))) ; % numeric integration 
Fvpa = integral(f,0,1)

Warning: Reached the limit on the maximum number of intervals in use. Approximate bound on error is 7.5e+00. The integral may not exist, or it may be difficult to approximate numerically to the requested accuracy.

Fvpa = 4.0483

It has evaluated the expression, but

(a) symbolically in first case,

(b) numerically in second case

[Howie]

thank you!

[Torsten]

Did you plot the function ?

syms x
f = x^-1*(sin(x^-1*log(x))) ;
fplot(f,[0.01 0.1])