# [Maxima] problem with changevar

Robert Marik marik at mendelu.cz
Mon Aug 4 09:21:19 CDT 2008

```Hello, I have some problems with chagevar,

changing variables x=2/cos(u)   in integral of x/sqrt(4-x^2) produces
-2*%i*integrate((sqrt(cos(u)^2/(cos(u)^2-1))*sin(u))/cos(u)^3,u) and I
think that there should be no minus sign.

Doing this substitution on the paper gives   integral of 2*tan(u)  and
back substitution gives correct answer:  sqrt(x^2-4)

Not let me try changevar
we do the substitution first and then remove the integral. We should
get a function equivalent to 2*tan(t)

f:diff(changevar('integrate(x/sqrt(x^2-4),x),x = 2/cos(t),t,x),t)\$

Now we evaluate the function at pi/4, it hte changing variables is
correct, then f(pi/4)=4
ev(f,t=%pi/4),numer;

-3.999999999999999 in maxima 5.13 (GCL, debian) and -3.999999999
%i/((-1)^(0.5)) in maxima 5.15 (GCL, Windows)

I cannot find the mistake, since I am not familiar with lisp and I
cannot check the changevar command in sources, but this problem
disappears if you do substitution x=1/cos(t)  in the integral
x/sqrt(1-x^2)

I know that there are better substitutions for this integral, but I
wish to know how much we should trust the changevar function.

Thank you
Robert
```