Am Samstag, den 02.04.2011, 07:20 +0200 schrieb Rene Grothmann:
> On of the previous versions of Maxima knew how to find
>
> integrate(sqrt(x^5)*sqrt(1-x),x)
>
> But the current version cannot do this. Is there a way to get it?
I think this has changed because expression like sqrt(1/x) and 1/sqrt(x)
are no longer treated as equivalent.
It is the flag radexpand, which switches on simplifications like
sqrt(1/x) -> 1/sqrt(x). Therefore we get:
(%i1) integrate(sqrt(x^5)*sqrt(1-x),x), radexpand:all;
(%o1)
-(-15*sqrt(1-x)/sqrt(x)+73*(1-x)^(3/2)/x^(3/2)+55*(1-x)^(5/2)/x^(5/2)
+15*(1-x)^(7/2)/x^(7/2))
/(768*(1-x)/x+1152*(1-x)^2/x^2+768*(1-x)^3/x^3+192*(1-x)^4/x^4
+192)
-5*atan(sqrt(1-x)/sqrt(x))/64
Another possibility is to assume the variable x to be positive:
(%i1) assume(x>0);
(%o1) [x > 0]
(%i2) integrate(sqrt(x^5)*sqrt(1-x),x);
(%o2)
-(-15*sqrt(1-x)/sqrt(x)+73*(1-x)^(3/2)/x^(3/2)+55*(1-x)^(5/2)/x^(5/2)
+15*(1-x)^(7/2)/x^(7/2))
/(768*(1-x)/x+1152*(1-x)^2/x^2+768*(1-x)^3/x^3+192*(1-x)^4/x^4
+192)
-5*atan(sqrt(1-x)/sqrt(x))/64
Dieter Kaiser