[Maxima] change of variables

[apeditedirra unasaltao]

Maxima knows how to integrate this:

integrate(u(x)*diff(u(x),x),x);

but not this:

integrate((u(x)^4+1)/(u(x)^5+3*u(x))*diff(u(x),x),x);

but it can compute it with the change of variables:

integrate((x^4+1)/(x^5+3*x),x);

  Why this limitation? 

 should'nt maxima try the trivial change of variables when it knows the
answer to the new integration?


       
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