Thinking about a kind of heavy integral

[parisse]

Xcas does not try to match to a long table of integral types. It identifies a trig fraction, and runs the change of variable t=tan(x/2) (except if symmetries allows t=sin(x), t=cos(x) or t=tan(x)). This raises a 4th order equation, and it can not be solved with symbolic coefficients (well it can theoretically, but the roots would be much too complicated unless you are using rootofs). If the coefficients have specific values, it can be solved. I get a complex answer for int(sin(x)/(2+sin(x)*cos(x)), x) but without rootof, and you can evalc it to get back to real. Maple returns a simpler expression, but with rootofs, it does not csolve(900x^4+15x^2+1). I don't get anything with Wolfy.