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The two expression should be equal but when I write bool(arcsin(x) == 2*arctan(x/(1+sqrt(1-x^2)))) it returns false.

Any clue - Why it does that? Any get around?

why integral ($ $$1/x$, $x$) returns $log(x)$? Shouldn't it return $log(|x|)$. Similarly, integral$(tan(x),x)$ returns $log(sec(x))$ shouldn't it return $log(|sec(x)|)$. Can anyone explain?

After previous post, I dig a little bit and find:

 sage: equation=integral(1/x+x,x).real()
 sage: equation
 1/2*real_part(x)^2 - 1/2*imag_part(x)^2 + log(abs(x))
 sage:

Now, anyway to set real_part(x)=x and imag_part(x)=0 in "eq" and get the resultant "eq"?

More>>

sage: integral(1/(x^3-1),x).real()
-1/3*sqrt(3)*real_part(arctan(1/3*(2*x + 1)*sqrt(3))) + 1/3*log(abs(x - 1)) - 1/6*log(abs(x^2 + x + 1))

Everything is fine in the above computation except the word "real_part". Anyway to get rid of that?

How can I find that x/x is undefined at x=0?

Or any way when I write x/x, it returns x/x instead of 1?

I am running a sage script that uses maxima_methods().exponentialize(). I have a time out wrapper that kills the sage after a specific amount of time say 20 secs. Normamly when I kill sage, the associated process including maxima are killed. But, in a case, it kills the sage but not the associated maxima process. And the maxima process is eating up all the memory. Any way to kill that associated maxima process when I kill the sage script. Shoud I need to change/tweak anything in the file sage/interfaces/maxima.py

Sage evaluates tan(pi/2) to unsigned infinity which is true, but I want the above expression to work. Any way?

When I apply arctan(tan(pi/2)) it gives error. Shouldn't it return pi/2.