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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?

why integral$(1/x,x)$ 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?

why integral $(1/x,x)$ ($1/x,x$) 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?

why integral ($1/x,x$) ($\frac1x$, $x$) 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?

why integral ($\frac1x$, (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?

why integral (1/x, ($ $$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?

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?

 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:

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"?

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))

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?