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### integral of 1/x, tan x

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?

### integral of 1/x, tan x

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?

### integral of 1/x, tan x

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?

### integral of 1/x, tan x

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?

### integral of 1/x, tan x

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

why integral ($$$1/x, x) returns log(x)? Shouldn't it return log(|x|). Similarly, integral(tan(x),x) returns log(sec(x)) shouldn't it return log(|sec(x)|). Can anyone explain? After previous post, I dig a little bit and find:  sage: equation=integral(1/x+x,x).real() sage: equation 1/2*real_part(x)^2 - 1/2*imag_part(x)^2 + log(abs(x)) sage:  Now, anyway to set real_part(x)=x and imag_part(x)=0 in "eq" and get the resultant "eq"? More>> sage: integral(1/(x^3-1),x).real() -1/3*sqrt(3)*real_part(arctan(1/3*(2*x + 1)*sqrt(3))) + 1/3*log(abs(x - 1)) - 1/6*log(abs(x^2 + x + 1))  Everything is fine in the above computation except the word "real_part". Anyway to get rid of that?  9 retagged Kelvin Li 503 ●5 ●12 ●17 ### integral of 1/x, tan x why integral ($$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?