Question: is there a logarithmic property thay says: ln ∣ a - b ∣ is equal to - ln ∣ a + b ∣   Im overthinking because of the two solutions given in the images where the only difference in their answers is the term "(-1/2) ln∣cscx+cotx∣" and " (1/2) ln∣cscx-cotx∣"

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
6th Edition
ISBN:9781337111348
Author:Bruce Crauder, Benny Evans, Alan Noell
Publisher:Bruce Crauder, Benny Evans, Alan Noell
ChapterA: Appendix
SectionA.2: Geometric Constructions
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Question: is there a logarithmic property thay says:

ln ∣ a - b ∣ is equal to - ln ∣ a + b ∣

 

Im overthinking because of the two solutions given in the images where the only difference in their answers is the term "(-1/2) ln∣cscx+cotx∣" and " (1/2) ln∣cscx-cotx∣"

YOUR INPUT:
f(x) =
"MANUALLY" COMPUTED ANTIDERIVATIVE:
ƒ ƒ(x) dx = F*(x) =
csc³ (x)
Simplify
"Manual" integration with steps:
The calculator finds an antiderivative in a comprehensible way. Note that due to some simplifications, it might
only be valid for parts of the function.
In(|csc(x) + cot(x)|) + cot(x) csc(x)
2
Show steps
+C
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Transcribed Image Text:YOUR INPUT: f(x) = "MANUALLY" COMPUTED ANTIDERIVATIVE: ƒ ƒ(x) dx = F*(x) = csc³ (x) Simplify "Manual" integration with steps: The calculator finds an antiderivative in a comprehensible way. Note that due to some simplifications, it might only be valid for parts of the function. In(|csc(x) + cot(x)|) + cot(x) csc(x) 2 Show steps +C Activate Windows
BIGGER THAN INFINITY
Determine the signs of mine
Coefficients of Poliest
Signs
of Coefficients X-CSC
of Polynom 5:43
/+g=tg-/fg'
9=
f'=csC²x — f = -cotx
eg=-CSCxcotx
[1 + cot²x=c5e³x]
Co²x=²X41
mins
A x (SC)
Colx sex
Determine the Signs of mine
Coefficients of Pole Signs
of Coefficients
of Polynom 4:15
= -(0xx (sex-√(sex (@CX-1) dx
=-COAXCSCX-/CSC²x dx +/cs cx dx
=> 2 / c²c²x dx = -colxcsex + √(sex dx
cx
Jestar(corresix+ In IS(X=cola
Transcribed Image Text:BIGGER THAN INFINITY Determine the signs of mine Coefficients of Poliest Signs of Coefficients X-CSC of Polynom 5:43 /+g=tg-/fg' 9= f'=csC²x — f = -cotx eg=-CSCxcotx [1 + cot²x=c5e³x] Co²x=²X41 mins A x (SC) Colx sex Determine the Signs of mine Coefficients of Pole Signs of Coefficients of Polynom 4:15 = -(0xx (sex-√(sex (@CX-1) dx =-COAXCSCX-/CSC²x dx +/cs cx dx => 2 / c²c²x dx = -colxcsex + √(sex dx cx Jestar(corresix+ In IS(X=cola
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does that mean that the property i provided doesn't exist?

 

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