Lambert W function principal branch | Desmos

Expression 2: StartFraction, 1 Over pi , EndFraction Start integral from 0 to pi , end integral, left parenthesis, ln left parenthesis, StartRoot, left parenthesis, 1 plus StartFraction, "x" sin left parenthesis, "t" , right parenthesis Over "t" , EndFraction "e" Superscript, "t" cot left parenthesis, "t" , right parenthesis , Baseline , right parenthesis squared , EndRoot , right parenthesis , right parenthesis "d" "t" left brace, "x" less than negative StartFraction, 1 Over "e" , EndFraction , right brace

2

Expression 3: StartFraction, 1 Over pi , EndFraction Start integral from 0 to pi , end integral, left parenthesis, arctan left parenthesis, 0 , 1 plus StartFraction, "x" sin left parenthesis, "t" , right parenthesis Over "t" , EndFraction "e" Superscript, "t" cot left parenthesis, "t" , right parenthesis , Baseline , right parenthesis , right parenthesis "d" "t" left brace, "x" less than negative StartFraction, 1 Over "e" , EndFraction , right brace

3

4

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