What is $int_1^oo 1/(1+x )-1/xdx$ ?

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Answer 1 · 2016-07-16T13:06:48

$= ln (1/2)$

$int_1^oo 1/(1+x )-1/xdx$

$= [ ln(1+x )- ln x ]_1^oo$

$= [ ln((1+x )/x) ]_1^oo$

$= [ ln((1/x+1 )/1) ]_1^oo$

$= lim_{x to oo} ln((1/x+1 )/1) - ln((1/1+1 )/1)$

$= ln 1 - ln 2 = ln (1/2)$

What is int_1^oo 1/(1+x )-1/xdxint_1^oo 1/(1+x )-1/xdx?