Science

Math

Humanities

... and beyond

Socratic Meta
Featured Answers

Topics

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

1 Answer

Jul 16, 2016

# = ln (1/2)#

Explanation:

#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) #

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

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

Related questions

See all questions in Definite and indefinite integrals

Impact of this question

1165 views around the world

You can reuse this answer
Creative Commons License