Hi, please show it on a piece of paper if possible, it will help me in your choo

Question

Hi, please show it on a piece of paper if possible, it will help me in your choosing especially if its neat and rules are explained !

basically the problem is INTEGRAL [ 1 / x SQRT(4x+1) ]dx

i did what chegg homework help told me to do, which is let u = sqrt 4x + 1 , which would in turn give me the eventual result of dx = 1/2 udu

after doing this, i am stuck after I got 2 * integral (1 / u^2 -1 ) du

the book just made the integral of 1 / u^2 -1 into somethign with LN, and this step is confusing me. Thanks !

Explanation / Answer

see..(2/(u^2-1) can be written as (2/(u-1)(u+1)) which is equals to (((u+1)-(u-1))/(u-1)(u+1)).now it reduces to ((1/(u-1))-(1/(u+1))...now its easy to solve....simply integral will come in terms of ln(u+1) and ln(u-1)

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