SOLUTION: Integrate: integral ( 1 to 2x ) {{{ (ln t / t) dt }}} I feel so lost. Here is where I am so far, but I am not sure where to go or if I am even doing it right. Thank you in a

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: Integrate: integral ( 1 to 2x ) {{{ (ln t / t) dt }}} I feel so lost. Here is where I am so far, but I am not sure where to go or if I am even doing it right. Thank you in a      Log On


   

Question 1032078: Integrate:
integral ( 1 to 2x ) +%28ln+t+%2F+t%29+dt+
I feel so lost. Here is where I am so far, but I am not sure where to go or if I am even doing it right.
Thank you in advance!
My work so far:
integral ( 1 to 2x ) +%28ln+t+%2F+t%29+dt+
= +%28ln+t%5E2+%2F+2%29+%2F+%28t%5E2%2F2%29+
= +ln+t%5E2+%2F+t%5E2+
= +%28ln+4x%5E2+%2F+4x%5E2%29+-+ln+x+
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!

=%28ln%282x%29%29%5E2%2F2+-+%28ln%281%29%29%5E2%2F2+=+%28ln%282x%29%29%5E2%2F2.
The second integral is true because of the relation d%28lnt%29+=+dt%2Ft.