Question

My integration is wrong, can someone explain what I did wrong? (Work posted as picture)

The question is integral of: ln(sqrt(x)) / sqrtx.
Here is the supposed answer: http://www.wolframalpha.com/input/?i=integral+of+ln%28sqrtx%29+%2F+%28sqrtx%29

Please explain what I forgot/didn't do.

Answer 1

i know that i didn't distribute the 2 to the second term at the end, but why does the first term not get a two??

Answer 2

Your results are correct, so is the "answer".
Check the answer, it should read:
\( \sqrt{x}\ ln(x)-2\sqrt{x} \)
which is equivalent to:
\( 2[\sqrt{x}\ ln(\sqrt{x})-\sqrt{x}] \)

Answer 3

OH I didn't see that there was an x not a root x in the ln of the simplified expression. Thanks

Answer 4

You're welcome! :)