Question

∫dx/(xln(x^6))

Answer 1

\[\Large\rm \int\limits \frac{1}{x \ln(x^6)}dx\]Using rule of logs, you can write,\[\Large\rm \ln(x^6)=6\ln x\]

Answer 2

But we're applying that rule `in the denominator` so be careful where you put the 6!

Answer 3

\[\Large\rm \int\limits\limits \frac{1}{6x \ln x}dx\]

Answer 4

I'm gonna rearrange things a tad bit, hopefully this isn't too confusing:\[\Large\rm \frac{1}{6}\int\limits \frac{1}{\ln x}\left(\frac{1}{x}dx\right)\]

Answer 5

From here we can make a nice u-substitution,\[\Large\rm u=\ln x\]

Answer 6

What do you get for your \(\Large\rm du\) ?

Answer 7

Oh this appears to be your first question Ms Lobster,
\(\Large\bf \color{#008353}{\text{Welcome to OpenStudy! :)}}\)

Answer 8

Thanks soo much! I completely understand it know!