1
$\begingroup$

I am having trouble integrating the following equation by first using u-sub and then integration by parts:

$$\int 8 \ln{\sqrt[3]{x}}~dx$$

I looked up the answer on Wolfram Alpha but it is still unclear to me.

Thank you in advance!

$\endgroup$
1
  • $\begingroup$ Hi. Can you show a bit of your work on this so far? This way it is easier to help you! $\endgroup$ – MattAllegro May 10 '14 at 7:35
0
$\begingroup$

Hint

Remember that $\log(x^a)=a \log(x)$. So $$\int 8 \ln{\sqrt[3]{x}}~dx=\frac{8}{3} \int \log(x)~dx$$ Now, use integration by parts.

I am sure that you can take from here.

$\endgroup$
2
  • $\begingroup$ You saved my life!!!!!!!!!!!!!!!!!!!! Thank you! Thank you both! $\endgroup$ – user4681 May 10 '14 at 7:04
  • $\begingroup$ I did not save your life and you are very welcome ! $\endgroup$ – Claude Leibovici May 10 '14 at 7:06
0
$\begingroup$

Call it $\frac{8}{3}\ln x$, and let $u=\ln x$, $dv=\frac{8}{3}\,dx$.

But you can actually integrate directly by parts, $u=8\ln(x^{1/3})$, $dv=dx$.

$\endgroup$
2
  • $\begingroup$ Thanks a lot!!!!! It helped me a lot! $\endgroup$ – user4681 May 10 '14 at 7:06
  • $\begingroup$ You are welcome. In this case, we don't need to bother with substitution, though it is a natural and often useful idea. $\endgroup$ – André Nicolas May 10 '14 at 7:08

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.