Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

enter image description here

For this problem I did the integration by parts and got that answer. But for some reason it is still wrong. Does anyone get any different answers? Any hints or suggestions would be of great help! Thanks!

share|cite|improve this question
You need to "cancel" an $x$ in that 2nd fraction – imranfat Feb 24 '14 at 17:12
up vote 2 down vote accepted

You would have to make $u= ln(x)$ and $du= (1/x)$. Then you would make $dv= x^3$ and v would then = $x^4/4$. Using the integration by parts formula, which is the integration of u dv = uv- integration of $vdu$. Substitute in your variables and your answer should be $(ln(x) x^4/4) - (x^4/16) + C$.

share|cite|improve this answer
Yah I saw the silly mistake that I made. Thank you for being clear and explaining it all. – AlecLeonK Feb 24 '14 at 17:19

By $u=\ln x$ then $u'=\frac 1x$ and $v'=x^3$ then $v=\frac14 x^4$ so

$$\int x^3\ln xdx=uv-\int u' vdx=\frac 14x^4\ln x-\frac14\int x^3 dx=\frac 14x^4\ln x-\frac1{16}x^4+C$$

share|cite|improve this answer
Got it...silly me! – amWhy Feb 24 '14 at 17:17

$$\int x^3\ln x\,\text{d}x=\int\ln x\cdot\text{d}\left(\dfrac{x^4}{4}\right)=\dfrac{x^4}{4}\ln x-\int \dfrac{x^4}{4}\cdot\text{d}(\ln x)=\dfrac{x^4}{4}\ln x-\int\, \dfrac{x^3}{4}\text{d}x=\cdots$$

share|cite|improve this answer

you integrated $\frac{1}{4}\frac{x^4}{x}$ and got $\frac{1}{20} \frac{x^5}{x}$ which is not right. Cancel the $x$ from the denominator of the first expression, then integrate.

share|cite|improve this answer
What a silly mistake, thank you for recognizing it! I got it right. – AlecLeonK Feb 24 '14 at 17:15

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

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