## anonymous 4 years ago more calculus help

1. anonymous

$\int\limits_{?}^{?}(1)/(xln(x ^{4}))$

2. bahrom7893

that 1/x is buggin me as a u sub.. but it's prolly integration by parts

3. anonymous

start with $\frac{1}{x\ln(x^4)}=\frac{1}{4x\ln(x)}$ then it should be easy

4. bahrom7893

Let u = ln(x^4)

5. bahrom7893

Ha I think i got this one!

6. bahrom7893

u = ln(x^4) du = 4/x simple u sub!

7. anonymous

good. because i am clueless???

8. anonymous

pull the 1/4 outside of the integral get $\frac{1}{4}\int \frac{dx}{x\ln(x)}$ then make $u=\ln(x),du=\frac{1}{x}dx$ and you are home free

9. bahrom7893

well yea pretty much the same thing as satellite did

10. anonymous

don't forget the properties of the log!

11. bahrom7893

lol my method works too though :)

12. anonymous

oookkk i got it

13. anonymous

yes it will work and you will see that if $u=\ln(x^4)$ then $du=\frac{4}{x}dx$ but that is telling you that $\ln(x^4)=4\ln(x)$

14. anonymous

would the fianl answer be 1/4ln (ln(x))+c?

15. anonymous

Final*

16. anonymous

it would be, yes

17. anonymous

sweet thanks again.

18. anonymous

btw if you notice you will get a different answer from wolfram and if you like i can explain why

19. anonymous

20. anonymous

here is what wolfram writes if you just type it in. you get $\frac{1}{4}\ln(\ln(x^4))+c$

21. anonymous

but $\ln(\ln(x^4))=\ln(4\ln(x))=\ln(4)+\ln(\ln(x))$ and $\ln(4)$ is a constant. so answers are the same, since the constant is just a constant, like the +C out at the end

22. anonymous

oo ok that is simple enough thanks again