## anonymous 5 years ago evaluate the definite integral.... from 1 to e^4 dx/(x(1+ln(x)))

1. anonymous

Note d/dx (ln(x)) = 1/(x) and do it from inspection.

2. anonymous

Or if you're a baby, let u = ln(x)

3. anonymous

$\int_1^{e^4} \frac{1}{x(1+1ln(x))} dx$ $$\text{Let u} = ln(x) \implies du = \frac{1}{x}dx \implies dx = x\ du$$

4. anonymous

Or if you're a douche you can learn all this stuff before hand then come online and make fun of other people who don't know how to do it yet.

5. anonymous

whats the final answer? i'm confused

6. anonymous

Did you try it with the u substitution I suggested?

7. anonymous

tryin now

8. anonymous

r u left with 1/u?

9. anonymous

$$\frac{1}{1+u}$$

10. anonymous

Actually a better u sub might be let u = 1+lnx

11. anonymous

Then you'll get 1/u

12. anonymous

Honestly, polpak, I know you hate me, but if you can't see this is clearly a case to use: $\int\limits \frac{f'(x)}{f(x)} \mathbb{d}x = f(x) + c$ you are silly. Ah well, I guess less intelligent people who learn maths by rote always fall back on subs. ..

13. anonymous

ln f(x) = the result, my bad

14. anonymous

so then how would i integrate 1/u? is it ln(u)?

15. anonymous

It's not a matter of whether or not I can see it. It's a matter of someone learning it for the first time needs to understand a bit about the process and how to do things even when it's somthing not so nice. And to do that, they have to first practice on nice things.

16. anonymous

Newton, nobody cares if you can do it. This is a place for helping others learn, not for trying to impress people by being awsome at math.

17. anonymous

Cambridge Part III Tripos would eat you alive, kiddo (polpak)

18. anonymous

Let −90f(x)dx=5 −9−6f(x)dx=7 −30f(x)dx=4 . Find −6−3f(x)dx= and −3−6(5f(x)−7)dx=

19. anonymous

sorry that didnt copy right

20. anonymous

Polpak, I told him both ways to do it faster than you LaTeX'd one, and you're bitter. grow up.

21. anonymous

I'm not bitter. I wouldn't have had a problem if you'd given him(her?) helpful advice, and then went on to explain how to do it easier. But to give a trite one line explanation and then tell him(her?) to do it by inspection is just you showing off, not trying to help. Then you go on to give him(her?) a way he might understand, while simultaneously insulting him(her?). You're just being an retriceat, and you've been at it all day. How about you go find the Cambridge math club and have yourself a nice circlejerk.

22. anonymous

I was taught to integrate things of that form by inspection. Maybe I shouldn't assume everyone was (though they should be) - and that is long before University, it is how it is taught to everyone who does Maths in England. Substitutions waste time.

23. anonymous

poketjjax: did you get it solved?

24. anonymous

yes i did. i have another one as well.