evaluate the definite integral.... from 1 to e^4 dx/(x(1+ln(x)))

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evaluate the definite integral.... from 1 to e^4 dx/(x(1+ln(x)))

Mathematics
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Note d/dx (ln(x)) = 1/(x) and do it from inspection.
Or if you're a baby, let u = ln(x)
\[\int_1^{e^4} \frac{1}{x(1+1ln(x))} dx\] \(\text{Let u} = ln(x) \implies du = \frac{1}{x}dx \implies dx = x\ du\)

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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.
whats the final answer? i'm confused
Did you try it with the u substitution I suggested?
tryin now
r u left with 1/u?
\(\frac{1}{1+u}\)
Actually a better u sub might be let u = 1+lnx
Then you'll get 1/u
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. ..
ln f(x) = the result, my bad
so then how would i integrate 1/u? is it ln(u)?
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.
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.
Cambridge Part III Tripos would eat you alive, kiddo (polpak)
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=
sorry that didnt copy right
Polpak, I told him both ways to do it faster than you LaTeX'd one, and you're bitter. grow up.
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.
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.
poketjjax: did you get it solved?
yes i did. i have another one as well.

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