Question

help with integration lol ?

Answer 1

\[\int\limits_{e}^{e^4}(dx)/(x \sqrt{lnx})\]

Answer 2

let \(u=\ln x\)

Answer 3

okay, so then find derivative of du /dx ?

Answer 4

the differential, not the derivative\[u=\ln x\implies du=?\]

Answer 5

du/x^-1 ? o-o

Answer 6

not sure lol

Answer 7

the differential is like the derivative, but you get left with a du or dx after

for example \[u=x^2\implies du=2xdx\]
do the same for your \(u\)

Answer 8

isn't it du/dx = u' then dx=du/u' ?

Answer 9

yeah it's all the same thing, but for our purposes you are over thinking it

Answer 10

oh... ok lol

Answer 11

so then my answer for the differentiation was right then ?

Answer 12

i don't see how you got a du and an x in the same thing

Answer 13

substitute\[u=\ln x\]then\[du=???\]

Answer 14

1/x ?

Answer 15

close, but remember to keep the differential dx\[u=\ln x\implies du=\frac{dx}{x}\]

Answer 16

the dx and du are important, don't lose them

Answer 17

didn't i say that before ? x^-1 = 1/x i thought...

Answer 18

you had du/x^-1 which is wrong

Answer 19

oh oops

Answer 20

should be dx*x^-1

Answer 21

yeah my bad lol.

Answer 22

it happens :P

Answer 23

so um next step ? ;p

Answer 24

so for dx would it be dux^-1 ?

Answer 25

substitute the expressions for lnx and dx in terms of u into the equation
you should never mix u's and x's in the integrand

Answer 26

du/x/xsqrtu ?

Answer 27

the x don't cancel out i get x^-2 -.-

Answer 28

your problem is\[\int{dx\over x{\sqrt{\ln x}}}\]and we used the substitution\[u=\ln x\]to get\[du=\frac{dx}x\]you can now rewrite the integral all in terms of u, no x's

Answer 29

well dx = du/x...

Answer 30

yes, but we have dx/x already in the integrand....