Question

need help integration

Answer 1

\[\int\limits_{1}^{2} \frac{ dx }{x \ln ^{p} x}\]

Answer 2

use a substitution

Answer 3

hint (ln(x))'=1/x

Answer 4

also i hoped you notice this is also an improper integral

Answer 5

??

Answer 6

im stuck with this question like forever

Answer 7

on the integration or the limits part?

Answer 8

can you evaluate:
\[\int\limits_{}^{}\frac{dx}{x \ln^p(x)}\]

Answer 9

the whole thing<< it sounds stupid

Answer 10

sorry that wasn't in the inside but you can still use that same substitution

Answer 11

\[\int\limits_{}^{}\frac{1}{x (\ln(x))^p} dx \]

Answer 12

again notice that derivative of ln(x) (wrt x) is 1/x

Answer 13

let u=ln(x)
du=1/x dx

Answer 14

do you see how to use this substitution?

Answer 15

aha yeah .. now how a i going to answer the question finding the values of p

Answer 16

so the question says to find the values of p where the limit exists right
well lets act like we are finding the limit before we determine that

Answer 17

there is no limits

Answer 18

so you already decided the integral diverges for all p?

Answer 19

the question says :
Find the values of p for which the following improper integral converges

Answer 20

no

Answer 21

right so act as if we are trying to find the limit first
then we can determine for what values of p the limit exists

Answer 22

excuse me can you solve the whole question for me as i have lots of assignments

Answer 23

\[\int\limits_{1}^{2} \frac{dx}{x \ln^p(x)}=\lim_{z \rightarrow 1^+} \int\limits_{z}^{2}\frac{dx}{x \ln^p(x)} \]

Answer 24

act as if you are going to evaluate that integral

Answer 25

then take care of the definite integral part

Answer 26

once you show me what you have after that
i will help you to determine what p needs to be

Answer 27

i'm dieing

Answer 28

I will not give the whole solution. I don't see how that would be helpful.

Answer 29

you are right, but you know i have many assignments, i promise you tomorrow i will solve any question that contains the same idea by my self