Question

∫[∞on top and 1 on the bottom](Inx)/(√(x))dx

Answer 1

\[\int\limits_{1}^{\infty}\frac{lnx}{\sqrt{x}}dx\]

Answer 2

use integration by parts is it?

Answer 3

no substitute lnx =t nd solve

Answer 4

and for e denominator use substitution?

Answer 5

????

Answer 6

the answer to your ques. is 4

Answer 7

using l'hopital's rule?

Answer 8

no substitution ....

Answer 9

\[u=lnx, \frac{du}{dx}=\frac{1}{x}, du=\frac{1}{x} dx\]
\[u=lnx, e^u=x, e^\frac{u}{2}=x^\frac{1}{2}\]
\[\int\limits_{}^{}\frac{lnx}{x}\sqrt{x}dx=\int\limits_{}^{}u*e^\frac{u}{2}du=2e^\frac{u}{2}*u-\int\limits_{}^{}2e^\frac{u}{2}du=2e^\frac{u}{2}*u-4e^\frac{u}{2}+C\]
\[=2e^\frac{lnx}{2}*lnx-4e^\frac{lnx}{2}+C=2e^{lnx^\frac{1}{2}}*lnx-4e^{lnx^\frac{1}{2}}+C\]
\[=2x^\frac{1}{2}*lnx-4x^\frac{1}{2}+C\]

Answer 10

i did substitution+integration by parts

Answer 11

now we need to go back in deal with our limits

Answer 12

yes,i got to this step. then sub. the values?

Answer 13

yes dat was wat i was sayng n m too lazy to type all this in equations..
thx myininaya

Answer 14

lol

Answer 15

ok can you finish it mathstina?

Answer 16

im gonna brush my teeth and i will be back

Answer 17

In ∞= 0 right

Answer 18

?

Answer 19

no, log grows with out bound. I don't think the integral converges.

Answer 20

i meant sub ∞ for that qn

Answer 21

mathstina...
wen u substitute x=inf int the integral wat u get is zero ..
inf-inf
\[ 2x ^{0.5}lnx-4x^{0.5}\]

Answer 22

singh,tks

Answer 23

\[\infty - \infty\]
is indeterminant.

\[2\lim_{x \to \infty}\; \sqrt{x}\;(\ln(x)-2) = \infty\]

Answer 24

@cruffo...
X is not approaching infinity x is infinity


@mathstina Happy to help :)

Answer 25

whatever....

Answer 26

ok.

Answer 27

thnks for everyone's help.

Answer 28

the integral diverges

Answer 29

ok

Answer 30

shall i ask 2qns on partial fractions? myininaya is it time for u to sleep?

Answer 31

we have
\[\lim_{b \rightarrow \infty}[(2b^\frac{1}{2}*lnb-4*b^\frac{1}{2})]-[2*1^\frac{1}{2}*\ln(1)-4*1^\frac{1}{2}]\]
\[\lim_{b \rightarrow \infty}(2\sqrt{b}*lnb-4\sqrt{b}+4)=4+\lim_{b \rightarrow \infty}2\sqrt{b}*(lnb-2)\]

Answer 32

\[=\infty\]

Answer 33

ok post a new thread because this is getting laggy

Answer 34

i thought the final ans is 4.

Answer 35

let me look at it again

Answer 36

am i right? is the ans infinity

Answer 37

the answer is four guys......

Answer 38

i checked the answer with my calculator its four :/

Answer 39

∞+4=4?

Answer 40

What did you type into the calculator?

Answer 41

i get it diverges with my calculator

Answer 42

or 0+4=4?

Answer 43

infinity+4=infinity

Answer 44

I agree with myininaya, the integral diverges.

Answer 45

and i agree with cruffo

Answer 46

lol

Answer 47

:)

Answer 48

singh,myninaya said the ans is infinity

Answer 49

man, do you have maple?

Answer 50

i did it on maple and it said it was infinity too

Answer 51

that site said error

Answer 52

http://www.solvemymath.com/online_math_calculator/calculus/definite_integral/

this one

Answer 53

http://www.wolframalpha.com/input/?i=integrate+from+1+to+infinty+ln%28x%29%2Fsqrt%28x%29

Answer 54

lol cruffo's site is right

Answer 55

will u chk out mine one too plz :

Answer 56

i did but my calculator is also saying it diverges

Answer 57

input at integral log(x)/sqrt(x)

nd upper limit inf

Answer 58

yes it says 4
but more evidence suggest it is infinity

Answer 59

doesn't look like that calculator works with improper integrals, just definite ones. I tried it with your input, but that's not the correct answer.

Answer 60

like maple and what we did above

Answer 61

people this ques. is like headbanging ..

I will b looking further into this lemme confirm what problem is with this problem

Answer 62

this thread is starting to get pretty laggy

Answer 63

In fact, I asked it to integrate x from 1 to inf, and it says the answer is approximatly -0.5

Answer 64

ok.i got the ans

Answer 65

from where?

Answer 66

im still confident the answer is infinity (or diverges)

Answer 67

working out.

Answer 68

mathstina just wants us to shut up already :)

Answer 69

lol

Answer 70

ha

Answer 71

omg i totally don't think that site works for improper integrals now
try x^2, from 1 to inf

Answer 72

watever, the ans is infinity right

Answer 73

right lol