# Comparison Test on Interval 0 to 1

## Homework Statement

Determine whether or not the integral from 0 to 1 of (5ln(x)) / ( x^(3/2) ) converges or not.

## The Attempt at a Solution

I just need to know which end of the integral they are talking about. As x=>0, y=>-infinity. As x=>1, y=>1. I'm assuming they want to know whether the function converges or diverges as x=>0, correct?

## Answers and Replies

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## Homework Statement

Determine whether or not the integral from 0 to 1 of (5ln(x)) / ( x^(3/2) ) converges or not.

## The Attempt at a Solution

I just need to know which end of the integral they are talking about. As x=>0, y=>-infinity. As x=>1, y=>1. I'm assuming they want to know whether the function converges or diverges as x=>0, correct?
Since this is an improper integral (the integrand is undefined at one of the interval endpoints), you need to use limits to evaluate the integral. If the limit below exists, the integral converges. If the limit doesn't exist or is infinite, the integral diverges.

$$\lim_{b \to 0^+}\int_b^1 \frac{5ln(x)dx}{x^{3/2}}$$

look for lnx ,x>1 but u should attention that its ln definition but when we solve that integral from 0 to 1 we want to account a surface from 0 to 1 so u should draw ln x it definition from 0 to 1 and when u draw that u know that. i hope that u understand my reason