Posted by **kathryn** on Tuesday, August 25, 2009 at 7:52pm.

how do you solve the integral of 1/[(square root of x)(lnx)] from 2 to infinity?

i did the p- integral theorem with 1/square root of x and got it to be a divergent integral. however i was told this was the wrong way and that i should do it by integration by parts. but i can't figure it out by that method. please help. thanks.

- calculus -
**Count Iblis**, Tuesday, August 25, 2009 at 9:07pm
You can proceed as follows. Substitute:

x = e^t. Then the integral becomes:

Integral from ln(2) to infinity of

e^(t/2)/t dt

We can get rid of the factor 2 in the exponential by putting y = t/2. The integral becomes:

Integral from 1/2 ln(2) to infinity of

e^(y)/y dy

For positive y we have

e^(y) > 1

It follows from this that the integral is larger than

Integral from 1/2 ln(2) to infinity of

1/y dy

but this is already divergent, so the integral diverges.

## Answer this Question

## Related Questions

- calculus - is this correct? use the integral test to determine if this series is...
- Calculus - Find the exact area of the region enclosed by the square root of (x...
- calculus - how do you determine the convergence of : definite integral from 1--&...
- Maths Calculus Derivative Integral - Urgent Please - Use 2nd Fundamental Theorem...
- Calculus - Hello Everyone, I need help with Calc II. 1. Integral from 0 to 1 of...
- Calculus check - The functions f and g are given by f(x)=sqrt(x^3) and g(x)=16-...
- Calculus - Evaluate the integral. The integral from 0 to the square root of 2 ...
- Calculus - I'm having some issues with computing this indefinite integral. I don...
- Calculus - Evaluate the integral. The integral from the square root of three ...
- Calculus AB (AP) - Hi, I have a calculus test tomorrow and I understand how to ...