# How can I integrate by parts this one?

## Homework Statement

I have to solve the following integral

1/(sqrt[x] * ln[x]) from 2 to infinity

## The Attempt at a Solution

u= ln[x] dv=1/sqrt(x)
du= 1/x v= 2 sqrt(x)

If I do this I get

lim (ln b/ sqrt[x] - 4 sqrt[x] - ln2/sqrt[x] + 4 sqrt[x])

Is this the actual result of the integral? Did I substitute correctly?
Thanks in advance!

## Answers and Replies

I don't think $$\int \frac{dx}{\sqrt{x}*ln(x)}$$ has an antiderivative.

Do you mean $$\int \frac{ln(x)}{\sqrt{x}}dx$$ ?

## Homework Statement

I have to solve the following integral

1/(sqrt[x] * ln[x]) from 2 to infinity

## The Attempt at a Solution

u= ln[x] dv=1/sqrt(x)
du= 1/x v= 2 sqrt(x)

If I do this I get

lim (ln b/ sqrt[x] - 4 sqrt[x] - ln2/sqrt[x] + 4 sqrt[x])

Is this the actual result of the integral? Did I substitute correctly?
Thanks in advance!

This problem can not be solved because the function is not strictly converging towards infinity. You can calculate definite integrals, f.ex. [2,100 000], [2, 1 000 000] and so on, but there is no way this integral reaches a certain limit as x goes towards infinity. I agree with Random Variable, this seems lik a typo.

Probably it was an error from the Professor. I'll check that.
Thanks!