How to integrate sqrt(arctanx)?

This question is posed here: How to integrate sqrt(arctanx)? - Yahoo! Answers

I think the presumption of the only answer by Robert V is correct and that the OP got the order of operation mixed up.

However, maybe someone here can provide a closed form answer to the original question?

(If not, then thanks for your efforts.)

Re: How to integrate sqrt(arctanx)?

Quote:

Originally Posted by

**NowIsForever** This question is posed here:

How to integrate sqrt(arctanx)? - Yahoo! Answers
I think the presumption of the only answer by Robert V is correct and that the OP got the order of operation mixed up.

However, maybe someone here can provide a closed form answer to the original question?

(If not, then thanks for your efforts.)

For:

Let

So

Now using integration by parts:

You can check if my answer is correct here:

int arctan((x)^(1/2)) - Wolfram|Alpha

Hope this helps.

Re: How to integrate sqrt(arctanx)?

[QUOTE

Hope this helps.[/QUOTE]

It doesn't, read the question.

Re: How to integrate sqrt(arctanx)?

Thanks, x3bnm, but you have answered the reverse question just as Robert V did in *Yahoo! Answers*. The original (albeit, possibly mistaken) question was int sqrt(arctan(x))?

wolframalpha.com couldn't do it either, though perhaps the Pro version could.

I suspect there is no closed form solution, although proving that could be incredibly difficult.