# An analytic solution?

1. Apr 7, 2010

### SW VandeCarr

Is there an analytic solution to the following integral? (Not a homework question, solved numerically).

$$\int_{0}^{\infty}{\frac{dx}{(1+x)\sqrt{x}}=\pi$$

2. Apr 7, 2010

Let u^2 = x

3. Apr 8, 2010

### SW VandeCarr

OK I get: $$2\int\frac{1}{1+u^2}du$$

I'm a bit rusty at this. I think I need to make some trig substitutions here, but I'm at a loss as to exactly what.

Last edited: Apr 8, 2010
4. Apr 8, 2010

### jrlaguna

It's just there, the arc tangent.

5. Apr 8, 2010

### SW VandeCarr

Right. I finally saw that. However, the solution: $$2\arctan(\sqrt{x})+C$$ contains a variable. The solution given in the CRC Standard Mathematical Tables 14th ed, page 342, Eq 489 is $$\pi$$.

EDIT:Yes, I know it's old, but I doubt a new solution has been invented. I bought it for \$2.

Last edited: Apr 8, 2010
6. Apr 8, 2010

### D H

Staff Emeritus
You looked up the indefinite integral. You have a definite integral. Apply the integration limits.

7. Apr 8, 2010

### SW VandeCarr

The form of the integral in the book is just as I wrote it in the first post, but I see how the solution $$\pi$$ is obtained. Thanks.