How Do You Solve This Complex Integral Involving Cosine and a Square Root?

[nemanja]

Hi,i would be gratefull if anyone could help me with this problem.

$$\frac{2}{\pi}$$$$\int \frac{cos(ux)}{\sqrt{x}} dx$$
x goes from zero to infinity.

thanks in advance.

 

[CompuChip]

Assuming you know a thing or two about Gaussian integrals, you could try substituting $y^2 = x$...

 

[nemanja]

yes I tried that and I got$$\frac{\sqrt{2}}{\sqrt{u\pi}}$$
but correct is $$\frac{1}{\sqrt{u}}$$ .
any other way of solving?

 

[nicksauce]

Are you sure 1/√u is correct? Maple and wolfram alpha agree with your answer.

 

[nemanja]

Ok my mistake,thank you all.Maple rules