Equations are in $\LaTeX$ format; I'm still trying to understand how MathJax works.
Given the following integral:
$\int_0^{+\infty } \frac{1}{x \sqrt{x}} \, dx$
I'm pretty sure that does not converge. And if the integral was a indefinite one, also I'm almost sure the result is $\ln(\sqrt x)$ using substitution. If I am correct, why wolfram alpha says that the result is $\frac{-2}{\sqrt x}$ instead of $\ln(\sqrt x)$?
MathWay shows the correct results for both definite and indefinite integrals. I'm new to any mathematical soft like Wolfram Alpha/Mathematica, and my idea is to test my pen and paper results with software that checks my results.
Any hints will be greatly appreciated. Thanks.