how do you show that intergrate from 0 to infinity of
1/ (x^2 + sq root x) dx converges?
i tried to do comparison test by saying that it is less than integrate from 0 to infinity of
1/ sq root x but it doesnt show that it converges.
If f(x) is the integrand function, we have
$\displaystyle \displaystyle\lim_{x \to{+}\infty}{\frac{f(x)}{1/x^2}}=\ldots=1\neq 0$
$\displaystyle \displaystyle\lim_{x \to 0^+}{\frac{f(x)}{1/\sqrt{x}}}=\ldots=1\neq 0$
So,
$\displaystyle \int_0^1 f(x)dx\;,\quad \int_1^{+\infty} f(x)dx$
are convergent