- #1

[tex]\int_0^1 \frac {x^2+1} {\sqrt x * (1-x)^{5/4}}[/tex]

I tried to divide it between 0-1/2 and 1/2-1 and on the first one i reached to:

[tex]\int_0^{1/2} \frac {x^2+1} {\sqrt x * (1-x)^{5/4}}<=\int_0^{1/2} \frac {x^2+1} {x^{14/4}}[/tex]

can i say that this integral converges and therefore the orgininal converges???, and more important, how would i justify that the last integral converges in an exam????

please correct any mistakes that i probably had made, and forgive me for me awful english.

Many Thanks, Paul.