# Math Help - convergence problem

1. ## convergence problem

$\int_{0}^\infty \frac{ln (1+x)} {x^{1/2}+x^{2}}dx$
the answer book gives us is convergence
but i think it diverges in (0,1)
so can anyone help me to solve the problem?
show it!

2. for x < 1

ln(1+x) < 1

and 1/(x^(1/2) +x^2) < 1/(x^(1/2)

ln(1+x)/[(x^(1/2) +x^2)] < 1/(x^)1/2))

the integral [1/(x^)1/2))]dx can easily be shown to converge on (0,1]

3. Originally Posted by Calculus26
for x < 1

ln(1+x) < 1

and 1/(x^(1/2) +x^2) < 1/(x^(1/2)

ln(1+x)/[(x^(1/2) +x^2)] < 1/(x^)1/2))

the integral [1/(x^)1/2))]dx can easily be shown to converge on (0,1]

thx for ur help!