# Math Help - Integral Test 2

1. ## Integral Test 2

$\sum^{infinity}_{n=2} \frac {1}{n \sqrt{ln(n)}}$

I don't know how to use the integral test for this....

2. Originally Posted by saiyanmx89
$\sum^{infinity}_{n=2} \frac {1}{n \sqrt{ln(n)}}$

I don't know how to use the integral test for this....
let $u=\ln(x) \implies du=\frac{1}{x}dx$ so we get

$\int\frac{1}{x\sqrt{\ln(x)}}dx=\int \frac{1}{u^{\frac{1}{2}}}du$

3. so, it converges at $2 \sqrt{ln2}$ ???

4. Originally Posted by saiyanmx89
so, it converges at $2 \sqrt{ln2}$ ???

Not quite the anti derivative is

$\lim_{b \to \infty} 2\sqrt{\ln(x)}\bigg|_{2}^{b}=\lim_{b \to \infty}2\sqrt{\ln(b)}-2\sqrt{\ln(2)}=\infty$