I am trying to find this integral and I can get the answer on wolfram of course but I do not know what is wrong with my method, having gone through it twice. $\int \frac{du}{u \sqrt{5-u^2}}$
$u = \sqrt{5} \sin\theta$ and $du= \sqrt{5} \cos \theta$
$\int \frac{\sqrt{5} \cos \theta}{\sqrt{5} \cos \theta \sqrt{5-(\sqrt{5} \sin \theta)^2}}$
$\int \frac{1}{\sqrt{5-(5 \cos^2 \theta)}}$
$\int \frac{1}{\sqrt{5(1- \cos^2 \theta)}}$ $\int \frac{1}{\sqrt{5(\sin^2 \theta)}}$
$\frac{1}{\sqrt5}\int \frac{1}{(\sin \theta)}$
$\frac{1}{\sqrt5}\int \csc\theta$
$\frac{\ln|\csc \theta - \tan \theta|}{\sqrt5} + c$