The question asks to find the Laplace transform of
$\int_0^t \frac{\cos{au} - \cos{bu}}{u} \, du$
I get stuck at
$ = \frac{1}{s} \left(\int_s^\infty \frac{u}{u^2+a^2}-\frac{u}{u^2+b^2}\, du \right)$
It says the answer is
$\frac{1}{s}ln{\frac{s^2+a^2}{s^2+b^2}}$
Could someone help?