How can I solve the following indefinite integral containing inverse $\cosh$? Does it have any antiderivative?
$$I(t,a) = \int \frac{\text{arccosh}\ t}{\sqrt{t^2-a^2}} dt.$$ The case $a = 1$ is elementary: $$I(t,1) = \dfrac{(\text{arccosh}\ t)^2}{2}.$$