show $\int\_0^12\arctan(1+a\ln(x)) \ dx = \frac{\pi}{2} - a -a^2 -a^3 + O(a^4) $ for $a \ll 1$

I've never seen this type of integral before, but it looks very familar to something to do with taylor, so I attempted this:

$I(x) = \displaystyle\int\_0^12\arctan(1+a\ln(x)) \ dx$

$I(1) = I(1) + I'(1)(x-1) + I''(1)(x-1)^2/2! +...$ however this gets very very messy by the second derivative so I'm assuming there is something I'm missing. Any help, thanks.