I'm stuck trying to find the closed form expression of an integral. I was able to upper bound it, but if anybody can help me find a way to determine the exact answer, it would be appreciated. Thanks in advance. $w$ and $t$ are constants.
$$\int_0^{\pi/3} \left(1-e^{(t^2 w\sec^2\phi)/24}\right)\,\mathrm{d}\phi$$