I am a condensed matter physicist and I am studying a function called Kubo-Toyabe function, the function depends on time $$t$$ and written as follows
$$ P_{\mu}^{LF}\left(t\right)=1-\frac{2\Delta^{2}}{\omega_{0}^{2}}\left[1-\exp\left(-\frac{\Delta^{2}t^{2}}{2}\right)\cos\omega_{0}t\right]+\frac{2\Delta^{4}}{\omega_{0}^{3}}\int_{0}^{t}\exp\left(-\frac{\Delta^{2}\tau^{2}}{2}\right)\sin\omega_{0}\tau\,d\tau$$, with $$\omega_{0}$$ and $$\Delta$$ are constants. I have come across a limit problem when the paper said the asymptotic value of this function to be $$P_{\mu}^{LF}\left(\infty\right)=1-\frac{2\Delta^{2}}{\omega_{0}^{2}}+\frac{2\Delta^{3}}{\omega_{0}^{3}}\exp\left(-\frac{\omega_{0}^{2}}{2\Delta^{2}}\right)\times \int_{0}^{\frac{\omega_{0}}{\Delta}}\exp\left(\frac{1}{2}u^{2}\right)\,du$$. Can someone explain how to find the third term of the asymptotic value of the function