Step by step, please! (Especially the integral part).

This is the starting equation.

And then you substitute for with the given Contois equation but then I'm not sure how to integrate that final expression to get this desired form:

A novel bacterial strain was isolated and its growth kinetics was identified to follow Contois equation instead of Monod equation, i.e. g=KSXX+SmS where g is the specific cell growth rate and m and KSX are the Contois constants. Assuming cell maintenance is insignificant and can be ignored: Show the following relation for a batch culture (where S0 is initial substrate concentration): X0X=(S0S)KSXYX/Semt dtdS=YSXgX X0X=(S0S)KSXYX/Semt