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How do you get from equation one to equation two?

For me it doesn't make any sense. If you seperate both variables and integrate on both sides, how come you get anything like in equation two? And wouldn't it still be a differential equation since dP/dt still appears in the solution. If anyone happen to know the answer, please help me out.

The reason why i'm asking, is because i want to derive the second formula, which should be done by integrating the differential equation, as they state in the book.

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# I Solving this equation?

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