How do I integrate a(1-e^-bt) with constants a and b?

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The integration of the function a(1-e^-bt) involves applying the rules of integration for constants and exponential functions. The integral can be computed as ∫a(1-e^-bt) dt = at + (a/b)e^-bt + C, where C is an arbitrary constant. This result combines the integration of a constant term and the exponential decay term, demonstrating the application of integration techniques for functions involving constants and exponentials.

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morgand
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Hey, just confused on how you would integrate:
a(1-e-bt)
with "a" and "b" being constants.
If you could provide steps that would be helpful.
 
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∫adt = at + C, ∫ae-bt = (-a/b)e-bt + D

where C and D are arbitrary constants. I hope you can put it together.
 

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