how to solve : integral (e^t -3) dt

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sciencesolve | Teacher | (Level 3) Educator Emeritus

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The request of the problem is vague, hence, considering that you need to evaluate `int e^(t-3) dt` , you should come up with the following substitution t-3 = u such that:

`t - 3 = u => dt = du`

`int e^(t-3) dt = int e^u du = e^u + c`

Substituting back t-3 for u yields:

`int e^(t-3) dt = e^(t-3) + c`

Hence, evaluating the given integral `int e^(t-3) dt ` yields `int e^(t-3) dt = e^(t-3) + c`

If you need to evaluate the integral `int (e^t - 3)dt` , then, you should use the property of linearity of integrals such that:

`int (e^t - 3) dt = int e^t dt - int 3 dt = e^t - 3t + c`

Hence, evaluating the given integral `int (e^t - 3) dt`  yields `int (e^t - 3) dt = e^t - 3t + c` .

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