What is the integral of e^{t-2} ?

The integral of e^{t-2} is e^{t-2}+C

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integral of e^{t-2}

\int e^{t - 2} d t

e^{t - 2} + C

Solution steps

\int e^{t - 2} d t

e^{t - 2} = e^{- 2} e^{t}

= \int e^{- 2} e^{t} d t

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= e^{- 2} \cdot \int e^{t} d t

Apply exponent rule:

a^{- b} = \frac{1}{a ^{b}}

= \frac{1}{e ^{2}} \cdot \int e^{t} d t

Use the common integral:

\int e^{t} d t = e^{t}

= \frac{1}{e ^{2}} e^{t}

Simplify

\frac{1}{e ^{2}} e^{t} : e^{t - 2}

= e^{t - 2}

Add a constant to the solution

= e^{t - 2} + C

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