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

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

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integral of e^{x-2}

integral

e^{x - 2}

e^{x - 2} + C

Solution steps

\int e^{x - 2} d x

e^{x - 2} = e^{- 2} e^{x}

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

Take the constant out:

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

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

Apply exponent rule:

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

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

Use the common integral:

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

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

Simplify

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

= e^{x - 2}

Add a constant to the solution

= e^{x - 2} + C

(4 - 2 x)^{3}

\frac{3}{x ^{3}}

\frac{1}{a ^{2} e ^{x} + e ^{- x}}

y + 1

\frac{( 3 x - 6 )}{( 3 x + 1 ) ( x - 1 )}