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}

\int e^{x - 2} d x

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

n = 0 \sum \infty 9 (\frac{1 - 3}{4})^{n}

\frac{d}{d x} (\frac{3 ^{x}}{x ^{3}})

\int_{0}^{1} (- x + 2) - (x^{2} - 1) d x

\int x^{3} e^{x} d x

(x^{3} + y^{3}) d x + 3 x y^{2} d y = 0