What is the integral of e^{x-3} ?

The integral of e^{x-3} is e^{x-3}+C

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integral of e^{x-3}

\int e^{x - 3} d x

e^{x - 3} + C

Solution steps

\int e^{x - 3} d x

e^{x - 3} = e^{- 3} e^{x}

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

Take the constant out:

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

= e^{- 3} \cdot \int e^{x} d x

Apply exponent rule:

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

= \frac{1}{e ^{3}} \cdot \int e^{x} d x

Use the common integral:

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

= \frac{1}{e ^{3}} e^{x}

Simplify

\frac{1}{e ^{3}} e^{x} : e^{x - 3}

= e^{x - 3}

Add a constant to the solution

= e^{x - 3} + C

e^{x}, e^{- 3 x}, x = ln (4)

\int \frac{x ^{2} - 2}{x} d x

\frac{150000}{( 4 x + 75 ) ^{2}}

π^{7} + 3 x

(x + 1)^{2} (2 - x)^{2}