What is the integral of e^{-1/3} ?

The integral of e^{-1/3} is 1/(e^{1/3)}x+C

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integral of e^{-1/3}

\int e^{- \frac{1}{3}} d x

\frac{1}{e ^{\frac{1}{3}}} x + C

Solution steps

\int e^{- \frac{1}{3}} d x

Integral of a constant:

\int a d x = a x

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

Apply exponent rule:

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

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

Add a constant to the solution

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