What is the integral of e^{-5}x ?

The integral of e^{-5}x is (x^2)/(2e^5)+C

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integral of e^{-5}x

integral

e^{- 5} x

\frac{x ^{2}}{2 e ^{5}} + C

Solution steps

\int e^{- 5} x d x

Take the constant out:

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

= e^{- 5} \cdot \int x d x

Apply exponent rule:

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

= \frac{1}{e ^{5}} \cdot \int x d x

Apply the Power Rule

= \frac{1}{e ^{5}} \cdot \frac{x ^{2}}{2}

Simplify

\frac{1}{e ^{5}} \cdot \frac{x ^{2}}{2} : \frac{x ^{2}}{2 e ^{5}}

= \frac{x ^{2}}{2 e ^{5}}

Add a constant to the solution

= \frac{x ^{2}}{2 e ^{5}} + C