What is the integral of (10)/(e^{x/4)} ?

The integral of (10)/(e^{x/4)} is -40e^{-x/4}+C

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integral of (10)/(e^{x/4)}

\int \frac{10}{e ^{\frac{x}{4}}} d x

- 40 e^{- \frac{x}{4}} + C

Solution steps

\int \frac{10}{e ^{\frac{x}{4}}} d x

Take the constant out:

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

= 10 \cdot \int \frac{1}{e ^{\frac{x}{4}}} d x

Apply exponent rule:

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

\frac{1}{e ^{\frac{x}{4}}} = e^{- \frac{x}{4}}

= 10 \cdot \int e^{- \frac{x}{4}} d x

Apply u-substitution

: \int - 4 e^{u} d u

= 10 \cdot \int - 4 e^{u} d u

Take the constant out:

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

= 10 (- 4 \cdot \int e^{u} d u)

Use the common integral:

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

= 10 (- 4 e^{u})

Substitute back

u = - \frac{x}{4}

= 10 (- 4 e^{- \frac{x}{4}})

Simplify

= - 40 e^{- \frac{x}{4}}

Add a constant to the solution

= - 40 e^{- \frac{x}{4}} + C

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What is the integral of (10)/(e^{x/4)} ?
The integral of (10)/(e^{x/4)} is -40e^{-x/4}+C