What is the integral of (10)/(e^{x/2)} ?

The integral of (10)/(e^{x/2)} is 10(x/(e^{x/2)}-e^{-x/2}(x+2))+C

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integral of (10)/(e^{x/2)}

\int \frac{10}{e ^{\frac{x}{2}}} d x

10 (\frac{x}{e ^{\frac{x}{2}}} - e^{- \frac{x}{2}} (x + 2)) + C

Solution steps

\int \frac{10}{e ^{\frac{x}{2}}} 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}{2}}} d x

Apply Integration By Parts

: \frac{x}{e ^{\frac{x}{2}}} - \int - \frac{1}{2} e^{- \frac{x}{2}} x d x

= 10 (\frac{x}{e ^{\frac{x}{2}}} - \int - \frac{1}{2} e^{- \frac{x}{2}} x d x)

\int - \frac{1}{2} e^{- \frac{x}{2}} x d x = e^{- \frac{x}{2}} (x + 2)

= 10 (\frac{x}{e ^{\frac{x}{2}}} - e^{- \frac{x}{2}} (x + 2))

Add a constant to the solution

= 10 (\frac{x}{e ^{\frac{x}{2}}} - e^{- \frac{x}{2}} (x + 2)) + C

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What is the integral of (10)/(e^{x/2)} ?
The integral of (10)/(e^{x/2)} is 10(x/(e^{x/2)}-e^{-x/2}(x+2))+C