What is the integral of 3/(e^{t/2)} ?

The integral of 3/(e^{t/2)} is 3(t/(e^{t/2)}-e^{-t/2}(t+2))+C

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integral of 3/(e^{t/2)}

\int \frac{3}{e ^{\frac{t}{2}}} d t

3 (\frac{t}{e ^{\frac{t}{2}}} - e^{- \frac{t}{2}} (t + 2)) + C

Solution steps

\int \frac{3}{e ^{\frac{t}{2}}} d t

Take the constant out:

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

= 3 \cdot \int \frac{1}{e ^{\frac{t}{2}}} d t

Apply Integration By Parts

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

= 3 (\frac{t}{e ^{\frac{t}{2}}} - \int - \frac{1}{2} e^{- \frac{t}{2}} t d t)

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

= 3 (\frac{t}{e ^{\frac{t}{2}}} - e^{- \frac{t}{2}} (t + 2))

Add a constant to the solution

= 3 (\frac{t}{e ^{\frac{t}{2}}} - e^{- \frac{t}{2}} (t + 2)) + C

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What is the integral of 3/(e^{t/2)} ?
The integral of 3/(e^{t/2)} is 3(t/(e^{t/2)}-e^{-t/2}(t+2))+C