What is the integral of 8te^{-t/5} ?

The integral of 8te^{-t/5} is 8(-5e^{-t/5}t-25e^{-t/5})+C

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integral of 8te^{-t/5}

\int 8 t e^{- \frac{t}{5}} d t

8 (- 5 e^{- \frac{t}{5}} t - 25 e^{- \frac{t}{5}}) + C

Solution steps

\int 8 t e^{- \frac{t}{5}} d t

Take the constant out:

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

= 8 \cdot \int t e^{- \frac{t}{5}} d t

Apply Integration By Parts

: - 5 e^{- \frac{t}{5}} t - \int - 5 e^{- \frac{t}{5}} d t

= 8 (- 5 e^{- \frac{t}{5}} t - \int - 5 e^{- \frac{t}{5}} d t)

\int - 5 e^{- \frac{t}{5}} d t = 25 e^{- \frac{t}{5}}

= 8 (- 5 e^{- \frac{t}{5}} t - 25 e^{- \frac{t}{5}})

Add a constant to the solution

= 8 (- 5 e^{- \frac{t}{5}} t - 25 e^{- \frac{t}{5}}) + C

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What is the integral of 8te^{-t/5} ?
The integral of 8te^{-t/5} is 8(-5e^{-t/5}t-25e^{-t/5})+C