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

The integral of t/(e^{3t)} is -1/3 e^{-3t}t-1/9 e^{-3t}+C

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

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

- \frac{1}{3} e^{- 3 t} t - \frac{1}{9} e^{- 3 t} + C

Solution steps

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

Apply Integration By Parts

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

\int - \frac{1}{3} e^{- 3 t} d t = \frac{1}{9} e^{- 3 t}

= - \frac{1}{3} e^{- 3 t} t - \frac{1}{9} e^{- 3 t}

Add a constant to the solution

= - \frac{1}{3} e^{- 3 t} t - \frac{1}{9} e^{- 3 t} + C

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

a re a 2 x^{2} - 4, x^{2}

d er i v a t i v e f (x) = (x - x^{2})

(y) d x + (y - x) d y = 0

\frac{d}{d x} (a n x + b 3 x)

What is the integral of t/(e^{3t)} ?
The integral of t/(e^{3t)} is -1/3 e^{-3t}t-1/9 e^{-3t}+C