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Popular >

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

Solution

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

Solution

- \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

= - \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

Popular Examples

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x \to 3 lim ([8 (- 10)])

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\int cos^{6} (x) sin (2 x) d x

(2y+2x-7)dx+(4y+2x-1)dy=0

(2 y + 2 x - 7) d x + (4 y + 2 x - 1) d y = 0

integral of (1/(sqrt(x^2-1)))

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

Frequently Asked Questions (FAQ)

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