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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

= - \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 3 e^{- 4 x} sin (e^{- 4 x}) d x

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

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

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

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