What is the integral of 6te^{-t/6} ?

The integral of 6te^{-t/6} is 6(-6e^{-t/6}t-36e^{-t/6})+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral of 6te^{-t/6}

\int 6 t e^{- \frac{t}{6}} d t

6 (- 6 e^{- \frac{t}{6}} t - 36 e^{- \frac{t}{6}}) + C

Solution steps

\int 6 t e^{- \frac{t}{6}} d t

Take the constant out:

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

= 6 \cdot \int t e^{- \frac{t}{6}} d t

Apply Integration By Parts

= 6 (- 6 e^{- \frac{t}{6}} t - \int - 6 e^{- \frac{t}{6}} d t)

\int - 6 e^{- \frac{t}{6}} d t = 36 e^{- \frac{t}{6}}

= 6 (- 6 e^{- \frac{t}{6}} t - 36 e^{- \frac{t}{6}})

Add a constant to the solution

= 6 (- 6 e^{- \frac{t}{6}} t - 36 e^{- \frac{t}{6}}) + C

What is the integral of 6te^{-t/6} ?
The integral of 6te^{-t/6} is 6(-6e^{-t/6}t-36e^{-t/6})+C