What is the integral of e^{-sqrt(3x-2)} ?

The integral of e^{-sqrt(3x-2)} is 2/3 (-e^{-sqrt(3x-2)}sqrt(3x-2)-e^{-sqrt(3x-2)})+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral of e^{-sqrt(3x-2)}

\int e^{- 3 x - 2} d x

\frac{2}{3} (- e^{- 3 x - 2} 3 x - 2 - e^{- 3 x - 2}) + C

Solution steps

\int e^{- 3 x - 2} d x

Apply u-substitution

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

Take the constant out:

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

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

Apply u-substitution

= \frac{1}{3} \cdot \int 2 e^{v} v d v

Take the constant out:

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

= \frac{1}{3} \cdot 2 \cdot \int e^{v} v d v

Apply Integration By Parts

= \frac{1}{3} \cdot 2 (e^{v} v - \int e^{v} d v)

\int e^{v} d v = e^{v}

= \frac{1}{3} \cdot 2 (e^{v} v - e^{v})

Substitute back

= \frac{1}{3} \cdot 2 (e^{- 3 x - 2} (- 3 x - 2) - e^{- 3 x - 2})

Simplify

\frac{1}{3} \cdot 2 (e^{- 3 x - 2} (- 3 x - 2) - e^{- 3 x - 2}) : \frac{2}{3} (- e^{- 3 x - 2} 3 x - 2 - e^{- 3 x - 2})

= \frac{2}{3} (- e^{- 3 x - 2} 3 x - 2 - e^{- 3 x - 2})

Add a constant to the solution

= \frac{2}{3} (- e^{- 3 x - 2} 3 x - 2 - e^{- 3 x - 2}) + C

What is the integral of e^{-sqrt(3x-2)} ?
The integral of e^{-sqrt(3x-2)} is 2/3 (-e^{-sqrt(3x-2)}sqrt(3x-2)-e^{-sqrt(3x-2)})+C