What is the integral of 1/8 e^{-1/8 x} ?

The integral of 1/8 e^{-1/8 x} is -e^{-x/8}+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of 1/8 e^{-1/8 x}

\int \frac{1}{8} e^{- \frac{1}{8} x} d x

- e^{- \frac{x}{8}} + C

Solution steps

\int \frac{1}{8} e^{- \frac{1}{8} x} d x

Take the constant out:

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

= \frac{1}{8} \cdot \int e^{- \frac{1}{8} x} d x

Simplify

- \frac{1}{8} x : - \frac{x}{8}

= \frac{1}{8} \cdot \int e^{- \frac{x}{8}} d x

Apply u-substitution

: \int - 8 e^{u} d u

= \frac{1}{8} \cdot \int - 8 e^{u} d u

Take the constant out:

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

= \frac{1}{8} (- 8 \cdot \int e^{u} d u)

Use the common integral:

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

= \frac{1}{8} (- 8 e^{u})

Substitute back

u = - \frac{x}{8}

= \frac{1}{8} (- 8 e^{- \frac{x}{8}})

Simplify

\frac{1}{8} (- 8 e^{- \frac{x}{8}}) : - e^{- \frac{x}{8}}

= - e^{- \frac{x}{8}}

Add a constant to the solution

= - e^{- \frac{x}{8}} + C

x \to 7 lim (2 x)

\int (12.5 - 0.02 x) d x

\int (cos (5 x))^{2} d x

n = 1 \sum \infty \frac{4}{n ^{2} + 3 n + 2}

\frac{d}{d x} (2 e^{\frac{s i n ( x )}{3}} + 1)

What is the integral of 1/8 e^{-1/8 x} ?
The integral of 1/8 e^{-1/8 x} is -e^{-x/8}+C