What is the integral of 0.25e^{-0.25x} ?

The integral of 0.25e^{-0.25x} is -e^{-0.25x}+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of 0.25e^{-0.25x}

\int 0.25 e^{- 0.25 x} d x

- e^{- 0.25 x} + C

Solution steps

\int 0.25 e^{- 0.25 x} d x

Take the constant out:

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

= 0.25 \cdot \int e^{- 0.25 x} d x

Apply u-substitution

: \int - \frac{1}{0.25} e^{u} d u

= 0.25 \cdot \int - \frac{1}{0.25} e^{u} d u

Take the constant out:

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

= 0.25 (- \frac{1}{0.25} \cdot \int e^{u} d u)

Simplify

= 0.25 (- 4 \cdot \int e^{u} d u)

Use the common integral:

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

= 0.25 (- 4 e^{u})

Substitute back

u = - 0.25 x

= 0.25 (- 4 e^{- 0.25 x})

Simplify

= - e^{- 0.25 x}

Add a constant to the solution

= - e^{- 0.25 x} + C

\int e^{2 x^{4}} d x

\int_{1}^{8} \frac{1}{x - 3} d x

sin (π x)

\frac{d}{d x} (\frac{3 + 2 x - x ^{3}}{6})

y^{^{'}} = t \cdot y

What is the integral of 0.25e^{-0.25x} ?
The integral of 0.25e^{-0.25x} is -e^{-0.25x}+C