What is the integral of 3/(e^{5x)} ?

The integral of 3/(e^{5x)} is -3/5 e^{-5x}+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of 3/(e^{5x)}

\int \frac{3}{e ^{5 x}} d x

- \frac{3}{5} e^{- 5 x} + C

Solution steps

\int \frac{3}{e ^{5 x}} d x

Take the constant out:

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

= 3 \cdot \int \frac{1}{e ^{5 x}} d x

Apply exponent rule:

\frac{1}{a ^{b}} = a^{- b}

\frac{1}{e ^{5 x}} = e^{- 5 x}

= 3 \cdot \int e^{- 5 x} d x

Apply u-substitution

: \int - \frac{1}{5} e^{u} d u

= 3 \cdot \int - \frac{1}{5} e^{u} d u

Take the constant out:

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

= 3 (- \frac{1}{5} \cdot \int e^{u} d u)

Use the common integral:

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

= 3 (- \frac{1}{5} e^{u})

Substitute back

u = - 5 x

= 3 (- \frac{1}{5} e^{- 5 x})

Simplify

3 (- \frac{1}{5} e^{- 5 x}) : - \frac{3}{5} e^{- 5 x}

= - \frac{3}{5} e^{- 5 x}

Add a constant to the solution

= - \frac{3}{5} e^{- 5 x} + C

f (x) = csc^{2} (x)

\int \frac{1}{1 - x} d x

\frac{d}{d x} (- 2 csc (x) + 4 cot (x))

\int (x^{2} + 2 x)^{2} d x

\frac{d P}{d t} = k \cdot P

What is the integral of 3/(e^{5x)} ?
The integral of 3/(e^{5x)} is -3/5 e^{-5x}+C