What is the integral of 5/(e^{4x)} ?

The integral of 5/(e^{4x)} is -5/4 e^{-4x}+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of 5/(e^{4x)}

\int \frac{5}{e ^{4 x}} d x

- \frac{5}{4} e^{- 4 x} + C

Solution steps

\int \frac{5}{e ^{4 x}} d x

Take the constant out:

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

= 5 \cdot \int \frac{1}{e ^{4 x}} d x

Apply exponent rule:

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

\frac{1}{e ^{4 x}} = e^{- 4 x}

= 5 \cdot \int e^{- 4 x} d x

Apply u-substitution

: \int - \frac{1}{4} e^{u} d u

= 5 \cdot \int - \frac{1}{4} e^{u} d u

Take the constant out:

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

= 5 (- \frac{1}{4} \cdot \int e^{u} d u)

Use the common integral:

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

= 5 (- \frac{1}{4} e^{u})

Substitute back

u = - 4 x

= 5 (- \frac{1}{4} e^{- 4 x})

Simplify

5 (- \frac{1}{4} e^{- 4 x}) : - \frac{5}{4} e^{- 4 x}

= - \frac{5}{4} e^{- 4 x}

Add a constant to the solution

= - \frac{5}{4} e^{- 4 x} + C

\int \frac{x - 76}{x ^{2} ( x + 4 )} d x

\int \frac{tan ^{4} ( x )}{cos ^{4} ( x )} d x

\int \frac{5 x}{( x - 2 ) ( x ^{2} + 1 )} d x

\int e^{x} \frac{1}{x ^{2}} d x

\int (x^{8} + 2 x^{9}) ln (x) d x

What is the integral of 5/(e^{4x)} ?
The integral of 5/(e^{4x)} is -5/4 e^{-4x}+C