What is the integral of 5e^{6-3x} ?

The integral of 5e^{6-3x} is -5/3 e^{6-3x}+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of 5e^{6-3x}

\int 5 e^{6 - 3 x} d x

- \frac{5}{3} e^{6 - 3 x} + C

Solution steps

\int 5 e^{6 - 3 x} d x

Take the constant out:

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

= 5 \cdot \int e^{6 - 3 x} d x

Apply u-substitution

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

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

Use the common integral:

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

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

Substitute back

u = 6 - 3 x

= 5 (- \frac{1}{3} e^{6 - 3 x})

Simplify

5 (- \frac{1}{3} e^{6 - 3 x}) : - \frac{5}{3} e^{6 - 3 x}

= - \frac{5}{3} e^{6 - 3 x}

Add a constant to the solution

= - \frac{5}{3} e^{6 - 3 x} + C

1 + 10 x - 1 - 3 x

\frac{d}{d x} (e^{m x} cos (n x))

\int \frac{u ^{2}}{1} d u

\int_{0}^{\infty} u e^{- u} d u

x \to 0 lim (\frac{( x + 1 ) ^{3}}{x})

What is the integral of 5e^{6-3x} ?
The integral of 5e^{6-3x} is -5/3 e^{6-3x}+C