What is the integral of 7e^{-3x} ?

The integral of 7e^{-3x} is -7/3 e^{-3x}+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of 7e^{-3x}

\int 7 e^{- 3 x} d x

- \frac{7}{3} e^{- 3 x} + C

Solution steps

\int 7 e^{- 3 x} d x

Take the constant out:

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

= 7 \cdot \int e^{- 3 x} d x

Apply u-substitution

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

= 7 \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

= 7 (- \frac{1}{3} \cdot \int e^{u} d u)

Use the common integral:

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

= 7 (- \frac{1}{3} e^{u})

Substitute back

u = - 3 x

= 7 (- \frac{1}{3} e^{- 3 x})

Simplify

7 (- \frac{1}{3} e^{- 3 x}) : - \frac{7}{3} e^{- 3 x}

= - \frac{7}{3} e^{- 3 x}

Add a constant to the solution

= - \frac{7}{3} e^{- 3 x} + C

\frac{\partial}{\partial x} (arcsin (7 x yz))

x \to - 5 lim (\frac{3}{x - 5})

\frac{\partial}{\partial x} (\frac{( x y )}{( x + y )})

\frac{d}{d x} (9 cos (9 x))

f (x) = cos (x^{l n (x^{2} + 1)})