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

The integral of e^{-7x} is -1/7 e^{-7x}+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of e^{-7x}

\int e^{- 7 x} d x

- \frac{1}{7} e^{- 7 x} + C

Solution steps

\int e^{- 7 x} d x

Apply u-substitution

: \int - \frac{1}{7} e^{u} d u

= \int - \frac{1}{7} e^{u} d u

Take the constant out:

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

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

Use the common integral:

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

= - \frac{1}{7} e^{u}

Substitute back

u = - 7 x

= - \frac{1}{7} e^{- 7 x}

Add a constant to the solution

= - \frac{1}{7} e^{- 7 x} + C

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

6 x^{2}, x^{2} + 2

n = 2 \sum \infty (\frac{1}{3})^{n}

\frac{d}{d x} (5 x^{4} - 2 x^{3} - 3 x + 2)

y^{^{''}} + 8 y^{^{'}} + 7 y = 0