What is the integral of a^{-x} ?

The integral of a^{-x} is -(a^{-x})/(ln(a))+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of a^{-x}

\int a^{- x} d x

- \frac{a ^{- x}}{ln ( a )} + C

Solution steps

\int a^{- x} d x

Apply u-substitution

: \int - a^{u} d u

= \int - a^{u} d u

Take the constant out:

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

= - \int a^{u} d u

\int a^{x} d x = \frac{a ^{x}}{ln a}

= - \frac{a ^{u}}{ln ( a )}

Substitute back

u = - x

= - \frac{a ^{- x}}{ln ( a )}

Add a constant to the solution

= - \frac{a ^{- x}}{ln ( a )} + C

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

\frac{1}{3 x}

\int 15 sin^{2} (x) d x

\frac{d}{d x} ((x + ln (x))^{5})

\int_{0}^{3} 2 x^{2} d x