What is the integral of 5/(2^x) ?

The integral of 5/(2^x) is -5/(ln(2)*2^x)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of 5/(2^x)

\int \frac{5}{2 ^{x}} d x

- \frac{5}{ln ( 2 ) \cdot 2 ^{x}} + C

Solution steps

\int \frac{5}{2 ^{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}{2 ^{x}} d x

Apply u-substitution

: \int \frac{1}{ln ( 2 ) u ^{2}} d u

= 5 \cdot \int \frac{1}{ln ( 2 ) u ^{2}} d u

Take the constant out:

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

= 5 \cdot \frac{1}{ln ( 2 )} \cdot \int \frac{1}{u ^{2}} d u

Apply the Power Rule

: - \frac{1}{u}

= 5 \cdot \frac{1}{ln ( 2 )} (- \frac{1}{u})

Substitute back

u = 2^{x}

= 5 \cdot \frac{1}{ln ( 2 )} (- \frac{1}{2 ^{x}})

Simplify

5 \cdot \frac{1}{ln ( 2 )} (- \frac{1}{2 ^{x}}) : - \frac{5}{ln ( 2 ) \cdot 2 ^{x}}

= - \frac{5}{ln ( 2 ) \cdot 2 ^{x}}

Add a constant to the solution

= - \frac{5}{ln ( 2 ) \cdot 2 ^{x}} + C

\int (x - 8)^{- \frac{2}{3}} d x

\int 6 x - 5 d x

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

\int (3 - 8 x)^{12} d x

\int \frac{1}{4} x^{2} e^{- \frac{x}{2}} d x