What is the integral of (3^{5x-2}) ?

The integral of (3^{5x-2}) is (3^{5x-2})/(5ln(3))+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral of (3^{5x-2})

\int (3^{5 x - 2}) d x

\frac{3 ^{5 x - 2}}{5 ln ( 3 )} + C

Solution steps

\int 3^{5 x - 2} d x

3^{5 x - 2} = 3^{- 2} \cdot 3^{5 x}

= \int 3^{- 2} \cdot 3^{5 x} d x

Take the constant out:

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

= 3^{- 2} \cdot \int 3^{5 x} d x

3^{- 2} = \frac{1}{9}

= \frac{1}{9} \cdot \int 3^{5 x} d x

Simplify

3^{5 x} : 24 3^{x}

= \frac{1}{9} \cdot \int 24 3^{x} d x

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

= \frac{1}{9} \cdot \frac{24 3 ^{x}}{ln ( 243 )}

Simplify

\frac{1}{9} \cdot \frac{24 3 ^{x}}{ln ( 243 )} : \frac{3 ^{5 x - 2}}{5 ln ( 3 )}

= \frac{3 ^{5 x - 2}}{5 ln ( 3 )}

Add a constant to the solution

= \frac{3 ^{5 x - 2}}{5 ln ( 3 )} + C

What is the integral of (3^{5x-2}) ?
The integral of (3^{5x-2}) is (3^{5x-2})/(5ln(3))+C