What is the integral of 2^{3x-1} ?

The integral of 2^{3x-1} is (2^{3x-1})/(3ln(2))+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of 2^{3x-1}

\int 2^{3 x - 1} d x

\frac{2 ^{3 x - 1}}{3 ln ( 2 )} + C

Solution steps

\int 2^{3 x - 1} d x

Apply u-substitution

: \int 2^{u} \cdot \frac{1}{3} d u

= \int 2^{u} \cdot \frac{1}{3} d u

Take the constant out:

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

= \frac{1}{3} \cdot \int 2^{u} d u

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

= \frac{1}{3} \cdot \frac{2 ^{u}}{ln ( 2 )}

Substitute back

u = 3 x - 1

= \frac{1}{3} \cdot \frac{2 ^{3 x - 1}}{ln ( 2 )}

Simplify

\frac{1}{3} \cdot \frac{2 ^{3 x - 1}}{ln ( 2 )} : \frac{2 ^{3 x - 1}}{3 ln ( 2 )}

= \frac{2 ^{3 x - 1}}{3 ln ( 2 )}

Add a constant to the solution

= \frac{2 ^{3 x - 1}}{3 ln ( 2 )} + C

\int 4 x + 0 d x

\int \frac{1}{13 - x ^{2}} d x

\int x^{5} 3 + x^{6} d x

\int \frac{6}{( 2 x - 3 ) ^{2}} d x

\int \frac{x ^{2} + 5 x - 1}{x} d x

What is the integral of 2^{3x-1} ?
The integral of 2^{3x-1} is (2^{3x-1})/(3ln(2))+C