What is the integral of (3x-1)^{1/8} ?

The integral of (3x-1)^{1/8} is 8/27 (3x-1)^{9/8}+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral of (3x-1)^{1/8}

\int (3 x - 1)^{\frac{1}{8}} d x

\frac{8}{27} (3 x - 1)^{\frac{9}{8}} + C

Solution steps

\int (3 x - 1)^{\frac{1}{8}} d x

Apply u-substitution

= \int \frac{u ^{\frac{1}{8}}}{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 u^{\frac{1}{8}} d u

Apply the Power Rule

= \frac{1}{3} \cdot \frac{8}{9} u^{\frac{9}{8}}

Substitute back

u = 3 x - 1

= \frac{1}{3} \cdot \frac{8}{9} (3 x - 1)^{\frac{9}{8}}

Simplify

\frac{1}{3} \cdot \frac{8}{9} (3 x - 1)^{\frac{9}{8}} : \frac{8}{27} (3 x - 1)^{\frac{9}{8}}

= \frac{8}{27} (3 x - 1)^{\frac{9}{8}}

Add a constant to the solution

= \frac{8}{27} (3 x - 1)^{\frac{9}{8}} + C

What is the integral of (3x-1)^{1/8} ?
The integral of (3x-1)^{1/8} is 8/27 (3x-1)^{9/8}+C