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

The integral of 3x^{1/8} is 8/3 x^{9/8}+C

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integral of 3x^{1/8}

\int 3 x^{\frac{1}{8}} d x

\frac{8}{3} x^{\frac{9}{8}} + C

Solution steps

\int 3 x^{\frac{1}{8}} d x

Take the constant out:

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

= 3 \cdot \int x^{\frac{1}{8}} d x

Apply the Power Rule

: \frac{8}{9} x^{\frac{9}{8}}

= 3 \cdot \frac{8}{9} x^{\frac{9}{8}}

Simplify

3 \cdot \frac{8}{9} x^{\frac{9}{8}} : \frac{8}{3} x^{\frac{9}{8}}

= \frac{8}{3} x^{\frac{9}{8}}

Add a constant to the solution

= \frac{8}{3} x^{\frac{9}{8}} + C

\frac{\partial}{\partial x} (e^{2})

- 3 x^{2} + 3 x + 1, at x = 1

n = 0 \sum \infty (\frac{6}{5})^{- n}

f (x) = x + 1, at x = 5

\int \frac{x}{4 x - 3} d x