What is the integral of 2x^{1/6} ?

The integral of 2x^{1/6} is 12/7 x^{7/6}+C

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integral of 2x^{1/6}

\int 2 x^{\frac{1}{6}} d x

\frac{12}{7} x^{\frac{7}{6}} + C

Solution steps

\int 2 x^{\frac{1}{6}} d x

Take the constant out:

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

= 2 \cdot \int x^{\frac{1}{6}} d x

Apply the Power Rule

: \frac{6}{7} x^{\frac{7}{6}}

= 2 \cdot \frac{6}{7} x^{\frac{7}{6}}

Simplify

2 \cdot \frac{6}{7} x^{\frac{7}{6}} : \frac{12}{7} x^{\frac{7}{6}}

= \frac{12}{7} x^{\frac{7}{6}}

Add a constant to the solution

= \frac{12}{7} x^{\frac{7}{6}} + C

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