What is the integral of 1/(2(x^{1/3))} ?

The integral of 1/(2(x^{1/3))} is 3/4 x^{2/3}+C

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integral of 1/(2(x^{1/3))}

\int \frac{1}{2 ( x ^{\frac{1}{3}} )} d x

\frac{3}{4} x^{\frac{2}{3}} + C

Solution steps

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

Take the constant out:

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

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

Apply the Power Rule

: \frac{3}{2} x^{\frac{2}{3}}

= \frac{1}{2} \cdot \frac{3}{2} x^{\frac{2}{3}}

Simplify

\frac{1}{2} \cdot \frac{3}{2} x^{\frac{2}{3}} : \frac{3}{4} x^{\frac{2}{3}}

= \frac{3}{4} x^{\frac{2}{3}}

Add a constant to the solution

= \frac{3}{4} x^{\frac{2}{3}} + C

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What is the integral of 1/(2(x^{1/3))} ?
The integral of 1/(2(x^{1/3))} is 3/4 x^{2/3}+C