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

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

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

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

\frac{x}{Q} - 3 x^{\frac{1}{3}} + C

Solution steps

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

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

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

\int \frac{1}{Q} d x = \frac{x}{Q}

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

= \frac{x}{Q} - 3 x^{\frac{1}{3}}

Add a constant to the solution

= \frac{x}{Q} - 3 x^{\frac{1}{3}} + C

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