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

The integral of 3x^{-1/3}-1/(sqrt(x)) is 9/2 x^{2/3}-2sqrt(x)+C

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

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

\frac{9}{2} x^{\frac{2}{3}} - 2 x + C

Solution steps

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

\int 3 x^{- \frac{1}{3}} d x = \frac{9}{2} x^{\frac{2}{3}}

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

= \frac{9}{2} x^{\frac{2}{3}} - 2 x

Add a constant to the solution

= \frac{9}{2} x^{\frac{2}{3}} - 2 x + C

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What is the integral of 3x^{-1/3}-1/(sqrt(x)) ?
The integral of 3x^{-1/3}-1/(sqrt(x)) is 9/2 x^{2/3}-2sqrt(x)+C