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

The integral of (3/(x^{1/3)}-3x^{2/3}) is 9/2 x^{2/3}-9/5 x^{5/3}+C

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

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

\frac{9}{2} x^{\frac{2}{3}} - \frac{9}{5} x^{\frac{5}{3}} + C

Solution steps

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

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

\int 3 x^{\frac{2}{3}} d x = \frac{9}{5} x^{\frac{5}{3}}

= \frac{9}{2} x^{\frac{2}{3}} - \frac{9}{5} x^{\frac{5}{3}}

Add a constant to the solution

= \frac{9}{2} x^{\frac{2}{3}} - \frac{9}{5} x^{\frac{5}{3}} + C

\frac{36 x}{x ^{2} + 36}

\frac{d}{d x} (- 4 e^{12 x})

\int (3^{4} + x^{15}) d x

\int x^{2} a^{2} - x^{2} d x

f (x) = x^{3} - x

What is the integral of (3/(x^{1/3)}-3x^{2/3}) ?
The integral of (3/(x^{1/3)}-3x^{2/3}) is 9/2 x^{2/3}-9/5 x^{5/3}+C