What is the integral of (x^{4/3}-4x^{1/3}) ?

The integral of (x^{4/3}-4x^{1/3}) is 3/7 x^{7/3}-3x^{4/3}+C

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integral of (x^{4/3}-4x^{1/3})

\int (x^{\frac{4}{3}} - 4 x^{\frac{1}{3}}) d x

\frac{3}{7} x^{\frac{7}{3}} - 3 x^{\frac{4}{3}} + C

Solution steps

\int x^{\frac{4}{3}} - 4 x^{\frac{1}{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 x^{\frac{4}{3}} d x - \int 4 x^{\frac{1}{3}} d x

\int x^{\frac{4}{3}} d x = \frac{3}{7} x^{\frac{7}{3}}

\int 4 x^{\frac{1}{3}} d x = 3 x^{\frac{4}{3}}

= \frac{3}{7} x^{\frac{7}{3}} - 3 x^{\frac{4}{3}}

Add a constant to the solution

= \frac{3}{7} x^{\frac{7}{3}} - 3 x^{\frac{4}{3}} + C

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What is the integral of (x^{4/3}-4x^{1/3}) ?
The integral of (x^{4/3}-4x^{1/3}) is 3/7 x^{7/3}-3x^{4/3}+C