What is the integral of 4/(\sqrt[3]{x)}-5\sqrt[3]{x^2} ?

The integral of 4/(\sqrt[3]{x)}-5\sqrt[3]{x^2} is 6x^{2/3}-3x^{5/3}+C

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integral of 4/(\sqrt[3]{x)}-5\sqrt[3]{x^2}

\int \frac{4}{3 x} - 5 3 x^{2} d x

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

Solution steps

\int \frac{4}{3 x} - 5 3 x^{2} 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{4}{3 x} d x - \int 5 3 x^{2} d x

\int \frac{4}{3 x} d x = 6 x^{\frac{2}{3}}

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

= 6 x^{\frac{2}{3}} - 3 x^{\frac{5}{3}}

Add a constant to the solution

= 6 x^{\frac{2}{3}} - 3 x^{\frac{5}{3}} + C

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

\int \frac{2}{t 4 t ^{4} - 1} d t

\int x^{2} (x^{3} - 1)^{7} d x

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

\int x^{\frac{1}{4}} + 5 d x

What is the integral of 4/(\sqrt[3]{x)}-5\sqrt[3]{x^2} ?
The integral of 4/(\sqrt[3]{x)}-5\sqrt[3]{x^2} is 6x^{2/3}-3x^{5/3}+C