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

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

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integral of \sqrt[3]{x}-5x^2

\frac{3}{4} x^{\frac{4}{3}} - \frac{5 x ^{3}}{3} + C

Solution steps

Apply the Sum Rule:

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

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

= \frac{3}{4} x^{\frac{4}{3}} - \frac{5 x ^{3}}{3}

Add a constant to the solution

= \frac{3}{4} x^{\frac{4}{3}} - \frac{5 x ^{3}}{3} + C

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