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

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

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

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

\int 2 d x = 2 x

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

Add a constant to the solution

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

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