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

The integral of \sqrt[3]{x}(5x^2-3x+2) is 3/2 x^{10/3}-9/7 x^{7/3}+3/2 x^{4/3}+C

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

\frac{3}{2} x^{\frac{10}{3}} - \frac{9}{7} x^{\frac{7}{3}} + \frac{3}{2} x^{\frac{4}{3}} + C

Solution steps

Expand

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^{\frac{7}{3}} d x = \frac{3}{2} x^{\frac{10}{3}}

\int 3 x^{\frac{4}{3}} d x = \frac{9}{7} x^{\frac{7}{3}}

= \frac{3}{2} x^{\frac{10}{3}} - \frac{9}{7} x^{\frac{7}{3}} + \frac{3}{2} x^{\frac{4}{3}}

Add a constant to the solution

= \frac{3}{2} x^{\frac{10}{3}} - \frac{9}{7} x^{\frac{7}{3}} + \frac{3}{2} x^{\frac{4}{3}} + C

What is the integral of \sqrt[3]{x}(5x^2-3x+2) ?
The integral of \sqrt[3]{x}(5x^2-3x+2) is 3/2 x^{10/3}-9/7 x^{7/3}+3/2 x^{4/3}+C