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

The integral of \sqrt[3]{x^2}(x+3) is 3/8 x^{8/3}+9/5 x^{5/3}+C

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

\frac{3}{8} x^{\frac{8}{3}} + \frac{9}{5} x^{\frac{5}{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

= \frac{3}{8} x^{\frac{8}{3}} + \frac{9}{5} x^{\frac{5}{3}}

Add a constant to the solution

= \frac{3}{8} x^{\frac{8}{3}} + \frac{9}{5} x^{\frac{5}{3}} + C

\frac{s - 9}{s ^{2} - 9}

\frac{d}{d x} (tan (4 x))

\frac{d y}{d x} + \frac{y}{x - 2} = 5 (x - 2) y^{\frac{1}{2}}

f (x) = \frac{6 x ^{2} - 1}{2 x}

\frac{d}{d x} (\frac{1}{2 x ^{2} + 1})

What is the integral of \sqrt[3]{x^2}(x+3) ?
The integral of \sqrt[3]{x^2}(x+3) is 3/8 x^{8/3}+9/5 x^{5/3}+C