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

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

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

\int (x - 5 3 x^{2}) d x

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

Solution steps

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

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

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

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

Add a constant to the solution

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

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