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

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

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

\int 3 x^{2} + x x d x

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

Solution steps

\int 3 x^{2} + x x 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 3 x^{2} d x + \int x x d x

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

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

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

Add a constant to the solution

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

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(3, 3), (2, - 2)

\int x cos (n) x d x

\frac{d}{d x} ((x + 3) ln (x^{2}))

y + 2 y^{7} = (y^{3} + 6 x) y^{^{'}}

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