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

The integral of 8sqrt(x^3)+9\sqrt[3]{x^2} is 16/5 x^{5/2}+27/5 x^{5/3}+C

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integral of 8sqrt(x^3)+9\sqrt[3]{x^2}

\frac{16}{5} x^{\frac{5}{2}} + \frac{27}{5} x^{\frac{5}{3}} + 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 8 x^{3} d x = \frac{16}{5} x^{\frac{5}{2}}

= \frac{16}{5} x^{\frac{5}{2}} + \frac{27}{5} x^{\frac{5}{3}}

Add a constant to the solution

= \frac{16}{5} x^{\frac{5}{2}} + \frac{27}{5} x^{\frac{5}{3}} + C

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

\int \frac{1}{25} x d x

\int x (x^{2} - 3)^{6} d x

\int - 5 e^{- 5 x} d x

\int x^{2} - 9 x + 8 d x

What is the integral of 8sqrt(x^3)+9\sqrt[3]{x^2} ?
The integral of 8sqrt(x^3)+9\sqrt[3]{x^2} is 16/5 x^{5/2}+27/5 x^{5/3}+C