What is the integral of 7sqrt(x^3)+8\sqrt[3]{x^2} ?

The integral of 7sqrt(x^3)+8\sqrt[3]{x^2} is 14/5 x^{5/2}+24/5 x^{5/3}+C

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integral of 7sqrt(x^3)+8\sqrt[3]{x^2}

\int 7 x^{3} + 8 3 x^{2} d x

\frac{14}{5} x^{\frac{5}{2}} + \frac{24}{5} x^{\frac{5}{3}} + C

Solution steps

\int 7 x^{3} + 8 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 7 x^{3} d x + \int 8 3 x^{2} d x

\int 7 x^{3} d x = \frac{14}{5} x^{\frac{5}{2}}

\int 8 3 x^{2} d x = \frac{24}{5} x^{\frac{5}{3}}

= \frac{14}{5} x^{\frac{5}{2}} + \frac{24}{5} x^{\frac{5}{3}}

Add a constant to the solution

= \frac{14}{5} x^{\frac{5}{2}} + \frac{24}{5} x^{\frac{5}{3}} + C

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What is the integral of 7sqrt(x^3)+8\sqrt[3]{x^2} ?
The integral of 7sqrt(x^3)+8\sqrt[3]{x^2} is 14/5 x^{5/2}+24/5 x^{5/3}+C