What is the integral of \sqrt[4]{x^3}+\sqrt[3]{x^2} ?

The integral of \sqrt[4]{x^3}+\sqrt[3]{x^2} is 4/7 x^{7/4}+3/5 x^{5/3}+C

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integral of \sqrt[4]{x^3}+\sqrt[3]{x^2}

\int 4 x^{3} + 3 x^{2} d x

\frac{4}{7} x^{\frac{7}{4}} + \frac{3}{5} x^{\frac{5}{3}} + C

Solution steps

\int 4 x^{3} + 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 4 x^{3} d x + \int 3 x^{2} d x

\int 4 x^{3} d x = \frac{4}{7} x^{\frac{7}{4}}

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

= \frac{4}{7} x^{\frac{7}{4}} + \frac{3}{5} x^{\frac{5}{3}}

Add a constant to the solution

= \frac{4}{7} x^{\frac{7}{4}} + \frac{3}{5} x^{\frac{5}{3}} + C

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What is the integral of \sqrt[4]{x^3}+\sqrt[3]{x^2} ?
The integral of \sqrt[4]{x^3}+\sqrt[3]{x^2} is 4/7 x^{7/4}+3/5 x^{5/3}+C